Control charts for the shape parameter of reflected power function distribution under classical estimators

Zaka, Azam; Akhter, Ahmad Saeed; Jabeen, Riffat; Sanaullah, Aamir

doi:10.1002/qre.2866

Cited by 7 publications

(7 citation statements)

References 19 publications

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“…And λ is a smoothing constant. We refer the Zaka et al [16] to get the details on generalizing EWMA Statistics,…”

Section: Ewma Control Chart Using Pementioning

confidence: 99%

Error Detection and Pattern Prediction Through Phase II Process Monitoring

Zaka¹,

Jabeen²,

Khan³

2022

Computers, Materials &Amp; Continua

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The continuous monitoring of the machine is beneficial in improving its process reliability through reflected power function distribution. It is substantial for identifying and removing errors at the early stages of production that ultimately benefit the firms in cost-saving and quality improvement. The current study introduces control charts that help the manufacturing concerns to keep the production process in control. It presents an exponentially weighted moving average and extended exponentially weighted moving average and then compared their performance. The percentiles estimator and the modified maximum likelihood estimator are used to constructing the control charts. The findings suggest that an extended exponentially weighted moving average control chart based on the percentiles estimator performs better than exponentially weighted moving average control charts based on the percentiles estimator and modified maximum likelihood estimator. Further, these results will help the firms in the early detection of errors that enhance the process reliability of the telecommunications and financing industry.

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“…And λ is a smoothing constant. We refer the Zaka et al [16] to get the details on generalizing EWMA Statistics,…”

Section: Ewma Control Chart Using Pementioning

confidence: 99%

Error Detection and Pattern Prediction Through Phase II Process Monitoring

Zaka¹,

Jabeen²,

Khan³

2022

Computers, Materials &Amp; Continua

Self Cite

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“…The literature provides some studies on the monitoring of shape parameter under classical method in manufacturing industry. Such as [ 13 ] developed and compared the Shewhart and EWMA charts. The memory-less and memory-type charts were constructed for the weighted power function distribution (WPFD) by [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process

Javed,

Abbas,

Abbas

2024

PLoS ONE

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Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

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“…In literature, we see some control charts constructed based on assumption of normality such as by Page, 1 Roberts, 2 Shamma and Shamma, 3 Haq, 4 Abbas et al, 5 Zwetsloot et al, 6 Sanusi et al, 7 Ajadi and Riaz, 8 Haq and Munir, 9 Li et al, 10 Nguyen et al, 11 Hossain et al, 12 Abu-Shawiesh and Saeed. 13 Some literature on control charts when the assumption of normality is not fulfilled such as Noorossana et al, 14 Lin et al, 15 Hossain et al, 16 Erto et al, 17 Karagoz, 18 Liang et al, 19 Ahmed et al, 20 Khan et al, 21 Saeed and Abu-Shawiesh, 22 and Zaka et al [23][24][25] proposed the control charts for the shape parameter of reflected power, power and weighted power function distributions under classical estimators, Jabeen and Zaka 26 discussed the modified EWMA control charts for the shape parameter of weighted power function distribution, Zaka et al 27 proposed the attribute control charts of the modified power function distribution and Zaka et al 28 discussed the modified EEWMA control charts for monitoring the shape parameter of reflected power function distribution.…”

Section: Introductionmentioning

confidence: 99%

Classical estimator based modified control charts for phase‐II monitoring in real life

Jabeen

Zaka

Khan

2022

Quality & Reliability Eng

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We discuss some classical estimator based modified control charts for phase‐II monitoring in real life. The modification of some existing control charts such as exponentially weighted moving average (EWMA) and extended exponentially weighted moving average (EEWMA) is proposed and compared for the situation when the assumption of normality is not fulfilled due to some unavoidable factors. We first estimate the shape parameter of power function distribution using percentile estimator and maximum likelihood estimator and then propose EWMA and EEWMA based on these estimators. Monte Carlo simulation studies are used to compare the introduced control charts. The findings will be helpful for the practitioners and statisticians to devise the real‐life solution to the problems.

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Control charts for the shape parameter of reflected power function distribution under classical estimators

Cited by 7 publications

References 19 publications

Error Detection and Pattern Prediction Through Phase II Process Monitoring

Error Detection and Pattern Prediction Through Phase II Process Monitoring

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process

Classical estimator based modified control charts for phase‐II monitoring in real life

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