Reliability analysis for independent Nadarajah–Haghighi competing risks model employing improved adaptive progressively censored data

Refah Alotaibi; Mazen Nassar; Ahmed Elshahhat; Refah Alotaibi; Mazen Nassar; Ahmed Elshahhat

doi:10.3934/math.2025679

AIMS Mathematics

2025, Volume 10, Issue 7: 15131-15164. doi: 10.3934/math.2025679

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Reliability analysis for independent Nadarajah–Haghighi competing risks model employing improved adaptive progressively censored data

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3.
Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, Egypt
4.
Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Received: 06 May 2025 Revised: 25 June 2025 Accepted: 26 June 2025 Published: 01 July 2025
MSC : 62F10, 62F15, 62N01, 62N05

The use of competing risk frameworks for the analysis of reliability/survival data has gained popularity in recent years, primarily because traditional techniques are inadequate for effectively analyzing such data. In this study, we examined the independent competing risks model with lifetimes of units distributed according to the Nadarajah–Haghighi distribution. Our focus was on estimating the unknown parameters, as well as the reliability and failure rate functions, using both frequentist and Bayesian estimation methods under an improved adaptive progressive Type-Ⅱ censoring mechanism. The frequentist estimation involved deriving point estimators and approximate confidence intervals using the asymptotic properties of classical estimators. Bayes estimators were obtained through symmetric squared loss and the Metropolis-Hastings algorithm, which generated samples from the joint posterior distribution. Additionally, the highest posterior density credible intervals were calculated. Given the complex nature of the acquired estimators, we conducted a comprehensive simulation study to numerically compare the performance of the proposed estimates across various experimental scenarios. To empirically validate the proposed inferential framework, we analyzed two real-world competing risk datasets, highlighting the effectiveness of the applied techniques in reliability data analysis.
- Nadarajah–Haghighi,
- survival analysis competing risks,
- improved adaptive progressive censoring,
- Bayesian,
- electrical appliances,
- multiple myeloma
Citation: Refah Alotaibi, Mazen Nassar, Ahmed Elshahhat. Reliability analysis for independent Nadarajah–Haghighi competing risks model employing improved adaptive progressively censored data[J]. AIMS Mathematics, 2025, 10(7): 15131-15164. doi: 10.3934/math.2025679

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Abstract

The use of competing risk frameworks for the analysis of reliability/survival data has gained popularity in recent years, primarily because traditional techniques are inadequate for effectively analyzing such data. In this study, we examined the independent competing risks model with lifetimes of units distributed according to the Nadarajah–Haghighi distribution. Our focus was on estimating the unknown parameters, as well as the reliability and failure rate functions, using both frequentist and Bayesian estimation methods under an improved adaptive progressive Type-Ⅱ censoring mechanism. The frequentist estimation involved deriving point estimators and approximate confidence intervals using the asymptotic properties of classical estimators. Bayes estimators were obtained through symmetric squared loss and the Metropolis-Hastings algorithm, which generated samples from the joint posterior distribution. Additionally, the highest posterior density credible intervals were calculated. Given the complex nature of the acquired estimators, we conducted a comprehensive simulation study to numerically compare the performance of the proposed estimates across various experimental scenarios. To empirically validate the proposed inferential framework, we analyzed two real-world competing risk datasets, highlighting the effectiveness of the applied techniques in reliability data analysis.

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