Max-EWMA chart for time and magnitude monitoring using generalized exponential distribution

Abstract

Joint monitoring of time and magnitude is an important issue in many industrial and non-industrial fields and several proposals exist in the literature. The aim of this article is to propose a new maximum exponentially weighted moving average (Max-EWMA) chart assuming generalized exponential distribution for time as well as magnitude. As the test-statistic of Max-EWMA chart consists of two EWMA statistics, it is easy to identify the out-of-control signal raised by the chart. The performance of the chart is evaluated using different run length characteristics including, average run length (ARL), standard deviation of run length (SDRL), and quantiles of the run length distribution. Besides extensive simulation studies, a real data set is also used to show the practicality of the proposed chart. The results show that the proposed chart is efficient in detecting different size of small to moderate shifts.

Keywords:

• Average run length
• Generalized exponential distribution
• Max EWMA chart
• Time and magnitude monitoring

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62P30

Acknowledgments

The authors would like to thanks the anonymous reviewers for their comments and suggestions to improve the quality of the work.