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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 74 Issue: 3

Point estimation of the process capability index $ S_{pmk}^{\prime} $ for the generalized KM exponential model with applications

Kadir Karakaya(SELÇUK ÜNİVERSİTESİ, FEN FAKÜLTESİ)0000-0002-0781-3587
Şule Sağlam(SELCUK UNIVERSITY)0000-0002-1851-8217
Pages
—
Publication Date
2025-09-23
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⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Process capability index · lifetime distribution · maximum likelihood estimation

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.

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Cite This Article

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, Volume: 74 Issue: 3. https://doi.org/10.31801/cfsuasmas.1592434

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