Parameter Estimation Effect of the Homogeneously Weighted Moving Average Chart to Monitor the Mean of Autocorrelated Observations With Measurement Errors

There is growing literature on new versions of “memory‐type” control charts, where deceptively good zero‐state average run‐length (ARL) performance is misleading. Using steady‐state run‐length analysis in combination with the conditional expected delay (CED) metric, we show that the increasingly discussed progressive mean (PM) and homogeneously weighted moving average (HWMA) control charts should not be used in practice. Previously reported performance of methods based on these two approaches is misleading, as we found that performance is good only when a process change occurs at the very start of monitoring. Traditional alternatives, such as exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, not only have more consistent detection behavior over a range of different change points, they can also lead to better out‐of‐control zero‐state ARL performance when properly designed.

Section: Other Hwma Researchmentioning

confidence: 99%

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

Knoth

Tercero-Gómez

Khakifirooz

et al. 2021

“…Subsequently, Abid et al 34 improved the work of Abbas 33 work by introducing an enhanced double HWMA (DHWMA) control chart. For more detailed work, see Abid et al, 35 Adeoti and Koleoso, 36 Riaz et al, 37 and Thanwane et al 38 and references therein.…”

Section: Introductionmentioning

confidence: 99%

An enhanced double homogeneously weighted moving average control chart to monitor process location with application in automobile field

Anwar

Aslam

Zaman

et al. 2021

Self Cite

The memory control charts, including cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts, are widely used to monitor small-to-moderate shifts in the process location and/or dispersion. The homogenously weighted moving average (HWMA) control chart is the advanced form of the EWMA control chart to monitor process location shifts. Besides, the auxiliary information-based memory control charts efficiently monitor process location shifts. The objective of this study is to propose an auxiliary information based double HWMA, symbolized as DHWMA AIB control chart to further enhance the monitoring of process location shifts. The DHWMA AIB control chart is modeled by mixing the auxiliary information-based HWMA plotting statistic features into the other HWMA control chart. For numerical results, Monte Carlo simulations are used as a computational technique. Famous performance measures including average run length (ARL), extra quadratic loss, relative ARL, and performance comparison index are used to compare the performance of proposed DHWMA AIB control chart against other control charts including classical CUSUM and EWMA, mixed EWMA-CUSUM, auxiliary information based EWMA (EWMA AIB ), HWMA, auxiliary information based HWMA (HWMA AIB ), and double HWMA control charts. The comparisons revealed that the proposed control chart outperformed other control charts, especially for small-to-moderate process location shifts. An automobile braking system application is also provided for users and practitioners to demonstrate the importance of the proposed study from a practical perspective.

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Thanwane

Malela‐Majika

Aslam

et al. 2021

Self Cite

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.