Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications
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.
Keywords
References
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Details
Primary Language
English
Subjects
Statistical Quality Control, Statistical Theory, Applied Statistics
Journal Section
Research Article
Publication Date
September 23, 2025
Submission Date
November 27, 2024
Acceptance Date
April 24, 2025
Published in Issue
Year 2025 Volume: 74 Number: 3
APA
Karakaya, K., & Sağlam, Ş. (2025). Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(3), 478-491. https://doi.org/10.31801/cfsuasmas.1592434
AMA
1.Karakaya K, Sağlam Ş. Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74(3):478-491. doi:10.31801/cfsuasmas.1592434
Chicago
Karakaya, Kadir, and Şule Sağlam. 2025. “Point Estimation of the Process Capability Index $ S_{pmk}^{\prime} $ for the Generalized KM Exponential Model With Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 (3): 478-91. https://doi.org/10.31801/cfsuasmas.1592434.
EndNote
Karakaya K, Sağlam Ş (September 1, 2025) Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 3 478–491.
IEEE
[1]K. Karakaya and Ş. Sağlam, “Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 3, pp. 478–491, Sept. 2025, doi: 10.31801/cfsuasmas.1592434.
ISNAD
Karakaya, Kadir - Sağlam, Şule. “Point Estimation of the Process Capability Index $ S_{pmk}^{\prime} $ for the Generalized KM Exponential Model With Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/3 (September 1, 2025): 478-491. https://doi.org/10.31801/cfsuasmas.1592434.
JAMA
1.Karakaya K, Sağlam Ş. Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74:478–491.
MLA
Karakaya, Kadir, and Şule Sağlam. “Point Estimation of the Process Capability Index $ S_{pmk}^{\prime} $ for the Generalized KM Exponential Model With Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 3, Sept. 2025, pp. 478-91, doi:10.31801/cfsuasmas.1592434.
Vancouver
1.Kadir Karakaya, Şule Sağlam. Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025 Sep. 1;74(3):478-91. doi:10.31801/cfsuasmas.1592434
