Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart $\overline{X}$ Chart

Abstract

In modern quality control applications, there often exist significant measurement errors because observations are measured quickly in time order. As a result, the errors influence the power of a control chart to detect a given change in the process parameter(s) of a quality characteristic. In this paper, by using a covariate error model, the properties of the Shewhart X ¯ chart integrated with run rules are investigated when errors exist in the measurement of quality characteristic. Two metrics, the average run length and 95% quantile of the run length, are adopted to evaluate the chart’s performance for different mean shifts and sample sizes. Numerous simulations are conducted, and the results indicate that the errors in the measurement significantly affect the performance of the run rule X ¯ chart, especially when the errors are large. To reduce this negative effect on the run rule X ¯ chart, measuring more times of each item in each subgroup and increasing the coefficient in the covariate error model are shown to be good choices for practitioners.