One‐Sided Combined Control Charts for Monitoring a Shifted Exponential Process in the Case of Individual Observations

ABSTRACT The shifted (or two‐parameter) exponential distribution is a well‐known flexible probability model for skewed data, such as failure times or survival times due to its two‐parameter representation. Control charts for monitoring a process that is modeled according to a shifted exponential distribution have been studied quite extensively in recent literature. However, all the available charts require the use of rational subgroups of size . In this work we focus on the case of individual observations (i.e., ) and propose the use of three one‐sided combined charts for monitoring this type of process. The proposed charts combine the structure of memory‐type charts with a Shewhart limit. Using Monte Carlo simulation, we evaluate the run length distribution of the proposed charts and suggest rules for their statistical design. The results of an extensive numerical study show that there is not a chart that outperforms uniformly all the others. To assist practitioners, we provide the best charts over a variety of different out‐of‐control situations. Finally, the implementation of the proposed combined charts in practice is illustrated via a real example about call durations of telemarketing promotions.