THE CRUCIAL ROLE OF OPTIMIZATION IN STATISTICAL CONTROL OF TECHNOLOGICAL PROCESSES

Abstract

Keywords: Technological Process, Statistical Process Control, Parameter Optimization, Modified Sequential Simplex Search, Six Sigma.

The purpose of this presentation is to review the contemporary paradigm of SPC and to provide support to the claim: to make SPC of a technological process practical it is crucial to tune up the process first by setting its controllable parameters to their optimal values.

The contemporary paradigm of SPC is based on detection of events that, under the hypothesis of the process being in the state of statistical control, have low probabilities. The approach to detection, in turn, is usually based on purely mathematical stratagems, not on features specific to real life processes.

Inadequacy of the paradigm is that low probability events do happen all the time. Strictly speaking, probability of occurrence of any particular value of any continuous characteristic of a process is nothing but zero. However, the owners of the process - operators or production managers - would strongly disapprove of some of those values (e.g., falling beyond 3 or 6 limits) while they would happily embrace others, like those falling on or close to the process' target - despite the same low probability of occurrence. In other words, it is not just the probability of occurrence, it is also the acceptability of the observed values that governs the owners' opinion about the process performance. The statistician is hardly capable of being a decision-maker here.

Moreover, the owners virtually always expect the statistician to provide much more than merely a warning that a low probability event has occurred; they want the statistician to tell what exactly went wrong. This usually is not attainable.

Stemming from its mathematical roots, statistics' universality delimits its ability to be specific to the smallest detail of a particular situation. However, this does not mean that no specificity can be addressed. I will discuss some features that are common to all technological processes and distinguish them from processes of other kinds we deal with in our lives.

Based on the discussion, I will show the importance of optimizing the process parameters. It not only reduces the process variation; it creates the situation where deviations from the optimal values lead to known consequences in the process performance. As a result, the statistician becomes capable of telling the process owner what is going wrong and what to do to improve the situation- at least to a certain extent. As a free bonus, the process will be brought to the attainable peak of its performance.

I will discuss then some of available methods of process optimization, both univariate and multivariate, focusing on a method of empirical optimization known as Modified Sequential Simplex Search (Zeliger, 1995). The most important features of the MSSS are:

1. its applicability in situations when only qualitative evaluation of the process outcome is possible (e.g., sensory evaluation),
2. the possibility of organizing parallel experiments, which in a certain sense converts any multivariate process into a univariate one thus dramatically - proportionally to the dimensionality of the original process - reduces the total experiment time.

Bio

George Zeliger is a graduate in Applied Mathematics of St. Petersburg University, Russia. He worked on his doctorate in Quality Control at the Russian National Institute for Standardization. Since immigration to this country eleven years ago, George worked as a statistician, statistical consultant and statistical programmer at various industrial companies. For a number of years he taught various statistical courses for the ASQ Boston Section.

George was a presenter at over ten national and international conferences. His current research interests lie in the field of process optimization and related issues of the SPC.