A mixed HWMA‐CUSUM mean chart with an application to manufacturing process

Transactions of the Institute of Measurement and Control

et al. 2020

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.

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Thanwane

Transactions of the Institute of Measurement and Control

et al. 2020

“…There are four different types of memory‐type control charts in the SPM literature and these are: (1) exponentially weighted moving average (EWMA) chart by Roberts, 2 (2) cumulative sum chart by Page, 3 (3) generally weighted moving average chart by Sheu and Lin, 4 and (4) homogeneously weighted moving average chart by Abbas 5 . For more detailed studies or literature reviews on the latter memory‐type schemes, see Hawkins and Olwell, 6 Ruggeri et al., 7 Mabude et al., 8 Nawaz and Han, 9 Abid et al., 10 Adegoke et al., 11 and Adeoti and Koleoso 12 . The focus of this paper is on improving the performance of the nonparametric EWMA‐type charts to monitor the process location, especially during start‐up period.…”

Section: Introductionmentioning

confidence: 99%

Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature

Letshedi

Quality & Reliability Eng

et al. 2021

The exponentially weighted moving average (EWMA) control chart is a memory‐type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small‐to‐moderate shifts. This paper proposes a new distribution‐free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank‐sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real‐life illustration is provided to show the application and implementation of the new chart.

“…So far in the SPM literature, there are ten publications discussing the HWMA-type monitoring schemes, see [7][8][9][10][11][12][13][14][15][16]. That is, Abbas [7] proposed a new HWMA ̅ scheme to monitor the process mean and derived its run-length properties.…”

Section: Introductionmentioning

confidence: 99%

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

Thanwane

Journal of Statistical Computation and Simulation

et al. 2020

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.