Failure rate monitoring in generalized gamma-distributed process

Advancement in technology brings a revolutionary change in the quality of the final product or items. Most of the manufacturing processes produce a large number of conforming items along with a few non-conforming items. For real-time monitoring of these highly efficient processes, monitoring of time-between-events is a well-known approach adopted in the literature of statistical process control. Usually, it is assumed that the time-between-events follows an exponential or gamma distribution. However, the generalized gamma distribution is the most popular choice for modelling skewed data. In this article, we consider a two-sided monitoring scheme based on the generalized gamma distribution. Two-sided monitoring schemes for skewed distributions often encounter bias in its run length properties. Therefore, we address this problem with modified control limits in a more general distributional setup. A Monte Carlo simulation-based study is designed, and results showed encouraging performance properties. A couple of practical applications in connection to monitoring renewable energy and coal mine explosions have been discussed.