## HCSL Publications

# Statistical Quality Control Design

### 1. Hatjimihail AT. Tool for Quality
Control Design and Evaluation. Wolfram
Demonstrations Project, 2010.

#### Abstract

This Demonstration can be used to estimate various
parameters of a measurement process and to design the
quality
control rule to be applied. You define the
parameters of the control measurements that are
the assigned mean, the observed mean, and the
standard deviation, in arbitrary measurement
units. In addition, you define the quality
specifications of the measurement process, that
is, the total allowable analytical
error (as a percentage of the assigned mean),
the maximum acceptable fraction of measurements
nonconforming to the specifications, and the
minimum acceptable probabilities for random and
systematic error detection. Finally, you choose
the number n of control
measurements.

#### Comment

S(1,n,d σ) is a
quality control rule that rejects the analytical run
if at least one of the n
control measurements is less than mo-d σ or greater than mo+d σ, where d is a positive real number and mo
and σ are the mean and
the standard deviation of the control measurements.
The quantities mo-d σ and mo+d σ are
the lower and the upper quality control decision
limits. Then the fraction nonconforming f, the critical random and systematic
errors of the measurement process, as well as the
quality control decision limits and the respective
probabilities for critical random and systematic
error detection and for false rejection are
estimated. Finally, by choosing the type of output,
you can see the estimated quality control (qc)
parameters or plot the probability density function
(pdf), the cumulative density function (cdf) of the
control measurements, or the power function graphs
for the random error (pfg re) and systematic error
(pfg se). The parameters are estimated and the functions are
plotted if 10^{-100}<= f <= fmax, where f is the fraction
nonconforming and fmax is the
maximum acceptable fraction nonconforming.

This is a free application available to clinical laboratories.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code

### 2. Hatjimihail AT. Calculation of
the confidence bounds for the fraction
nonconforming of normal populations of
measurements in clinical laboratory medicine
[HCSL Technical Report No IV]. Drama: Hellenic
Complex Systems Laboratory, 2015.

#### Abstract

## The fraction nonconforming is a key quality measure
used in statistical quality control design in
clinical laboratory medicine. The confidence bounds
of normal populations of measurements for the
fraction nonconforming each of the lower and upper
quality specification limits when both the random and
the systematic error are unknown can be calculated
using the noncentral t-distribution, as it is
described in detail and illustrated with
examples.

Abstract
in arXiv.org e-Print archive

Technical Report (Full
text, PDF format)

Supporting Information
File (MATLAB_Figures.zip)