A variable parameters multivariate control chart for simultaneous monitoring of the process mean and variability with measurement errors

Abstract

Evaluating the effect of measurement errors on either adaptive or simultaneous control charts has been a topic of interest for the researchers in the recent years. Nevertheless, the effect of measurement errors on both adaptive and simultaneous monitoring control charts has not been considered yet. In this paper, through extensive numerical studies, we evaluate the effect of measurement errors on an adaptive (variable parameters) simultaneous multivariate control chart for the mean vector and the variancecovariance matrix of p quality characteristics assumed to follow a multivariate normal distribution. In order to do so, (a) we use eight performance measures computed using a Markov chain model, (b) we consider the effects of multiple measurements as well as the error model's parameters, and (c) we also consider the overall performance of this adaptive simultaneous chart including the chart parameters values optimization, which have never been considered so far for this scheme. At last, a real case is presented in order to illustrate the proposed scheme. K E Y W O R D S

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 …”

Max-Half-Mchart: A Simultaneous Control Chart Using a Half-Normal Distribution for Subgroup Observations

“…Then, Thaga and Gabaitiri [14] extended The Bivariate Max-Chart [13] to the Maximum Multivariate chart (Max-Mchart) combined the Hotelling 2 and GV statistics using the normal standard distribution. Sabahno et al [15] expanded Max-Mchart using the gamma distribution in GV for monitoring process variability. Max-Mchart for individual observation was…”

Monitoring multivariate coefficient of variation with upward Shewhart and EWMA charts in the presence of measurement errors using the linear covariate error model

“…Sabahno et al 16 examined the effect of measurement errors on the performance of the VSI Hotelling's T 2 chart. Additionally, Sabahno et al 17 investigated the performance of VSS Hotelling's T 2 chart in the presence of measurement errors, while Sabahno et al 18 presented the variable parameters multivariate chart for monitoring the multivariate process mean and variance when measurement errors are present. Subsequently, Ayyoub et al 19 studied the effect of a false assumption of no measurement error on two one‐sided MCV charts with measurement errors.…”