Optimal condition-based warranty policy for multi-state products with three guarantees service

ABSTRACT

Within a certain period of time after products are sold, many manufacturers offer free repairing, replacing and refunding for the defective products, referred to as three guarantees service. Under the assumption that the working states of the product can be partitioned into three non-overlapping sets and its degradation can be modeled by homogeneous Markov chain, a three-stage and conditioned-based warranty model is proposed. Under the model, the whole warranty period is divided into a compulsory replacement period, a condition-based maintenance period, and a minimal repair period. Over the condition-based maintenance period, depending on the state set that the working state before the failure belongs to, failed products are rectified minimally, imperfectly, replaced by an identical one and the warranty terms are renewed, respectively. Markov process and renewal process theories are used to analyze the failure process and the warranty servicing cost over the whole warranty period. Based on double Riemann sum, a recursive algorithm for finding the optimal partition method of working states and the warranty period is proposed. A numerical example is given to illustrate the validity of the warranty strategy.

KEYWORDS:

• Three guaranteed service
• condition-based warranty policy
• Markov process
• renewal process

Acknowledgments

This work is supported partly by the NSF of China Grants (72071071) and Universities in Hebei province science and technology research project (ZD2018073).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Universities in Hebei province science and technology research project [ZD2018073]; National Natural Science Foundation of China [72071071].

Notes on contributors

Liying Wang

Liying Wang received her PhD in 2011 from School of Management and Economics, Beijing Institute of Technology(China). She is currently a professor in Shijiazhuang Tiedao University(China). Her research interests are reliability engineering, stochastic models, applications of probability and statistics.

Yu Shuang Song

Yushuang Song received her Bachelor degree in 2016 from Department of mathematics and physics, Shijiazhuang Tiedao University(China). She is studying for a master degree in Applied Mathematics at Shijiazhuang Tiedao University(China). Her research interests are reliability Engineer, stochastic models, applications of probability and statistics.

Zhaona Pei

Zhaona Pei received her master degree in 2019 from Department of Mathematics &Physics,Shijiazhuang Tiedao University(China).She is currently a Ph.D. candidate in Management Science and Engineering at Tianjin University(China).Her research interests are reliability Engineer, stochastic models, applications of probability and statistics.