Nonparametric statistical process control: Bootstrap control charts

The most commonly used techniques in statistical process control are parametric, and thus require assumptions regarding the statistical properties of the underlying process. For example, all traditional methods of statistical process control, Shewhart control charts, CUSUM charts, and EWMA charts assume that the observations are independent, and that the statistic of interest is normally distributed. These assumptions are often violated in practice; for example, a test for normality of the variable being measured may be rejected, or there may be considerable serial correlation in the data. In such cases the control limits may not be accurate. Bootstrap, a computer intensive resampling procedure that does not require a priori distribution assumptions, can be used in these situations. We first extend the bootstrap percentile method to include a series of subgroups, which are typically used in assessing process control limits. We show how the subgroup bootstrap is used to assess process control limits for x and $\rm s\sp2$ charts. Via simulation, we then compare subgroup bootstrap and parametric methods for determining process control limits for a quality related characteristic of a manufacturing process under various conditions. Our results show that bootstrap methods for x and $\rm s\sp2$ control charts generally achieve comparatively better control limit estimates than standard parametric methods, particularly when the assumption of a normal process distribution is not valid. We also develop bootstrap methodology to (1) assess process control limits for individual process charts, and (2) establish statistical process control in the presence of data correlation through two specialized charts: Common Cause Control charts and Special Cause Control charts. As an example we show how specified control limits are determined for a serially correlated ARMA(1,1) manufacturing process. We further extend the bootstrap approach for correlated processes to include variance and range charts. Bootstrap is easily implementable on a personal computer as a general methodology for statistical process control, and hence, a potentially useful pragmatic quality improvement tool.