Extended optimal replacement policy for a system subject to non-homogeneous pure birth shocks

• Published in: Computers & industrial engineering Vol. 64; no. 2; pp. 573 - 579
• Main Authors: Sheu, Shey-Huei, Chen, Yen-Luan, Chang, Chin-Chih, Zhang, Zhe George
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.02.2013; Pergamon Press Inc
• Subjects: Birth process; Failure; Maintenance; Operating systems; Optimization; Probability; Product life cycle; Repair; Replacement; Shock model; Studies; Replacement; Maintenance; Repair; Birth process; Shock model; Optimization
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2012.11.009

► We study the optimal replacement policy with general repairs. ► Use shocks occurring to a non-homogeneous pure birth process (NHPBP). ► Include two types of failures: type-I failure (minor failure) and type-II failure (catastrophic failure). ► Optimize bivariate replacement policy (n,T) under a cost structure. ► Present numerical examples. This article studies the optimal replacement policy with general repairs for an operating system subject to shocks occurring to a non-homogeneous pure birth process (NHPBP). A shock causes that the system experiences one of two types of failures: type-I failure (minor failure) is rectified by a general repair, or type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a bivariate replacement policy (n,T) under which the system is replaced at planned life age T, or at the nth type-I failure, or at any type-II failure, whichever occurs first. The optimal replacement schedule which minimizes the expected cost rate model is derived analytically and discussed numerically.