Open Access

ARTICLE

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

Azam Zaka¹, Ahmad Saeed Akhter¹, Riffat Jabeen^2,*, Aamir Sanaullah²
1 College of Statistical & Actuarial Sciences, University of the Punjab, Lahore, 54000, Pakistan
2 COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan
* Corresponding Author: Riffat Jabeen. Email:
(This article belongs to this Special Issue: Intelligent Computing for Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 127(3), 1201-1223. https://doi.org/10.32604/cmes.2021.014477

Received 30 September 2020; Accepted 20 February 2021; Issue published 24 May 2021

Abstract

In practice, the control charts for monitoring of process mean are based on the normality assumption. But the performance of the control charts is seriously affected if the process of quality characteristics departs from normality. For such situations, we have modified the already existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA) control chart and hybrid exponentially weighted moving average (HEWMA) control chart by assuming that the distribution of underlying process follows Power function distribution (PFD). By considering the situation that the parameters of PFD are unknown, we estimate them by using three classical estimation methods, i.e., percentile estimator (P.E), maximum likelihood estimator (MLE) and modified maximum likelihood estimator (MMLE). We construct Shewhart, EWMA and HEWMA control charts based on P.E, MLE and MMLE. We have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.

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Keywords

Average run length; control chart; percentile estimator; power function distribution

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