Statistical Inference Of Non-Normal Process Cpability Indices

Process capability refers to the uniformity of the process. It also means the ability of a process to produce output within specification limits which considered international standards, national standards, industry standards and customer requirements. Process capability indices (PCIs) is a statistical measure of process capability. It’s also an important indicator in quality management. The concept of PCIs only holds meaning for processes that are in a state of statistical control. PCIs are usually calculated by the specification limits ratio process fluctuation. The standard PCIs calculations require the quality characteristics should follow a normal distribution. In fact, the distribution of the underlying quality characteristics data is not normal. If with the departures from the normality assumption could lead to erroneous results when applying conventional statistical capability measures to non-normal distributions. Since non-normally distributed processes are not uncommon in practice, process capability for non-normal data has been widely studied in quality management. In this paper, we use the approach proposed by Clements(1989) to handle non-normal data, focusing on the study in statistical inference of corresponding distribution. Take three common non-normal distributions as examples is Weibull distribution, Lognormal distribution and Generalized Exponential distribution. Our goal is to explore the frequency property of generalized confidence interval applying the method which Weerahandi (1993) put forward with. First, we construct generalized pivotal quantity (GPQ) for the parameters and process fluctuation. Secondly using simulation method in Matlab. Given different confidence level, choose different sample size and get the coverage of generalized confidence interval. Eventually, we find the frequency property of generalized confidence interval under all the confidence level is satisfied. Even chosen small sample, the difference between the actual coverage with nominal coverage is still small. That is, generalized confidence interval estimation has a good effect in statistical inference of non-normal PCIs. We hope it will lay the theoretical foundation for its application in practice.