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

Abstract

Fast initial response (FIR) features are generally used to improve the sensitivity of memory-type control charts by shrinking time-varying control limits in the earlier stage of the monitoring regime. This paper incorporates FIR features to increase the sensitivity of the homogeneously weighted moving average (HWMA) monitoring schemes with and without measurement errors under constant as well as linearly increasing variance scenarios. The robustness and the performance of the HWMA monitoring schemes are investigated in terms of numerous run-length properties assuming that the underlying process parameters are known and unknown. It is found that the FIR features improves the performance of the HWMA monitoring scheme as compared to the standard no FIR feature HWMA scheme, and at the same time, it is observed that the simultaneous use of a recently proposed FIR feature and multiple measurements significantly reduces the negative effect of measurement errors. An illustrative example on the volume of milk in bottles is used to demonstrate a real-life application.

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).…”

Homogeneously Weighted Moving Average Control Charts: Overview, Controversies, and New Directions

“…When the smoothing parameters λ 1 and λ 2 of the HHWMA chart are equal, the HHWMA chart reduces to the DHWMA chart. For more details on the properties summarised in Table 1, readers are referred to [3,22,25,[35][36][37][38][39][40].…”

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].…”