A Power Generalized DUS–Kumaraswamy Distribution with Applications to Parallel System Reliability

Ann  Sania; Vellamattathil  Mani Chacko

Authors

Ann Sania Department of Statistics, St. Thomas College (Autonomous), Affiliated to University of Calicut, Thrissur, Kerala, India
Vellamattathil Mani Chacko Department of Statistics, St. Thomas College (Autonomous), Affiliated to University of Calicut, Thrissur, Kerala, India

Keywords:

Kumaraswamy distribution, invariance, Bayesian estimation, MPS estimation, multicomponent stress-strength model

Abstract

In reliability engineering, modeling parallel systems requires lifetime distributions that combine hazard rate flexibility with structural tractability for reliability analysis. In this article, we introduce a new lifetime distribution obtained by applying the Power Generalized DUS transformation to the Kumaraswamy distribution, referred to as the PGDUS-Kumaraswamy (PGDUS-K) distribution. The proposed model provides enhanced flexibility for modeling parallel systems and accommodates various monotone and non-monotone hazard rate shapes. Several statistical properties of the PGDUS-K distribution are derived, including moments, entropy measures, quantile function, and stress-strength reliability expressions for single- and multi-component systems. The model is invariant and closed under exponentiation, and preserves its form under maxima, making it suitable for parallel systems. Parameter estimation is carried out using method of maximum likelihood, method of maximum product of spacings, method of moments, method of least squares, and Bayesian approaches. A simulation study is conducted to evaluate the performance of the estimators. The practical utility of the model is illustrated through real data analysis, where it demonstrates superior goodness-of-fit compared with competing models based on standard model selection criteria. In addition, the derived stress–strength expressions enable direct reliability computation, demonstrating practical applicability.

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