The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme with estimated parameters

Abstract

Classical monitoring schemes are typically designed under the assumption of known process parameters, perfect measurements and normality. In real-life applications, these assumptions are often violated. Thus, their Phase II performances are negatively affected by both measurement errors and parameter estimation. In this paper, the performance of the homogenously weighted moving average (HWMA) scheme is investigated under the assumption of unknown process parameters with and without measurement errors using the characteristics of the run-length distribution through intensive simulations. The negative effect of measurement errors is reduced using multiple measurements sampling strategy. The effects of the Phase I sample size on the Phase II performance as well as the robustness to non-normality of the HWMA scheme are also investigated. Moreover, it is found that the negative effect of the measurement errors is higher as the smoothing parameter increases and the larger the Phase I sample size, the smaller the effect of measurement errors. Moreover, the Phase II performance of the HWMA ̅ scheme is compared with the corresponding memory-type monitoring schemes under the effect of both parameter estimation and measurement errors. An illustrative example is given to demonstrate the implementation in real-life applications.

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

“…The HWMĀ * scheme under the negative effect of measurement errors in Case U were discussed in Thanwane et al 19 and its plotting statistic is given by…”

“…The HWMA scheme under the negative effect of measurement errors in Case U were discussed in Thanwane et al 19 and its plotting statistic is given by where is given in Equation (), is the mean of the previous t –1 sample means computed by …”

“…8 The HWMA scheme is a memory-type scheme that allocates a specific weight (equal to the smoothing parameter ) to the current sample and distributes equally or homogenously the remaining weights (ie, equal to 1 − ) to all the previous samples. The HWMA scheme is mostly considered for its effectiveness in monitoring small-to-moderate shifts in the process parameters; see also the following publications on different HWMA schemes: Adegoke et al, 9,10 Abbas et al, 11 Nawaz and Han, 12 Raza et al, 13 Adeoti and Koleoso, 14 Abid et al, 15,16 Dawod et al, 17 and Thanwane et al [18][19][20] The HWMA scheme has similar limitations as the CUSUM and EWMA schemes in that it can be less sensitive in spotting start-up problems (ie, the resistance of a scheme to detect OOC samples at the beginning of the monitoring process). It is therefore a reason why this paper seeks to incorporate fast initial response (FIR) features on the HWMA scheme to enhance its responsiveness to any significant shift at the initial start-up period.…”

“…Since measurements errors are unavoidable, they need to be taken into account when monitoring items with measurements. 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.…”

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart X ¯ Chart

“…For a full account of publications on measurement errors prior to 2017, readers are referred to Maleki et al [24]. For the most recent works on control charts with measurement errors, we suggest the research in Cheng and Wang [25]; Shongwe et al [26]; Nguyen et al [27]; Nguyen et al [28]; anwane et al [29]; anwane et al [30]; and so on. Even the above research works are on the control charts with measurement errors.…”