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Reliability estimation of s-out-of-k system with Kumaraswamy distribution based on partially constant stress accelerated life tests

Dongzhu Lamu ,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China

Rongfang Yan

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China;b Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou, People's Republic of China

Pages | Received 28 Sep. 2023, Accepted 09 May. 2024, Published online: 05 Jun. 2024,
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In reliability theory, the reliability inference for s-out-of-k systems holds significant importance. In this paper, we explore the estimation of reliability for s-out-of-k systems based on partially constant stress accelerated life tests. Assume that the latent failure times of the components follow the Kumaraswamy distribution. Maximum likelihood estimates for the unknown parameters are established, and their uniqueness is demonstrated. In addition, confidence intervals for the unknown parameters are constructed using the covariance matrix. Confidence intervals for the reliability functions are determined by the Delta method, while Bootstrap intervals are provided for comparison purposes. Subsequently, Bayesian point and interval estimates based on MCMC techniques considering different loss functions are discussed. Lastly, we conduct an extensive simulation study and analyse one real data set, which reveals that the Bayesian approach yields the best results.


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To cite this article: Dongzhu Lamu & Rongfang Yan (05 Jun 2024): Reliability estimation of sout-of-k system with Kumaraswamy distribution based on partially constant stress accelerated life tests, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2024.2359826

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