Inference on process capability index $$S_{pmk}$$ for a new lifetime distribution

In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index \(S_{pmk}\) is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the \(S_{pmk}\) is also studied. The asymptotic confidence interval is also constructed for \(S_{pmk}\). The simulation results indicate that estimators for both the unknown parameters of the new distribution and the \(S_{pmk}\) provide reasonable results. Some practical analyses are also performed on both the new distribution and the \(S_{pmk}\). The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for \(S_{pmk}\) illustrate that the new distribution can be utilized for process capability indices by quality controllers.