The effect of gauge measurement errors on double sampling X¯ control chart

Abstract

In recent years, the impact of measurement errors on the performance of various control charts have been well evaluated. However, as far as we know, the multiple sampling control charts in the literature have been proposed based on the assumption that the measurements are precise. In this paper, we investigate the effect of measurement errors with both constant and linearly increasing variance on the performance of double sampling (DS)-$\overline{X}$ chart. We study the capability of multiple measurements procedure to reduce the undesired effect of imprecise measurements on detection capability of DS-$\overline{X}$ chart. Using simulation experiments, we compare the performance of DS-$\overline{X}$ and classical $\overline{X}$ charts in terms of average run length (ARL) and standard deviation of run length (SDRL) metrics. The results show that the measurement errors negatively affect the performance of both DS-$\overline{X}$ and classical $\overline{X}$ charts. The comparison results also confirm that under measurement errors, the DS-$\overline{X}$ control chart outperforms the classical $\overline{X}$ chart in all out-of-control scenarios. Moreover, the results indicate that taking several measurements on each item can effectively reduce the undesired impact of error on chart’s performance. Finally, the undesired impact of measurement errors on detection capability of DS-$\overline{X}$ control chart is illustrated using a real-life example.

Keywords:

• Average run length
• double sampling $\overline{\mathit{X}}$ control chart
• measurement errors
• additive covariate model
• multiple measurements