Statistical Process Control, Theory and Applications: Understanding and Implementation of Modern Developments

Abstract:

Several aspects of univariate distribution-free / nonparametric statistical quality control techniques are considered. First, a nonparametric Shewhart-type Phase I control chart for monitoring the location of a continuous variable is proposed. The chart is based on the pooled median of the available Phase I samples and the charting statistics are the counts (number of observations) in each sample that are less than the pooled median. The derivations recognize that in Phase I the signalling events are dependent and that more than one comparison is made against the same estimated limits simultaneously; this leads to working with the joint distribution of a set of dependant random variables. Second, Phase II control charts are considered for the case when the underlying parameters of the process distribution are known or specified. For this ‘standard(s) known’ case Shewhart-type, exponentially weighted moving average (EWMA)-type and cumulative sum (CUSUM)-type charts are proposed based on the sign and signed-rank statistics, respectively. Lastly, Phase II control charts are considered for the case when the underlying parameters of the process distribution are unknown and need to be estimated. For this ‘standard(s) unknown’ case Shewhart-type, EWMA-type and CUSUM-type nonparametric charts are proposed based on the exceedance statistics. A summary and some concluding remarks are given.