A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles

Lijun Shang, Yongjun Du, Cang Wu and Chengye Ma
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Lijun Shang: School of Quality Management and Standardization, Foshan University, Foshan 528225, China
Yongjun Du: School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050, China
Cang Wu: School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Chengye Ma: School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050, China

Mathematics, 2022, vol. 10, issue 13, 1-16

Abstract: A monitoring system (MS) has been used to monitor products’ job cycles. It is indicated that by incorporating the job cycle into the product’s life cycle, warrantors can devise novel warranty models and consumers can define and model random maintenances sustaining the reliability of the product through warranty. In this study, by incorporating limited job cycles and a refund into the traditional free repair warranty, a two-dimensional free repair warranty with a refund (2DFRW-R) is devised for guaranteeing the product reliability to consumers. Under the condition that 2DFRW-R is planned to guarantee product reliability, a bivariate random periodic replacement (BRPR) (i.e., a random periodic replacement where the accomplishment of the N th job cycle and the replacement time T are designed as replacement limits) is modeled to sustain the post-warranty reliability from the point of view of the consumer. From the point of view of the warrantor, the warranty cost related to 2DFRW-R is derived, and the characteristics of 2DFRW-R are explored. From the point of view of consumers, the expected cost rate related to BRPR is constructed, and the existence and uniqueness of the optimal BRPR are summarized as well. By discussing parameters, several special cases are derived. The characteristics of the proposed models are analyzed in numerical examples.

Keywords: job cycle; warranty; refund; random periodic replacement; expected cost rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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