A balanced two-sided CUSUM chart for monitoring time between events

The time-between-event (TBE) charts are used to monitor the failure rate λ by examining the time interval T between events. This article proposes a two-sided CUSUM chart (the balanced two-sided CUSUM chart) for detecting both increasing and decreasing shifts in λ. The performance studies show that the balanced CUSUM chart can significantly improve the overall performance across the entire process shift range. On average, this chart is more effective than the conventional two-sided CUSUM chart by nearly 20%. Meanwhile, the proposed chart is relatively easy to be designed and does not increase the difficulty of implementation. An asymmetrical loss function is also proposed as the objective function for the design of the balanced CUSUM chart. It takes into consideration of the asymmetry of the probability distribution of T and the different impacts of the increasing and decreasing shifts in λ. [Received 31 October 2011; Revised 14 February 2013; Revised 30 July 2013; Accepted 01 August 2013[