Exponential cumulative sums chart for detecting shifts in time-between-events. Issue 10 (19th May 2018) - Qu, Liang
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.