EWMA Control Chart Performance with Estimated Parameters under Non-normality

• Published in: Quality and reliability engineering international Vol. 32; no. 5; pp. 1637 - 1654
• Main Authors: Noorossana, R., Fathizadan, S., Nayebpour, M. R.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.07.2016; Wiley Subscription Services, Inc
• Subjects: average run length; Control charts; exponentially weighted moving average; Markov chain; Mathematical models; non-normality; Parameter estimation; Performance evaluation; Process parameters; Robustness; Standard deviation; standard deviation of run length; Symmetry
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.1896

Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non‐normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non‐normality using skewed and heavy‐tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non‐normal observations. Copyright © 2015 John Wiley & Sons, Ltd.