The Chen–Perks Distribution: Properties and Reliability Applications

Luis Carlos Méndez-González (), Luis Alberto Rodríguez-Picón, Manuel Iván Rodríguez Borbón () and Hansuk Sohn
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Luis Carlos Méndez-González: Department of Industrial Engineering and Manufacturing, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Mexico
Luis Alberto Rodríguez-Picón: Department of Industrial Engineering and Manufacturing, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Mexico
Manuel Iván Rodríguez Borbón: Department of Industrial Engineering, New Mexico State University, Las Cruces, NM 88003, USA
Hansuk Sohn: Department of Industrial Engineering, New Mexico State University, Las Cruces, NM 88003, USA

Mathematics, 2023, vol. 11, issue 13, 1-19

Abstract: In this paper, a statistical distribution is presented that possesses the ability to describe failure rates exhibiting both monotonic and non-monotonic behaviors, and the bathtub curve, which represents the performance of a device in reliability engineering. The proposed distribution is based on the sum of the hazard functions of the Chen distribution and the Perks distribution, thus presenting the Chen–Perks distribution (CPD). Statistical properties of the CPD focused on reliability engineering are presented to make the model attractive to practitioners of the discipline. The parameters of the CPD were calculated via the maximum likelihood estimator. On the other hand, a comparative analysis was conducted in three study cases to determine the behavior of the CPD relative to other distributions that can describe failure times with the shape of a bathtub curve. The results show that the CPD can offer competitive results, which practitioners can consider when conducting reliability analysis.

Keywords: bathtub distribution; Chen–Perks distribution; non-monotone data; maximum likelihood estimator; reliability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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