Adjustment of Measurement Error Effects on Dispersion Control Chart with Distribution-Free Quality Variable

In industrial processes, control charts are useful tools to monitor the quality of products and detect possibly out-of-control processes. While many types of control charts have been available for data analysts, they were developed by assuming that the variables are precisely measured. In applications, however, measurement error is ubiquitous when data are falsely recorded by investigators or imprecisely collected by unadjusted machines. Even though the impacts of measurement error for different types of control charts have been explored, error-corrected control charts are still unavailable. In this study, we propose a new dispersion control chart with error correction to fill out this research gap. Our key idea is to convert the observed distribution-free process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic. Finally, we develop an exponentially weight-moving average dispersion control chart with measurement error correction based on the corrected sign statistic. The proposed error-corrected dispersion control chart not only eliminates measurement error effects, but also provides more reliable control limits for monitoring process dispersion. Throughout the numerical examination, we find that the proposed error-corrected dispersion control chart is effective in handling moderate and large levels of measurement error and shows good out-of-control detection performance. Finally, the proposed error-corrected dispersion control chart is implemented in the semiconductor data.