Process Capability Analysis in Non Normal Linear Regression Profiles

Abstract

When the distribution of a process characterized by a profile is non normal, process capability analysis using normal assumption often leads to erroneous interpretations of the process performance. Profile monitoring is a relatively new set of techniques in quality control that is used in situations where the state of product or process is represented by a function of two or more quality characteristics. Such profiles can be modeled using linear or nonlinear regression models. In some applications, it is assumed that the quality characteristics follow a normal distribution; however, in certain applications this assumption may fail to hold and may yield misleading results. In this article, we consider process capability analysis of non normal linear profiles. We investigate and compare five methods to estimate non normal process capability index (PCI) in profiles. In three of the methods, an estimation of the cumulative distribution function (cdf) of the process is required to analyze process capability in profiles. In order to estimate cdf of the process, we use a Burr XII distribution as well as empirical distributions. However, the resulted PCI with estimating cdf of the process is sometimes far from its true value. So, here we apply artificial neural network with supervised learning which allows the estimation of PCIs in profiles without the need to estimate cdf of the process. Box-Cox transformation technique is also developed to deal with non normal situations. Finally, a comparison study is performed through the simulation of Gamma, Weibull, Lognormal, Beta and student-t data.

Keywords:

• Burr XII distribution
• Linear regression
• Neural networks
• Non normality
• Process capability indices
• Profile

Mathematics Subject Classification:

• 62P30
• 62J05
• 62M45

Acknowledgment

The authors appreciate the constructive comments of the Editor and anonymous referees that helped to improve this article.

Notes

The proportions P _U(profile) and P _L(profile) of non conforming items for profiles are obtained by

using (8), in each level of X, we have:

then: