No abstract

Purpose -The purpose of this paper is to generalize Yeh and Zhang's 2004 random threshold failure model for deteriorating systems. Design/methodology/approach -An N-policy was adopted by which the system was replaced after the Nth failure. Findings -The model was found to have practical applications in warranty cost analysis. Originality/value -By identifying the instance of a shock as the failure of the system and the threshold times as the warranty period offered and changing the definition of lethal shock (system failure in this case) as the occurrence of a shock within a threshold period in our generalized model, one can study the renewing warranty cost analysis.

This study investigates two random threshold shock models for a repairable deteriorating system with nonnegligible maintenance times, with and without a spare via a phase-type geometric process. The system fails whenever the intershock arrival time is less than a random threshold. The provision of stochastic lead time is incorporated in Model II so that an ordering policy N−1 and a replacement policy N based on the number of failures of the system are also considered. An explicit expression of the average cost rate is derived for both models and the optimal replacement policy N* is obtained by minimizing the long-run average cost rate analytically. The numerical illustrations and sensitivity analysis provided therein conform to the observations made in the study. KEYWORDS phase-type geometric process, random threshold, stochastic lead time Appl Stochastic Models Bus Ind. 2018;34:407-422. wileyonlinelibrary.com/journal/asmb 407 408SARADA AND SHENBAGAM this model, Lam studied two kinds of replacement policies, ie, one based on the working age T of the system (T-policy) and the other based on the failure number N of the system (N-policy). The objective is to choose the optimal replacement policies T* and N*, respectively, such that the long-run average cost per unit time is minimized. Other works on the geometric process model in maintenance analysis include those of Lam, 12 Stanley, 13 Pérez-Ocón and Torres-Castro, 14 Wang and Zhang, 15 Liang et al, 16 Zong et al, 17 and Cheng et al 18Under the assumption of geometric repair times, Lam and Zhang 9 and Tang and Lam 19 studied the -shock model, in which shocks arrive according to a Poisson process and renewal process, respectively, whereas Lam 20 introduced a geometric process -Shock model in a repairable deteriorating system and obtained an optimal replacement policy (N*). Liang et al 16 spelt an optimal replacement policy N* in a geometric process model with a -shock for a deteriorating and improving system. Retaining the geometric repair times modeling and assuming the shock arrival process to be a Poisson process with the threshold value to be an exponential random variable, Zong et al 17 dealt with the determination of the optimal replacement policy N* to minimize the long-run average cost rate. However, in realistic systems, phase-type distribution, introduced by Neuts, 21,22 plays an important role and has been applied in telecommunication, reliability, queueing, and inventory theory. It is generally assumed that the system replacement is immediate on failure, which may not be true always, as it would be expensive to maintain a spare, consequently hiking the system operating cost (eg, the work of Yu et al 23,24 ).From a thorough review of the existing literary works done, it is observed that the -shock model with a random threshold through stochastic lead time via phase-type geometric processes has not been studied from the viewpoint of deteriorating systems. Thus, in an attempt to establish the importance of the simplified computational implementation of phas...

No abstract

No abstract