Optimal replacement policy under cumulative damage model and strength degradation with applications

• Published in: Annals of operations research Vol. 315; no. 2; pp. 1345 - 1371
• Main Authors: Nanda, Phalguni, Bhuyan, Prajamitra, Dewanji, Anup
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Business and Management; Case studies; Combinatorics; Cumulative damage; Damage assessment; Degradation; Failure; Fatigue; Fatigue testing machines; Human error; Mailboxes; Maintenance; Materials; Microbalances; Nuclear power plants; Operations research; Operations Research/Decision Theory; Preventive maintenance; Random variables; S.I.: Business Analytics and Operations Research; Simulation; System failures (Engineering); Theory of Computation; Thresholds; India; Grid search; Expected cost rate; Convolution; Simulation; Renewal process; Simulated annealing
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-021-04080-6

In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in the minimum expected cost per unit time under cumulative damage model with strength degradation. In the most general setting, we propose to find optimal choices of three thresholds on operation time, number of arriving shocks and amount of cumulative damage such that replacement of the system due to failure or reaching any of the three thresholds, whichever occurs first, results in the minimum expected cost per unit time. The existing recommendations are applicable only under the assumption of Exponential damage distribution including Poisson arrival of shocks and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application including non-Poisson arrival of shocks and non-Exponential damage distributions. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.