Monitoring Regularly Maintained Systems Based on the Renewal Process with Generalized Exponential Distribution of Time between Events

In the modern industrial age, regular system maintenance is an integral process because systems, both engineering and nonengineering, deteriorate over time. Statistical process monitoring techniques, especially control charts, are very helpful in monitoring the performance of such systems and consequently help in decision making on whether maintenance is advantageous or the system has reached a phase where no further maintenance is useful. The aim of this article is to introduce an approach that would integrate maintenance decisions with statistical quality monitoring techniques by assuming an exponentiated class of distributions of interarrival times of the renewal process. This article includes generalized exponential, generalized Rayleigh, and exponentiated Pareto distributions as special cases. An extensive simulation study to compute average run length and average length of inspection (or average time to signal) is conducted, and a comparison is given with approximated exponential control charts. The effect of cost for the regularly maintained generalized exponential systems is also discussed in this study. We focus on the generalized exponential distribution because of its practical relevance in reliability and closeness to Weibull distribution. Finally, an illustrative example is also a part of this article.