Research Article
The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data
Faisal Muhammad Amiru*,
Umar Usman,
Suleiman Shamsuddeen,
Umar Muhammad Adamu,
Badamasi Abba
Issue:
Volume 11, Issue 1, March 2025
Pages:
1-10
Received:
30 December 2024
Accepted:
16 January 2025
Published:
11 February 2025
DOI:
10.11648/j.ijsda.20251101.11
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Views:
Abstract: To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address this, the Chen distribution, which accommodates increasing or bathtub-shaped failure rates, has been proposed. Yet, this model lacks a scale parameter. This article presents a new four parameter lifetime distribution with bathtub-shaped failure rate called Additive Dhillon-Chen (ADC) distribution. We applied the additive methodology to establish the model, for which the Dhillon distribution was considered as baseline distribution. Some statistical properties such as quartile function, mode, moment and moment generating function, order statistics and asymptotic behavior of the distribution are studied. Parameters of the distribution are estimated using the maximum likelihood estimation method. The ADC distribution is applied to two lifetime dataset and compared with an existing distribution in the literature. Model selection was carried out based on Log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected Akaike Information Criterion (AICc). The results, based on parameter estimation from real-life data, demonstrate that the ADC distribution fits the data well and offers a valuable alternative for modeling datasets with non-monotonic behavior.
Abstract: To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address ...
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