Median control charts for monitoring asymmetric quality characteristics double bounded

• Published in: Quality and reliability engineering international Vol. 36; no. 7; pp. 2285 - 2308
• Main Authors: Lima‐Filho, Luiz M. A., Bourguignon, Marcelo, Ho, Linda L., Fernandes, Fidel Henrique
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01-11-2020
• Subjects: average run length; Control charts; Distribution functions; double‐bounded processes; Kumaraswamy distribution; Monitoring; Parameters; Probability density functions; Probability distribution functions; reparameterization; Skewed distributions; unit‐Weibull distribution
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2696

In many practical situations, the quality characteristics of interest assume values in the range (0,1), like rates and proportions (but they are not results from Bernoulli experiments). Most control charts built for these quality characteristics rely on monitoring parameters of their probability distribution functions or on their averages after some reparameterization of their density probability function. However, for highly asymmetric distributions, the median is a more appropriate location parameter than the average. In this paper, we propose Shewhart‐type control charts for monitoring the median of observations taken from quality characteristics double bounded after reparameterization of two probability density functions: Kumaraswamy and unit Weibull. The performance of the control charts is evaluated and compared in terms of run length (RL) analysis considering three estimators for the median. Finally, we also carry out two applications to demonstrate the applicability of these control charts.