The effect of measurement error on the performance of Mann‐Whitney and Signed‐Rank nonparametric control charts

Abstract

Mann-Whitney and Signed-Rank control charts are two well-known nonparametric charts used for controlling the center of the process when the distribution of the process parameter is unknown or nonnormal. Considering the effect of measurement error on the performance of control charts, the mentioned effect with additive model is investigated on Mann-Whitney and Signed-Rank charts. Furthermore, a comparison is made between the two charts and a Shewhart-typē X chart (as a parametric one) in the presence of the error. To do so, a simulation program is used and average run length (ARL) of the charts are calculated under three distributions. The results for all three distributions show that the existence of measurement error weakens the performances of both nonparametric charts and larger values of the variance of the error will increase the effect. A numerical example is also discussed to show the effect on the performance of the charts. Multiple measurements is used as a way to decrease the effect of measurement error. Knowing the fact that it requires extra time and money, it can be used in real cases depending on the financial limitations of the user.

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

“…Huwang and Hung [21] examined the effect of measurement error on the sample generalized variance chart and the likelihood ratio test chart for monitoring multivariate process variability. Nojavan et al [22] examined the effect of measurement error on Mann-Whitney and signed-rank charts for monitoring the process center when the distribution is unknown. While these methods discuss the effect of different measurement error models on control charts, they do not provide suitable strategies to correct for measurement error effects.…”