Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model

Lina Bian, Bo Peng and Yong Ye ()
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Lina Bian: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Bo Peng: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
Yong Ye: School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China

Mathematics, 2023, vol. 11, issue 21, 1-19

Abstract: A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored δ shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored δ shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N , based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N * by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model.

Keywords: reliability indices; generalized Pólya process; censored ? shock model; failure rate; optimal replacement policy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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