Point estimation of the process capability index S′pmk for the generalized KM exponential model with applications

In this paper, we conduct statistical inferences on the process capability index S′pmk for a lifetime distribution called the generalized KM exponential distribution. Some statistical properties of the distribution are reported, accompanied by figures that illustrate its shape characteristics based on the probability density function and the hazard rate function. The process capability index S′pmk is used to evaluate processes that deviate from a non-normal distribution. The maximum likelihood estimate for S′pmk is obtained using the invariance property of the maximum likelihood estimator. Furthermore, point estimates for S′pmk are derived based on least squares, weighted least squares, Anderson-Darling, and Cramér-von Mises estimators. Furthermore, two real data analyses are performed to assess the applicability of the S′pmk process capability index to the generalized KM exponential distribution.