A Bayesian Approach to Maintenance Policy Based on Cost and Downtime After Non-Renewing Warranty

Abstract

This article adopts a Bayesian approach to derive an optimal maintenance policy following the expiration of non renewing warranty. If the system fails during its warranty period, it is replaced with a new one. If the system failure occurs after the warranty period is expired, then it is minimally repaired at each failure. As the criteria to determine the optimal replacement period, we use the expected cost and the expected downtime during the life cycle of the system. Under the replacement model considered, we first derive the formulas to compute the expected downtime per unit time and the expected cost rate per unit time in general. When the failure times are assumed to follow a Weibull distribution with unknown parameters, we propose an optimal maintenance policy based on the Bayesian approach, under which such unknown parameters are updated using the observed data. The overall value function suggested by Jiang and Ji (2002) is utilized to combine the expected downtime and the expected cost rate and to determine the optimal maintenance period. Numerical examples are presented for illustrative purpose.

Keywords:

• Adaptive policy
• Bayesian approach
• Cost and downtime
• Non-renewing policy
• Optimal maintenance policy
• Overall value function

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62C10

Acknowledgment

We would like to express our sincere thanks for valuable suggestions and comments by the referees and the Associate Editor. The corresponding author's work was also supported by National Research Foundation of Korea Grant funded by the Korean Government (2009-0072742).

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00060).

Notes

*Denotes the time of failure before the NPRW period is expired.

*Denotes the time of failure before the NFRW period is expired.