Exponential cumulative sums chart for detecting shifts in time-between-events

Abstract

Time-between-events (TBE) charts use the time interval T between events to monitor process shifts (or failure rates λ). This paper presents a two-sided TBE cumulative sums (CUSUM) chart called a weighted CUSUM(WCUSUM)chart for detecting either a deterioration (decrease in T) or an improvement (increase in T) in the condition of a process. A new kind of WCUSUM chart that has an additional charting power parameter w is proposed here. A WCUSUM chart’s efficiency can be improved by using the parameter w, based on an estimated value of the mean shift. In addition, a methodology and optimal design are presented for minimising the average loss. Construction of the WCUSUM chart is illustrated by considering a random shift δ in λ (including both increasing and decreasing shifts) in the design.

Keywords:

• time-between-events
• CUSUM chart
• exponential of the sample mean shift
• increasing and decreasing shifts
• average loss

Acknowledgments

The authors would like to thank the Editor and the anonymous referees for their helpful and valuable comments and suggestions that have resulted in significant improvements in the quality of the article.