Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications
Year: 2025
Type: article
Abstract: In this paper, we conduct statistical inferences on the process capability index $S_{pmk}^{\prime }$ 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 $S_{pmk}^{\prime }$ is used to evaluate processes that deviate from a non-normal distribution. The maximum likelihood estimate for $S_{pmk}^{\prime}$ is obtained using the invariance property of the maximum likelihood estimator. Furthermore, point estimates for $S_{pmk}^{^{\prime}}$ 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 $S_{pmk}^{^{\prime}}$ process capability index to the generalized KM exponential distribution.
Authors: Kadir Karakaya, Şule Sağlam
Institution: Selçuk University
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4414437237