A new EWMA chart for simultaneously monitoring the parameters of a shifted exponential distribution

Abstract

In various scenarios where products and services are accompanied by warranties to ensure their reliability over a specified time, the two-parameter (shifted) exponential distribution serves as a fundamental model for time-to-event data. In modern production process, the products often come with warranties, and their quality can be manifested by the changes in the scale and origin parameters of a shifted exponential (SE) distribution. This paper introduces the Max-EWMA chart, employing maximum likelihood estimators and exponentially weighted moving average (EWMA) statistics, to jointly monitor SE distribution parameters. Additionally, we extend two additional charts, namely the Max-DEWMA and Max-TEWMA charts to enhance early-stage shift detection. Performance evaluations under zero-state and steady-state conditions compare these charts with the existing Max-CUSUM chart in terms of expected value and standard deviation of the run length (RL) distribution. Our findings reveal that among the Max-EWMA schemes, the Max-EWMA SE chart outperforms the others in terms of steady-state performance, while the Max-TEWMA chart surpasses the Max-EWMA and Max-DEWMA SE charts in respect to zero-state performance. Moreover, the proposed Max-EWMA schemes demonstrate advantages over Max-CUSUM, especially for small to moderate smoothing constants. We also provide an illustrative example to demonstrate the implementation of the proposed schemes.

Keywords:

• Simultaneous monitoring
• TEWMA
• shifted exponential distribution
• Monte Carlo simulation

Acknowledgments

The authors would like to thank the editor and two anonymous reviewers for their detailed comments that have improved the paper. The second author's work was supported by the Banaras Hindu University, India, under the IoE Scheme (Grant Number 20640-6031).

Disclosure statement

No potential conflict of interest was reported by the author(s).