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

Abstract

Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA [Formula: see text] scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA [Formula: see text] scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) [Formula: see text] schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.

The impracticality of homogeneously weighted moving average and progressive mean control chart approaches

“…Since the first paper on HWMA by Abbas, 22 there has been a rapid growth in research to investigate other versions of the HWMA method. One can refer to Adegoke et al 60 (multivariate HWMA), Adeoti and Koleoso 61 (HWMA for the process mean), Alevizakos et al 62 (double HWMA, or DWMA), Abid et al 63 (DWMA control chart for the process mean), Raza et al 64 (nonparametric HWMA), Riaz et al 65 (nonparametric DWMA), Abid et al 66 (mixed HWMA-CUSUM control chart), Abid et al 67 (mixed HWMA-CUSUM control chart for the process mean), Thanwane et al [68][69][70][71] (the effect of measurement error on HWMA), and Riaz et al 72 (triple HWMA or TWMA).…”

New extended distribution-free homogenously weighted monitoring schemes for monitoring abrupt shifts in the location parameter

“…The charting statistic of the HWMA scheme assigns a weight λ (i.e., a smoothing parameter, where 0 < λ < 1) to the current sample and a weight (1 − λ) is homogeneously (or equally) distributed to all the previous samples. Some recent publications on HWMA schemes can be found in [15][16][17][18][19][20][21].…”

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

“…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.…”