The effect of measurement errors on the performance of the Exponentially Weighted Moving Average control charts for the Ratio of Two Normally Distributed Variables

Abstract

Investigating the effect of measurement errors on the control chart monitoring the ratio of two normal random variables is an important task to facilitate the use of this kind of control chart in practice. Moreover, a deep insight into the problem can help practitioners to find a way to reduce unexpected impacts of measurement errors on the chart performance. This paper provides a study on the performance of the exponentially weighted moving average control chart monitoring the ratio in the presence of measurement errors. We extend the linear covariate error model applied in previous studies to a more general situation, which makes the study more realistic. The numerical results show that although the precision error and the accuracy error have negative influences on the proposed chart performance when these errors are not large these influences are not significant.

The performance of the hypergeometric np chart with estimated parameter

“…Over the years, and especially in recent times, numerous articles have been published on control charts to optimize process monitoring through various improvements, amendments, and adaptations to current practical needs, see e.g. Teoh et al [40], Mitra et al [31], Filho & Valk [18], Song et al [37,38], Nguyen et al [35], just to name a few relevant works.…”

Run sum ratio chart when measurement errors are present

“…The variable sampling intervals (VSI) EWMA and CUSUM schemes to monitor the ratio of two normal variables were suggested by Nguyen et al 11,12 Abubakar et al 13 propounded the run sum ratio scheme for two normal variables. Nguyen and Tran 14 considered two one-sided Shewhart charts to monitor the ratio of two normal variables when measurement errors are present, while Nguyen et al 15 evaluated the effects of measurement errors on the EWMA scheme to monitor the ratio of two normal variables. In another new development, the one-sided Shewhart charts for monitoring the ratio of two normal variables in short production runs were investigated by Tran et al 16 Numerous investigations concerning the effect of measurement errors on the run-length characteristics for univariate and multivariate schemes were suggested in the literature.…”

The use of fast initial response features on the homogeneously weighted moving average chart with estimated parameters under the effect of measurement errors

“…Note that the effect of measurement errors on the performance of HWMA scheme to monitor the process mean is discussed in Thanwane et al 18,19 for Cases K and U, respectively. For some early discussions on measurement errors in SPM context, see Linna and Woodall, 27 Maravelakis et al, 28 and Maravelakis 29 ; however, for some recent contributions, see Riaz et al, 30 Sabanho et al, 31,32 Zaidi et al, 33,34 Nguyen et al, 35 and Noor-ul-Amin et al 36 The objective of this paper is to incorporate FIR features in the time-varying control limits of the HWMA scheme to monitor the mean of processes with and without measurement errors so that its sensitivity in detecting start-up problems can be improved. In the review papers by Jensen et al, 37 Psarakis et al, 38 and Does et al, 4 it is stated that the estimation of the process parameters significantly degrades the performance of a monitoring scheme; thus, the investigation of the effect of parameter estimation on the performance of the HWMĀscheme for both a constant and linearly increasing measurement system error variances is conducted.…”

“…Note that the effect of measurement errors on the performance of HWMA scheme to monitor the process mean is discussed in Thanwane et al 18,19 for Cases K and U, respectively. For some early discussions on measurement errors in SPM context, see Linna and Woodall, 27 Maravelakis et al, 28 and Maravelakis 29 ; however, for some recent contributions, see Riaz et al, 30 Sabanho et al, 31,32 Zaidi et al, 33,34 Nguyen et al, 35 and Noor‐ul‐Amin et al 36 …”