Open Access

ARTICLE

Control Charts for the Shape Parameter of Skewed Distribution

Azam Zaka¹, Riffat Jabeen^2,*, Kanwal Iqbal Khan³

1 Department of Statistics, Government Graduate College of Science, Wahdat Road, Lahore, Pakistan
2 Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
3 Institute of Business & Management, University of Engineering and Technology, Lahore, Pakistan

* Corresponding Author: Riffat Jabeen. Email:

Intelligent Automation & Soft Computing 2021, 30(3), 1007-1018. https://doi.org/10.32604/iasc.2021.016491

Received 03 January 2021; Accepted 14 March 2021; Issue published 20 August 2021

Abstract

The weighted distributions are useful when the sampling is done using an unequal probability of the sampling units. The Weighted Power function distribution (WPFD) has applications in the fields of reliability engineering, management sciences and survival analysis. WPFD is more beneficial in Statistical process control (SPC). SPC is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help to monitor process behaviour, discover problems in internal systems, and find solutions for production issues. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows WPFD, we develop control charts to keep the process in control. A memory-based control chart like an exponentially weighted moving average (EWMA) control chart and an extended exponentially weighted moving average (EEWMA) control chart are discussed and compared each other. The proposal of these control charts is based on the modified maximum likelihood estimator (MMLE) under the shape parameter of WPFD. We have presented Monte Carlo simulation technique and a real-life application to compare the proposed control charts. This study shows that an EEWMA control chart based on MMLE performs better than EWMA control chart, when the underlying distribution of the errors in process monitoring follows WPFD. These findings can be useful for researchers and practitioners in dealing with production errors and optimizing the output.

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