Intelligent Quality

A software tool for exploring  the application of convolution neural networks  on quality control samples of very small size

Rallou Chatzimichail, PhD 
rallou@hcsl.com
Aristides T. Hatjimihail, MD, PhD
 ath@hcsl.com

Hellenic Complex Systems Laboratory, Kostis Palamas 21, 66131 Drama, Greece.

Clear["`*"]
Off[General::stop];
minfn=(10^(-100));
ag=100;
pg=100;
wp=200;
pfr[1,1]=0.12724`;
prn[1,1,1]={{0.12724`,0.12724`},{0.16824`,0.13113`},{0.2057`,0.13683`},{0.24066`,0.14475`},{0.27748`,0.15741`},{0.30849`,0.17319`},{0.34451`,0.19298`},{0.3697`,0.21563`},{0.39689`,0.24599`},{0.41983`,0.27418`},{0.44485`,0.30802`},{0.46922`,0.33974`},{0.48695`,0.37869`},{0.50905`,0.41291`},{0.5237`,0.44979`},{0.54303`,0.49473`},{0.55927`,0.52998`},{0.57375`,0.56989`},{0.58485`,0.61016`},{0.6001`,0.64757`},{0.60917`,0.68431`},{0.62089`,0.71476`},{0.63329`,0.75057`},{0.64493`,0.78091`},{0.65399`,0.809`},{0.66216`,0.83498`},{0.6719`,0.86232`},{0.68048`,0.88136`},{0.68878`,0.89914`},{0.69468`,0.91507`},{0.70487`,0.92923`},{0.71041`,0.94202`},{0.715`,0.95323`},{0.72128`,0.96157`},{0.72916`,0.96986`},{0.73387`,0.9761`},{0.73968`,0.98064`},{0.74545`,0.98509`},{0.74974`,0.98861`},{0.75422`,0.99115`},{0.76134`,0.99352`},{0.76484`,0.99496`},{0.7691`,0.99615`},{0.77579`,0.99743`},{0.77652`,0.99812`},{0.77973`,0.99831`},{0.78817`,0.99878`},{0.78994`,0.99927`},{0.79212`,0.99951`},{0.79603`,0.99976`},{0.79895`,0.99976`},{0.803`,0.99984`},{0.80664`,0.99989`},{0.809`,0.99991`},{0.81`,0.99998`},{0.81357`,0.99996`},{0.81925`,0.99994`},{0.81912`,0.99997`},{0.82284`,1.`},{0.82236`,1.`},{0.8297`,1.`}};
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pfr[2,1]=0.114545`;
prn[2,1,1]={{0.114545`,0.114545`},{0.13889`,0.116765`},{0.16719`,0.11853`},{0.19738`,0.12467`},{0.224985`,0.13335`},{0.255045`,0.144985`},{0.28333`,0.15828`},{0.31039`,0.17505`},{0.336545`,0.192125`},{0.35933`,0.21458`},{0.383095`,0.239455`},{0.406665`,0.262685`},{0.426215`,0.292615`},{0.44587`,0.32011`},{0.46064`,0.35282`},{0.479615`,0.38828`},{0.49778`,0.42572`},{0.51404`,0.45754`},{0.529355`,0.496225`},{0.541035`,0.531925`},{0.555785`,0.568505`},{0.56851`,0.602985`},{0.57974`,0.64078`},{0.59139`,0.67439`},{0.602935`,0.709845`},{0.61151`,0.740625`},{0.622185`,0.770135`},{0.632085`,0.79921`},{0.641355`,0.822825`},{0.65024`,0.849735`},{0.656695`,0.870155`},{0.66446`,0.890665`},{0.673855`,0.90637`},{0.67982`,0.92161`},{0.68696`,0.934665`},{0.692655`,0.94683`},{0.698435`,0.95708`},{0.70485`,0.964335`},{0.710625`,0.972195`},{0.716225`,0.97703`},{0.72188`,0.982245`},{0.72707`,0.986265`},{0.73235`,0.989195`},{0.73923`,0.991765`},{0.74038`,0.99364`},{0.74514`,0.9955`},{0.75017`,0.996445`},{0.75521`,0.99732`},{0.759125`,0.99806`},{0.76349`,0.99883`},{0.767325`,0.99897`},{0.76898`,0.99928`},{0.77406`,0.999515`},{0.77609`,0.99969`},{0.780895`,0.999755`},{0.78219`,0.9998`},{0.788055`,0.99987`},{0.79227`,0.999925`},{0.792685`,0.99993`},{0.79741`,0.999955`},{0.799345`,0.999975`}};
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strn[1,3]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[2,3]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[3,3]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[4,3]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"4\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";
strn[1,4]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[2,4]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[3,4]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[4,4]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"4\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";
strn[1,6]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[2,6]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[3,6]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[4,6]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"4\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";
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strn[1,12]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[2,12]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[3,12]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[4,12]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"4\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";
strn[1,16]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[2,16]="(Subscript[N, 16])(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[3,16]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";strn[4,16]="\!\(\*SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"]\)(\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], StyleBox[\"1\",FontSlant->\"Plain\"]],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\",\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"4\"],FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontSlant->\"Italic\"]\)";
pce[em_,m_,s_,taae_]:=N[(2^(-1))(Erfc[((m-em (1-taae))/((Sqrt[2]) s))]+Erfc[((-m+em(1+ taae))/((Sqrt[2]) s))]),{100,100}]
ped[em_,m_,s_,d_,dm_,sd_,c_]:=N[1-(2^(-c)) (((-Erf[((dm-d s)/((Sqrt[2]) sd))]+Erf[((dm+d s)/((Sqrt[2]) sd))]))^c),{100,100}]
ped[m_,s_,d_,c_]:=N[1-(2^(-c)) ((( -Erf[((-d +m)/((Sqrt[2]) s))]+ Erf[((d +m)/((Sqrt[2])s))]))^c)]
qd[m_,s_,se_,re_,p_,c_]:=d/.Quiet[FindRoot[N[1-(2^(-c)) ((( -Erf[((-d s+m+se)/((Sqrt[2]) re s))]+ Erf[((d s+m+se)/((Sqrt[2]) re s))]))^c),{ag,pg} ]==p,{d,1,20,0,30},AccuracyGoal->ag,PrecisionGoal->pg, WorkingPrecision->wp]]
qd[m_,s_,p_,c_]:=d/.Quiet[FindRoot[N[1-(2^(-c)) ((( -Erf[((-d +m)/((Sqrt[2]) s))]+ Erf[((d +m)/((Sqrt[2]) s))]))^c),{ag,pg} ]==p,{d,1,20,0,30},AccuracyGoal->ag,PrecisionGoal->pg, WorkingPrecision->wp]]
dl[p_,c_]:=dl[p,c]=qd[0,1,p,c]
pedfr[t_,m_,s_,n_,k_,p_]:=Block[{d},d=dl[p,n]Switch[t,1,If[k<n,ped[0,s,d,k]+ped[0,1,d,n-k]-ped[0,s,d,k]ped[0,1,d,n-k],ped[0,s,d,n]],2,If[k<n,ped[m,1,d,k]+ped[0,1,d,n-k]-ped[m,1,d,k]ped[0,1,d,n-k],ped[m,1,d,n]]]]
sqcn[t_,n_,k_,i_]:=ListInterpolation[Transpose[prn[n,k,i]][[t]],{2-t,2-t+6}]
sqcs[t_,n_,k_,i_]:=ListInterpolation[Transpose[prs[n,k,i]][[t]],{2-t,2-t+6}]
qcn[t_,n_,k_,i_,r_]:=ListInterpolation[Transpose[prn[n,k,i]][[t]],{2-t,2-t+r}]
qcs[t_,n_,k_,i_,r_]:=ListInterpolation[Transpose[prs[n,k,i]][[t]],{2-t,2-t+r}]
pns[t_,n_,k_,i_,r_,de_,o_]:=Block[{la,lb,ila,ilb},
la=Transpose[prn[n,k,i]];
lb=Transpose[prs[n,k,i]];
ila={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],la[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],la[[2]]}]};
ilb={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lb[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lb[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ila[[1]],ilb[[1]]},InterpolationOrder->o,PlotLabel->"probability for rejection",PlotLegends->Placed[{stn[n,k,i,t],sts[n,k,i,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ila[[2]],ilb[[2]]},InterpolationOrder->o,PlotLabel->"probability for rejection",PlotLegends->Placed[{stn[n,k,i,t],sts[n,k,i,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
dpns[t_,n_,k_,i_,r_,de_,o_]:=Block[{la,lb,lc,ilc},
la=Transpose[prn[n,k,i]];
lb=Transpose[prs[n,k,i]];
lc=la-lb;
ilc={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lc[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lc[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ilc[[1]]},InterpolationOrder->o,PlotLabel->stn[n,k,i,t]<>" - "<>sts[n,k,i,t], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ilc[[2]]},InterpolationOrder->o,PlotLabel->stn[n,k,i,t]<>" - "<>sts[n,k,i,t], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
rdpns[t_,n_,k_,i_,r_,de_,o_]:=Block[{la,lb,lc,ilc},
la=Transpose[prn[n,k,i]];
lb=Transpose[prs[n,k,i]];
lc=(la-lb)/la;
ilc={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lc[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lc[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ilc[[1]]},InterpolationOrder->o,PlotLabel->"("<>stn[n,k,i,t]<>" - "<>sts[n,k,i,t]<>") / "<>stn[n,k,i,t], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ilc[[2]]},InterpolationOrder->o,PlotLabel->"("<>stn[n,k,i,t]<>" - "<>sts[n,k,i,t]<>") / "<>stn[n,k,i,t],AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
rpns[t_,n_,k_,i_,r_,de_,o_]:=Block[{la,lb,lc,ilc},
la=Transpose[prn[n,k,i]];
lb=Transpose[prs[n,k,i]];
lc=la/lb;
ilc={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lc[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lc[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ilc[[1]]},InterpolationOrder->o,PlotLabel->stn[n,k,i,t]<>" / "<>sts[n,k,i,t],  AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ilc[[2]]},InterpolationOrder->o,PlotLabel->sts[n,k,i,t]<>" / "<>stn[n,k,i,t],  AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
fpns[t_,n1_,k1_,i1_,n2_,k2_,p2_,r_]:=Switch[t,1,Pane[Plot[{qcn[t,n1,k1,i1,r][s],pedfr[t,0,s,n2,k2,p2]},{s,1,1+r},PlotLabel->"probability for rejection",PlotLegends->Placed[{stn[n1,k1,i1,t],fsts[p2,n2,k2,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{qcn[t,n1,k1,i1,r][m],pedfr[t,m,1,n2,k2,p2]},{m,0,r},PlotLabel->"probability for rejection",PlotLegends->Placed[{stn[n1,k1,i1,t],fsts[p2,n2,k2,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
dfpns[t_,n1_,k1_,i1_,n2_,k2_,p2_,r_]:=
Switch[t,1,Pane[Plot[{qcn[t,n1,k1,i1,r][s]-pedfr[t,0,s,n2,k2,p2]},{s,1,1+r},PlotLabel->PlotLabel->"difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{qcn[t,n1,k1,i1,r][m]-pedfr[t,m,1,n2,k2,p2]},{m,0,r},PlotLabel->"difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
rdfpns[t_,n1_,k1_,i1_,n2_,k2_,p2_,r_]:=
Switch[t,1,Pane[Plot[{(qcn[t,n1,k1,i1,r][s]-pedfr[t,0,s,n2,k2,p2])/qcn[t,n1,k1,i1,r][s]},{s,1,r+1},PlotLabel->PlotLabel->"relative difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{(qcn[t,n1,k1,i1,r][m]-pedfr[t,m,1,n2,k2,p2])/qcn[t,n1,k1,i1,r][m]},{m,0,r},PlotLabel->"relative difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
rfpns[t_,n1_,k1_,i1_,n2_,k2_,p2_,r_]:=
Switch[t,1,Pane[Plot[{qcn[t,n1,k1,i1,r][s]/pedfr[t,0,s,n2,k2,p2]},{s,1,r+1},PlotLabel->PlotLabel->"ratio of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{qcn[t,n1,k1,i1,r][m]/pedfr[t,m,1,n2,k2,p2]},{m,0,r},PlotLabel->"ratio of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
pnn[t_,n1_,k1_,i1_,n2_,k2_,i2_,r_,de_,o_]:=Block[{la,lb,ila,ilb},
la=Transpose[prn[n1,k1,i1]];
lb=Transpose[prn[n2,k2,i2]];
ila={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],la[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],la[[2]]}]};
ilb={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lb[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lb[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ila[[1]],ilb[[1]]},InterpolationOrder->o,PlotLabel->"probability for rejection",PlotLegends->Placed[{stn[n1,k1,i1,t],stn[n2,k2,i2,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ila[[2]],ilb[[2]]},InterpolationOrder->o,PlotLabel->"probability for rejection",PlotLegends->Placed[{stn[n1,k1,i1,t],stn[n2,k2,i2,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
dpnn[t_,n1_,k1_,i1_,n2_,k2_,i2_,r_,de_,o_]:=Block[{la,lb,lc,ilc},
la=Transpose[prn[n1,k1,i1]];
lb=Transpose[prn[n2,k2,i2]];
lc=la-lb;
ilc={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lc[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lc[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ilc[[1]]},InterpolationOrder->o,PlotLabel->stn[n1,k1,i1,t]<>" - "<>stn[n2,k2,i2,t], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ilc[[2]]},InterpolationOrder->o,PlotLabel->stn[n1,k1,i1,t]<>" - "<>stn[n2,k2,i2,t], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
rdpnn[t_,n1_,k1_,i1_,n2_,k2_,i2_,r_,de_,o_]:=Block[{la,lb,lc,ilc},
la=Transpose[prn[n1,k1,i1]];
lb=Transpose[prn[n2,k2,i2]];
lc=(la-lb)/la;
ilc={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lc[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lc[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ilc[[1]]},InterpolationOrder->o,PlotLabel->"("<>stn[n1,k1,i1,t]<>" - "<>stn[n2,k2,i2,t]<>") / "<>stn[n1,k1,i1,t], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ilc[[2]]},InterpolationOrder->o,PlotLabel->"("<>stn[n1,k1,i1,t]<>" - "<>stn[n2,k2,i2,t]<>") / "<>stn[n1,k1,i1,t], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
rpnn[t_,n1_,k1_,i1_,n2_,k2_,i2_,r_,de_,o_]:=Block[{la,lb,lc,ilc},
la=Transpose[prn[n1,k1,i1]];
lb=Transpose[prn[n2,k2,i2]];
lc=lb/la;
ilc={MapThread[{#1,#2}&,{Table[j,{j,1,r+1,de}],lc[[1]]}],MapThread[{#1,#2}&,{Table[j,{j,0,r,de}],lc[[2]]}]};
Switch[t,1,Pane[ListLinePlot[{ilc[[1]]},InterpolationOrder->o,PlotLabel->stn[n1,k1,i1,t]<>" / "<>stn[n2,k2,i2,t],  AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[ListLinePlot[{ilc[[2]]},InterpolationOrder->o,PlotLabel->stn[n1,k1,i1,t]<>" / "<>stn[n2,k2,i2,t],  AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"N2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]]
pss[t_,n1_,k1_,p1_,n2_,k2_,p2_,r_]:=Switch[t,1,Pane[Plot[{pedfr[t,0,s,n1,k1,p1],pedfr[t,0,s,n2,k2,p2]},{s,1,1+r},PlotLabel->"probability for rejection",PlotLegends->Placed[{fsts[p1,n1,k1,t],fsts[p2,n2,k2,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{pedfr[t,m,1,n1,k1,p1],pedfr[t,m,1,n2,k2,p2]},{m,0,r},PlotLabel->"probability for rejection",PlotLegends->Placed[{fsts[p1,n1,k1,t],fsts[p2,n2,k2,t]},Right], AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]

dpss[t_,n1_,k1_,p1_,n2_,k2_,p2_,r_]:=
Switch[t,1,Pane[Plot[{pedfr[t,0,s,n1,k1,p1]-pedfr[t,0,s,n2,k2,p2]},{s,1,1+r},PlotLabel->PlotLabel->"difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{pedfr[t,m,1,n1,k1,p1]-pedfr[t,m,1,n2,k2,p2]},{m,0,r},PlotLabel->"difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
rdpss[t_,n1_,k1_,p1_,n2_,k2_,p2_,r_]:=
Switch[t,1,Pane[Plot[{(pedfr[t,0,s,n1,k1,p1]-pedfr[t,0,s,n2,k2,p2])/pedfr[t,0,s,n1,k1,p1]},{s,1,r+1},PlotLabel->PlotLabel->"relative difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{(pedfr[t,m,1,n1,k1,p1]-pedfr[t,m,1,n2,k2,p2])/pedfr[t,m,1,n1,k1,p1]},{m,0,r},PlotLabel->"relative difference of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","(\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"-\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\))\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
rpss[t_,n1_,k1_,p1_,n2_,k2_,p2_,r_]:=
Switch[t,1,Pane[Plot[{pedfr[t,0,s,n1,k1,p1]/pedfr[t,0,s,n2,k2,p2]},{s,1,r+1},PlotLabel->PlotLabel->"ratio of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"σ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}],2,Pane[Plot[{pedfr[t,m,1,n1,k1,p1]/pedfr[t,m,1,n2,k2,p2]},{m,0,r},PlotLabel->"ratio of probabilities for rejection", AxesLabel->{"\!\(\*StyleBox[\"μ\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)","\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S1\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\"/\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[SubscriptBox[StyleBox[\"p\",FontWeight->\"Plain\",FontSlant->\"Italic\"], \"S2\"],FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"}],{600}]]
fsts[p_,n_,k_,t_]:=Text@Switch[t,0,StringJoin["\!\(\*StyleBox[SubscriptBox[\"P\", \"S\"],FontSlant->\"Italic\"]\)","(",ToString[n],",",ToString[k],",0,1;", ToString[NumberForm[dl[p,n],2]],")"],1,StringJoin["\!\(\*StyleBox[SubscriptBox[\"P\", \"S\"],FontSlant->\"Italic\"]\)","(",ToString[n],",",ToString[k],",0,σ;", ToString[NumberForm[dl[p,n],2]],")"],2,StringJoin["\!\(\*StyleBox[SubscriptBox[\"P\", \"S\"],FontSlant->\"Italic\"]\)","(",ToString[n],",",ToString[k],",μ,1;", ToString[NumberForm[dl[p,n],2]],")"]]
strs[p_,n_]:=Text@StringJoin["\!\(\*StyleBox[\"S\",FontSlant->\"Italic\"]\)",Switch[n,1,"(\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"1\"]\)",2,"(\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"1\"]\),\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"]\)",3,"(\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"1\"]\),\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"]\),\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"]\)",4,"(\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"1\"]\),\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"2\"]\),\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"3\"]\),\!\(\*SubscriptBox[StyleBox[\"x\",FontSlant->\"Italic\"], \"4\"]\)"],";", ToString[NumberForm[dl[p,n],2]],")"]
gpfrnns[n_,k_,i_]:=Text[Grid[Transpose[{{"QC function","decision limit","pfr"},{strn[n,i]," - ",ToString[NumberForm[pfr[n,i],6]]},{strs[pfr[n,i],n],ToString[NumberForm[dl[pfr[n,i],n],2]],ToString[NumberForm[pfr[n,i],6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{All,Automatic}],BaseStyle->{Medium}]
gpfrnns[n_,k_,i_,mc_,sc_]:=Text[Grid[Transpose[{{"critical mean \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)",
"critical standard deviation \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)","QC function","decision limit","size \!\(\*StyleBox[\"n\",FontSlant->\"Italic\"]\) of QC samples","number \!\(\*StyleBox[\"k\",FontSlant->\"Italic\"]\) of out of control measurements per QC sample", "probability for \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection",
"probability for \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection","pfr"},{ToString[NumberForm[mc,6]],ToString[NumberForm[sc,6]],strn[n,i]," - ",ToString[n],ToString[k],ToString[NumberForm[sqcn[2,n,k,i][mc],6]],ToString[NumberForm[sqcn[1,n,k,i][sc],6]],ToString[NumberForm[pfr[n,i],6]]},{SpanFromLeft,SpanFromLeft,strs[pfr[n,i],n],ToString[NumberForm[dl[pfr[n,i],n],2]],ToString[n],ToString[k],ToString[NumberForm[pedfr[2,mc,1,n,k,pfr[n,i]],6]],ToString[NumberForm[pedfr[1,0,sc,n,k,pfr[n,i]],6]],ToString[NumberForm[pfr[n,i],6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{Automatic,Automatic}],BaseStyle->{Medium}]
gpfrns[n1_,k1_,i1_,n2_,k2_,p2_]:=Text[Grid[Transpose[{{"QC function","decision limit","pfr"},{strn[n1,i1]," - ",ToString[NumberForm[pfr[n1,i1],6]]},{strs[p2,n2],ToString[NumberForm[dl[p2,n2],2]],ToString[NumberForm[p2,6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{All,Automatic}],BaseStyle->{Medium}]
gpfrns[n1_,k1_,i1_,n2_,k2_,p2_,mc_,sc_]:=Text[Grid[Transpose[{{"critical mean \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)",
"critical standard deviation \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)","QC function","decision limit","size \!\(\*StyleBox[\"n\",FontSlant->\"Italic\"]\) of QC samples","number \!\(\*StyleBox[\"k\",FontSlant->\"Italic\"]\) of out of control measurements per QC sample","probability for \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection",
"probability for \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection","pfr"},{ToString[NumberForm[mc,6]],ToString[NumberForm[sc,6]],strn[n1,i1]," - ",ToString[n1],ToString[k1],ToString[NumberForm[sqcn[2,n1,k1,i1][mc],6]],ToString[NumberForm[sqcn[1,n1,k1,i1][sc],6]],ToString[NumberForm[pfr[n1,i1],6]]},{SpanFromLeft,SpanFromLeft,strs[p2,n2],ToString[NumberForm[dl[p2,n2],2]],ToString[n2],ToString[k2],ToString[NumberForm[pedfr[2,mc,1,n2,k2,p2],6]],ToString[NumberForm[pedfr[1,0,sc,n2,k2,p2],6]],ToString[NumberForm[p2,6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{Automatic,Automatic}],BaseStyle->{Medium}]
gpfrnn[n1_,k1_,i1_,n2_,k2_,i2_]:=Text[Grid[Transpose[{{"QC function","pfr"},{strn[n1,i1],ToString[NumberForm[pfr[n1,i1],6]]},{strn[n2,i2],ToString[NumberForm[pfr[n2,i2],6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{All,Automatic}],BaseStyle->{Medium}]
gpfrnn[n1_,k1_,i1_,n2_,k2_,i2_,mc_,sc_]:=Text[Grid[Transpose[{{"critical mean \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)",
"critical standard deviation \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)","QC function","size \!\(\*StyleBox[\"n\",FontSlant->\"Italic\"]\) of QC samples","number \!\(\*StyleBox[\"k\",FontSlant->\"Italic\"]\) of out of control measurements per QC sample","probability for \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection",
"probability for \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection","pfr"},{ToString[NumberForm[mc,6]],ToString[NumberForm[sc,6]],strn[n1,i1],ToString[n1],ToString[k1],ToString[NumberForm[sqcn[2,n1,k1,i1][mc],6]],ToString[NumberForm[sqcn[1,n1,k1,i1][sc],6]],ToString[NumberForm[pfr[n1,i1],6]]},{SpanFromLeft,SpanFromLeft,strn[n2,i2],ToString[n2],ToString[k2],ToString[NumberForm[sqcn[2,n2,k2,i2][mc],6]],ToString[NumberForm[sqcn[1,n2,k2,i2][sc],6]],ToString[NumberForm[pfr[n2,i2],6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{Automatic,Automatic}],BaseStyle->{Medium}]
gpfrss[n1_,k1_,p1_,n2_,k2_,p2_]:=Text[Grid[Transpose[{{"QC function","decision limit","pfr"},{strs[p1,n1],ToString[NumberForm[dl[p1,n1],2]],ToString[NumberForm[p1,6]]},{strs[p2,n2],ToString[NumberForm[dl[p2,n2],2]],ToString[NumberForm[p2,6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{All,Automatic}],BaseStyle->{Medium}]
gpfrss[n1_,k1_,p1_,n2_,k2_,p2_,mc_,sc_]:=Text[Grid[Transpose[{{"critical mean \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)",
"critical standard deviation \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)","QC function","decision limit","size \!\(\*StyleBox[\"n\",FontSlant->\"Italic\"]\) of QC samples","number \!\(\*StyleBox[\"k\",FontSlant->\"Italic\"]\) of out of control measurements per QC sample","probability for \!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection",
"probability for \!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\) detection","pfr"},{ToString[NumberForm[mc,6]],ToString[NumberForm[sc,6]],strs[p1,n1],ToString[NumberForm[dl[p1,n1],2]],ToString[n1],ToString[k1],ToString[NumberForm[pedfr[2,mc,1,n1,k1,p1],6]],ToString[NumberForm[pedfr[1,0,sc,n1,k1,p1],6]],ToString[NumberForm[p1,6]]},{SpanFromLeft,SpanFromLeft,strs[p2,n1],ToString[NumberForm[dl[p2,n2],2]],ToString[n1],ToString[k1],ToString[NumberForm[pedfr[2,mc,1,n2,k2,p2],6]],ToString[NumberForm[pedfr[1,0,sc,n2,k2,p2],6]],ToString[NumberForm[p2,6]]}}],Frame->All, FrameStyle->Blend[{Blue,Cyan},0.35],Spacings->{1,1},ItemSize->{Automatic,Automatic}],BaseStyle->{Medium}]
TabView[{
"QC plots"->
TabView[{
"NN vs a SSV QC function with equal pfr"->
Manipulate[If[k>n,k=n];
Column[{Switch[f,vf,pns[t,n,k,i,6,0.1,2],df,dpns[t,n,k,i,6,0.1,2],rdf, rdpns[t,n,k,i,6,0.1,2],rf,rpns[t,n,k,i,6,0.1,2]],Text@gpfrnns[n,k,i]},Center],
{{f,vf,"type"},{vf->"probabilities",df->"difference",rdf->"relative difference", rf->"ratio"},ControlPlacement->Left},
{{t,2,"vs"},{1->"σ",2->"μ"},ControlPlacement->Left},
Delimiter,
Style["QC functions",Bold],
Style["neural network",Plain],
{{i,6,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC samples",Plain],
{{n,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k,n,"k"},1,Dynamic[n],1,ImageSize->Tiny,Appearance->"Labeled"},
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left],
"NN vs SSV QC function"->
Manipulate[If[k1>n1,k1=n1];If[k2>n2,k2=n2];
Column[{Switch[f,vf,fpns[t,n1,k1,i1,n2,k2,p2,6],df,dfpns[t,n1,k1,i1,n2,k2,p2,6],rdf, rdfpns[t,n1,k1,i1,n2,k2,p2,6],rf,rfpns[t,n1,k1,i1,n2,k2,p2,6]],Text@gpfrns[n1,k1,i1,n2,k2,p2]},Center],
{{f,vf,"type"},{vf->"probabilities",df->"difference",rdf->"relative difference", rf->"ratio"},ControlPlacement->Left},
{{t,2,"vs"},{1->"σ",2->"μ"},ControlPlacement->Left},
Delimiter,
Style["neural network QC function",Bold],
Style["neural network",Plain],
{{i1,6,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC sample",Plain],
{{n1,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k1,n1,"k"},1,Dynamic[n1],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["SSV QC function",Bold],
Style["size of QC sample",Plain],
{{n2,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k2,n2,"k"},1,Dynamic[n2],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["probability for for false rejection",Plain],
{{p2,0.01,"pfr"},0.000001,0.1,0.000001,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left],
"NN vs NN QC function"->
Manipulate[If[k1>n1,k1=n1];If[k2>n2,k2=n2];
Column[{Switch[f,vf,pnn[t,n1,k1,i1,n2,k2,i2,6,0.1,2],df,dpnn[t,n1,k1,i1,n2,k2,i2,6,0.1,2],rdf, rdpnn[t,n1,k1,i1,n2,k2,i2,6,0.1,2],rf,rpnn[t,n1,k1,i1,n2,k2,i2,6,0.1,2]],Text@gpfrnn[n1,k1,i1,n2,k2,i2]},Center],
{{f,vf,"type"},{vf->"probabilities",df->"difference",rdf->"relative difference", rf->"ratio"},ControlPlacement->Left},
{{t,2,"vs"},{1->"σ",2->"μ"},ControlPlacement->Left},
Delimiter,
Style["first neural network QC funtion",Bold],
Style["neural network",Plain],
{{i1,6,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC sample",Plain],
{{n1,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k1,n1,"k"},1,Dynamic[n1],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["second neural network QC function",Bold],
Style["neural network",Plain],
{{i2,8,"NN"},{1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC sample",Plain],
{{n2,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k2,n2,"k"},1,Dynamic[n2],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left],
"SSV vs SSV QC function"->
Manipulate[If[k1>n1,k1=n1];If[k2>n2,k2=n2];
Column[{Switch[f,vf,pss[t,n1,k1,p1,n2,k2,p2,6],df,dpss[t,n1,k1,p1,n2,k2,p2,6],rdf, rdpss[t,n1,k1,p1,n2,k2,p2,6],rf,rpss[t,n1,k1,p1,n2,k2,p2,6]],Text@gpfrss[n1,k1,p1,n2,k2,p2]},Center],
{{f,vf,"type"},{vf->"probabilities",df->"difference",rdf->"relative difference", rf->"ratio"},ControlPlacement->Left},
{{t,2,"vs"},{1->"σ",2->"μ"},ControlPlacement->Left},
Delimiter,
Style["first SSV QC function",Bold],
Style["size of QC sample",Plain],
{{n1,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k1,n1,"k"},1,Dynamic[n1],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["probability for for false rejection",Plain],
{{p1,0.01,"pfr"},0.000001,0.1,0.000001,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["second SSV QC function",Bold],
Style["size of QC sample",Plain],
{{n2,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k2,n2,"k"},1,Dynamic[n2],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["probability for for false rejection",Plain],
{{p2,0.005,"pfr"},0.000001,0.1,0.000001,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left]},
ImageSize->All],
"QC calculators"->
TabView[{
"NN vs a SSV QC function with equal pfr"->
Manipulate[If[k>n,k=n];
Text@gpfrnns[n,k,i,mcr,scr],
Style["parameters of the measurement process ",Bold],
"standardized critical mean",
{{mcr,3,"\!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},0,6,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
"standardized critical standard deviation",
{{scr,4,"\!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},1,7,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["QC functions",Bold],
Style["neural network",Plain],
{{i,6,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC samples",Plain],
{{n,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k,n,"k"},1,Dynamic[n],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left],
"NN vs SSV QC function"->
Manipulate[If[k1>n1,k1=n1];If[k2>n2,k2=n2];
Text@gpfrns[n1,k1,i1,n2,k2,p2,mcr,scr],
Style["parameters of the measurement process ",Bold],
"standardized critical mean",
{{mcr,3,"\!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},0,6,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
"standardized critical standard deviation",
{{scr,4,"\!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},1,7,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["neural network QC function",Bold],
Style["neural network",Plain],
{{i1,6,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC sample",Plain],
{{n1,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k1,n1,"k"},1,Dynamic[n1],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["SSV QC function",Bold],
Style["size of QC sample",Plain],
{{n2,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k2,n2,"k"},1,Dynamic[n2],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["probability for for false rejection",Plain],
{{p2,0.01,"pfr"},0.000001,0.1,0.000001,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left],
"NN vs NN QC function"->
Manipulate[If[k1>n1,k1=n1];If[k2>n2,k2=n2];
Text@gpfrnn[n1,k1,i1,n2,k2,i2,mcr,scr],
Style["parameters of the measurement process ",Bold],
"standardized critical mean",
{{mcr,3,"\!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},0,6,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
"standardized critical standard deviation",
{{scr,4,"\!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},1,7,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["first neural network QC function",Bold],
Style["neural network",Plain],
{{i1,6,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC sample",Plain],
{{n1,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k1,n1,"k"},1,Dynamic[n1],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["second neural network QC function",Bold],
Style["neural network",Plain],
{{i2,8,"NN"},{
1->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"1\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
2->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"2\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
3->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"3\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",
4->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"4\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",6->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"6\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)",8->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"8\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 12->"\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"12\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)", 16-> "\!\(\*StyleBox[SubscriptBox[StyleBox[\"N\",FontSlant->\"Italic\"], \"16\"],FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"(\",FontWeight->\"Plain\"]\)\!\(\*StyleBox[\"x\",FontWeight->\"Bold\",FontSlant->\"Italic\"]\)\!\(\*StyleBox[\")\",FontWeight->\"Plain\",FontSlant->\"Italic\"]\)"},ControlPlacement->Left},
Delimiter,
Style["size of QC sample",Plain],
{{n2,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k2,n2,"k"},1,Dynamic[n2],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left],
"SSV vs SSV QC function"->
Manipulate[If[k1>n1,k1=n1];If[k2>n2,k2=n2];
Text@gpfrss[n1,k1,p1,n2,k2,p2,mcr,scr],
Style["parameters of the measurement process ",Bold],
"standardized critical mean",
{{mcr,3,"\!\(\*SubscriptBox[\"μ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},0,6,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
"standardized critical standard deviation",
{{scr,4,"\!\(\*SubscriptBox[\"σ\", StyleBox[\"c\",FontSlant->\"Italic\"]]\)"},1,7,0.01,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["first SSV QC function",Bold],
Style["size of QC sample",Plain],
{{n1,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k1,n1,"k"},1,Dynamic[n1],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["probability for for false rejection",Plain],
{{p1,0.01,"pfr"},0.000001,0.1,0.000001,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["second SSV QC function",Bold],
Style["size of QC sample",Plain],
{{n2,4,"n"},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["number of out of control measurements per QC sample",Plain],
{{k2,n2,"k"},1,Dynamic[n2],1,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
Style["probability for for false rejection",Plain],
{{p2,0.005,"pfr"},0.000001,0.1,0.000001,ImageSize->Tiny,Appearance->"Labeled"},
Delimiter,
SaveDefinitions->True,TrackedSymbols->True,ControlPlacement->Left]},
ImageSize->All]
},
 ImageSize->Automatic
]

Abbreviations
QC: quality control
NN: neural network
SSV: statistical single-value  (QC function)
pfr: probability for false rejection

Notation
(Subscript[N, i])(x): neural network QC function applied on a tuple x of QC measurements. The index i is related to the ratio of the simulated QC measurements  of the training set distributed as  𝒩(0,1) and 𝒩(μ,(σ^2)).
(Subscript[S, i])(x): SSV QC function  applied on a tuple x of QC measurements; (Subscript[N, i])(x) and (Subscript[S, i])(x) have equal probabilities for false rejection. 
S(x;l): SSV QC function with decision limit l, applied on a tuple x of QC measurements.
𝒩(μ,(σ^2)): normal distribution with mean μ and standard deviation σ.
(Subscript[P, N,i])(n,k,μ,σ): probability for rejection of the neural network QC function (Subscript[N, i])(x) applied on a n-tuple x of control measurements, k of them distributed as 𝒩(μ,(σ^2)) and n-k as 𝒩(0,1), where 0<|μ|≤6 or 1<|σ|≤7.
 (Subscript[P, S,i])(n,k,μ,σ): probability for rejection of the SSV QC function (Subscript[S, i])(x) applied on a tuple x of n control measurements, k of them distributed as 𝒩(μ,(σ^2)) and n-k as 𝒩(0,1), for 0<|μ|≤6 or 1<|σ|≤7.
(Subscript[P, S])(n,k,μ,σ;l): probability for rejection of the SSV QC function  S(x;l) applied on a tuple x of n control measurements, k of them distributed as 𝒩(μ,(σ^2)) and n-k as 𝒩(0,1), for 0<|μ|≤6 or 1<|σ|≤7.

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About
Intelligent Quality
Version Number 1.1.3.4
Hellenic Complex Systems Laboratory 2024
The notebook is distributed under  an Attribution - NonCommercial - ShareAlike 4.0 International Creative Commons License.