# A new Î´-shock model for systems subject to multiple failure types and its optimal order-replacement policy

Listed:
• Yi Jiang

## Abstract

In this article, a generalized Î´ -shock model with multi-failure thresholds is studied. For the new model, the system fails depending on the interval times between two consecutive shocks which arrive according to a Poisson process. The shorter interval times may cause more serious failures and thus result in longer down times and more costs for repair. Assuming that the repair is imperfect, an order-replacement policy N is adopted. Explicitly, the spare system for replacement is ordered at the end of ( N â€‰â€“â€‰1)th repair and the aging system is replaced at the N th failure or at an unrepairable failure, whichever occurs first. In addition, the system must meet the requirement of availability, that is, the long-run average operating time per unit time should not be lower than a certain level. The average cost rate C ( N ) and the stationary availability A ( N ) are derived analytically. Some convergence properties of A ( N ) and C ( N ) are also investigated. The optimal order-replacement policy N * can be obtained numerically with the constraint of availability. Finally, an illustrative example is given and some sensitivity analyses are conducted to demonstrate the proposed shock model.

## Suggested Citation

• Yi Jiang, 2020. "A new Î´-shock model for systems subject to multiple failure types and its optimal order-replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 138-150, February.
• Handle: RePEc:sae:risrel:v:234:y:2020:i:1:p:138-150
DOI: 10.1177/1748006X19865801
as

File URL: https://journals.sagepub.com/doi/10.1177/1748006X19865801

## References listed on IDEAS

as
1. Rafiee, Koosha & Feng, Qianmei & Coit, David W., 2017. "Reliability assessment of competing risks with generalized mixed shock models," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 1-11.
2. Lam, Yeh & Zhang, Yuan Lin & Zheng, Yao Hui, 2002. "A geometric process equivalent model for a multistate degenerative system," European Journal of Operational Research, Elsevier, vol. 142(1), pages 21-29, October.
3. Serkan Eryilmaz & Konul Bayramoglu, 2014. "Life behavior of $$\delta$$ δ -shock models for uniformly distributed interarrival times," Statistical Papers, Springer, vol. 55(3), pages 841-852, August.
4. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
Full references (including those not matched with items on IDEAS)

### Keywords

Î´-shock model; multiple failure types; geometric process; order-replacement policy;

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