On a random lead time and threshold shock model using phase‐type geometric processes. (8th February 2018)

• Record Type: Journal Article
• Authors: Sarada, Y.; Shenbagam, R.
• Other Names: Nicolis Orietta guestEditor.; Pascual Rodrigo guestEditor.
• Is Part Of: Applied stochastic models in business and industry. Volume 34:Number 3(2018)
• Page Start: 407
• Page End: 422
• Publication Date: 2018-02-08
• Subjects: phase‐type geometric process -- random threshold -- stochastic lead time; Stochastic analysis -- Periodicals; Stochastic processes -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Industrial management -- Mathematical models -- Periodicals; 338.00151923
• DOI: 10.1002/asmb.2308
• Languages: English
• ISSNs: 1524-1904

Abstract

Abstract : 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.