Design of attribute EWMA type control charts with reliable run length performance

Abstract

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent sample sizes, Shewhart type attribute control charts are known to be less efficient than their measurement counterparts (like the $\overline{X}$ chart) and, for this reason, practitioners often compensate it by supplementing them with an EWMA (Exponentially Weighted Moving Average) scheme. However, because of the discrete nature of count data, it is unfortunately impossible to compute exactly and accurately (by means of Markov chain of integral equation methods) the run length (RL) properties, such as its mean (ARL) and its standard deviation (SDRL) of these EWMA attribute control charts and, consequently, it is impossible to efficiently design them in order to minimize some out-of-control characteristics. For this reason, we propose in this paper a dedicated approach called “continuousify” method which, coupled with a classical Markov chain technique, allows to compute the RL properties of any EWMA attribute control chart in a reliable way. A numerical comparison shows that the RL properties obtained by using the proposed “continuousify” approach are very much alike to the ones calculated via simulation and without the “continuousify” approach. Illustrative examples are also provided to show how the proposed method can be implemented in practice.

Keywords:

• Attribute EWMA chart
• Average run length
• Binomial
• Markov chain
• Normal mixture
• Poisson
• Statistical process monitoring

Additional information

Funding

This study was funded by National Natural Science Foundation of China [Grant No.11701437].