Control Charts for Simultaneous Monitoring of Parameters of a Shifted Exponential Distribution

Since their introduction in the 1920s, control charts have played a key role in process monitoring and control in a variety of areas, from manufacturing to healthcare. Many of these charts are designed to monitor a single process parameter, such as the mean or the variance, of a normally distributed process, although recently, a number of charts have been developed for jointly monitoring the mean and variance. In practice, however, there are processes that follow multi-parameter nonnormal distributions, but the joint monitoring of parameters of nonnormal distributions remains largely unaddressed in the literature. This paper proposes several control charts and monitoring schemes for the origin and the scale parameters of a process that follows the two-parameter (or the shifted) exponential distribution. This distribution arises in various applications in practice, particularly with time to an event data, such as in reliability studies, and has been studied extensively in the statistical testing and estimation literature. Exact derivations and computer simulations are used to study performance properties of the proposed charts. An illustrative example is provided along with a summary and some conclusions.