Optimal preventive maintenance level for a repairable product under warranty subject to multimode failure process

Azmat Ullah*, Muhammad Ayat, Hakeen Ur Rehman, Lochan Kumar Batala

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
3 Downloads (Pure)


The purpose of this paper is to develop a model that determines whether how much effort of preventive maintenance action is worthwhile for the consumer over the post-sale product life cycle of a repairable complex product where the product is under warranty and subject to stochastic multimode failure process, that is, damaging failure and light failure with different probabilities.

The expected life cycle cost is designed for a warranted product from the consumer perspective. The product failure is quantified with failure rate function, which is the number of failures incurred over the product life cycle. The authors consider the failure rate function reduction method in their model where the scale parameter of a failure rate function is maximized by applying the optimal preventive maintenance level. The scale parameter of any failure distribution refers to the meantime to failure (MTTF). The first-order condition is applied with respect to the maintenance level in order to achieve the convexity of the nonlinear function of the expected life cycle cost function.

The authors have found analytically the close form of the preventive maintenance level, which can be used to find the optimal reduced form of the failure rate function of the product and the minimum product expected life cycle cost under the given condition of multimode stochastic failure process. The authors have suggested different maintenance policies to consumers in order to implement the proposed preventive maintenance model under different conditions. A numerical example further illustrated the analytical model by considering the Weibull distribution.

Practical implications
The consumer may use this study in the accurate modeling of the life cycle cost of a product that is under warranty and fails with a multimode failure process. Also, the suggested preventive maintenance approach of this study helps the consumer in making appropriate maintenance decisions such as to minimize the expected life cycle cost of a product.

This study proposes an accurate estimation of a life cycle cost for a product that is under the support of warranty and fails with multimode. Furthermore, for such a kind of product, which is under warranty and fails with multimode, this study suggests a new preventive maintenance approach that assures the minimum expected life cycle cost.
Original languageEnglish
Pages (from-to)1193-1214
Number of pages22
JournalInternational Journal of Quality and Reliability Management
Issue number5
Early online date10 Nov 2020
Publication statusPublished - 6 Apr 2021
Externally publishedYes


  • product life cycle
  • warranty
  • failure rate function
  • multimode failures
  • damaging failure
  • preventive maintenance


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