A Max-type Run Sum Chart for Monitoring a Shifted Exponential Process

The shifted (or two-parameter) exponential distribution is a probability model that is widely used in many practical applications to model time-to-event data. In reliability analysis it has been frequently used for modeling the lifetime of products with a warranty period. In this paper, we propose and study the properties of a run sum chart for monitoring shifted exponential lifetimes in order to detect a change in either or in both process parameters. Using the Markov chain method, we evaluate several performance measures, based on the run length distribution of the proposed chart, and investigate its performance for increasing and/or decreasing shifts in process parameters. The results of an extensive numerical study show that a properly designed run sum chart has an improved detection ability compared to that of a Shewhart-type Max chart for shifted exponential distribution. In addition, the proposed chart can be considered as a viable alternative to the CUSUM-type Max chart for shifted exponential distribution, since for a large number of out-of-control situations it requires approximately the same, if not less, time to detect them. Finally, for supporting the use of the proposed run sum chart in practice, we provide guidelines and empirical rules for selecting the values of its parameters, along with an illustrative numerical example.