Journal
MATHEMATICS
Volume 10, Issue 13, Pages -Publisher
MDPI
DOI: 10.3390/math10132225
Keywords
job cycle; warranty; refund; random periodic replacement; expected cost rate
Categories
Funding
- characteristic innovation projects of colleges and universities in Guangdong Province [2021WTSCX081]
- base and basic applied study of Guangdong Province [2020A1515011360]
- national natural science foundation of China [72161025, 71871181]
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A monitoring system has been used to monitor the job cycles of products. 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 proposed to guarantee product reliability. The characteristics and costs of the proposed models from the perspectives of consumers and warrantors are explored.
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 Nth 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.
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