STATISTICAL PROCESS-CONTROL VIA THE SUBGROUP BOOTSTRAP

The most commonly used techniques in statistical process control are p arametric, and so they require assumptions regarding the statistical p roperties of the underlying process. For example, Shewhart control cha rts assume that the observations are independent, and that the statist ic of interest is normally distributed, These assumptions are often vi olated in practice; for example, the distribution of the variable bein g measured may be strongly skewed or may fail a test for normality. In such cases the control limits, especially for small subgroup samples, may not be accurate. The bootstrap is a computer intensive rp samplin g procedure that does not require a priori distribution assumptions. I t was developed to find the distribution of a statistic when the distr ibution is not known. We first extend the bootstrap percentile method to include a series of subgroups, which are typically used in assessin g process control limits. We show, via examples, how the subgroup boot strap is used to assess process control limits for (X) over bar and S- 2 charts, Via simulation, we then empirically compare the subgroup boo tstrap and parametric methods for determining process control limits f or a quality related characteristic of a manufacturing process under v arious conditions, The results show that bootstrap methods for (X) ove r bar and S-2 control charts generally achieve comparatively better co ntrol limit estimates than standard parametric methods, particularly w hen the assumption of a normal process distribution is not valid. The subgroup bootstrap is easily implemented on a personal computer as a g eneral methodology for statistical process control, and hence, is a po tentially useful pragmatic quality improvement tool.