The effect of parameter estimation on X¯ control charts for the lognormal distribution

Abstract

Statistical process control (SPC) is a method of monitoring, controlling and improving a process through statistical analysis. In real applications, many industrial process data may follow a positively-skewed distribution such as the lognormal distribution. In this article, under lognormal process, we study the performance of three $\overline{X}$ control charts, Shewhart control chart, weighted variance control chart and weighted standard deviation control chart, based on the in-control expected average run length (AARL). The standard deviation of ARL (SDARL) metric is used to evaluate the performance for various amounts of phase I data. A formula to approximate the ARL by the normal approximation method is established in this study. The in-control and out-of-control performance of the three $\overline{X}$ control charts are compared based on the normal approximation and simulation.

Keywords:

• Average run length
• Average of ARL
• Lognormal distribution
• Standard deviation of ARL
• $\overline{\mathit{X}}$-chart

Acknowledgements

The author would like to thank the reviewers for their valuable suggestions and constructive comments.

Additional information

Funding

This study was supported by the Ministry of Science and Technology, MOST 108-2118-M-035-005-MY3, Taiwan.