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

Shang, Lijun; Du, Yongjun; Wu, Cang; Ma, Chunguang

doi:10.3390/math10132225

Cited by 6 publications

(2 citation statements)

References 33 publications

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“…For example, integrating one of the types of cycles into the warranty and post-warranty stages, Refs. [37][38][39][40][41][42][43][44][45][46] proposed some random warranty and random maintenance models for ensuring the life cycle reliability of the product with monitored working/mission/task cycles.…”

Section: Introductionmentioning

confidence: 99%

Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity

Shang,

Liu,

Gao

et al. 2023

Mathematics

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Driven by the wide application of industrial software integrated with digital technologies, the real information of task cycles for some products in the real world can be monitored in real time and transmitted to the management center. Monitored task cycles hide consumers’ usage characteristics, which are signals of the products’ usage heterogeneity because they vary from one consumer to another consumer. By classifying monitored task cycles into different categories, this paper customizes two random maintenance models to ensure the life cycle reliability of the product with monitored task cycles on the basis of usage categories. The first model is customized using usage categories, the key objective of which is, from the perspective of heterogeneity, to ensure warranty-stage reliability. In view of using minimal repair service, the first model is named a random free repair warranty with heterogeneity (RFRW-H), which is modeled from the viewpoints of cost and time measures. By calculating the limits of cost and time measures, some specific cases are presented to model other warranties. The second model is customized using the same usage categories, which aims to ensure post-warranty-stage reliability. In view of using each of ‘whichever occurs first/last’, the second model is named a customized random periodic replacement first (CRPRF) model or a customized random periodic replacement last (CRPRL) model, respectively, which are modeled from the viewpoint of the cost rate function. By calculating the limits of the cost rate function, the cost rate functions of other maintenance models are obtained. Finally, from the numerical viewpoint, some of the features of the customized models are mined, and the performances are compared.

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Section: Introductionmentioning

confidence: 99%

Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity

Shang,

Liu,

Gao

et al. 2023

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The second type of research is to devise random post-warranty maintenance policies by incorporating random working cycles into the post-warranty stage, which have been provided in Refs. [38][39][40][41]. The objective of the third type of research is to devise condition-based post-warranty maintenance policies, wherein system deterioration is characterized as a stochastic process.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge

Shang

Yu²,

et al. 2022

Mathematics

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Facilitated by advanced digital technologies, reliability managers can monitor system working cycles during the whole life cycle. Such a technological realization can help reliability managers ensure system reliability in real time by monitoring working cycles. In this paper, by incorporating a limited random working cycle, rebate and charge into warranty theory, a random free repair warranty with rebate and charge (RFRW-RC) is devised to ensure system reliability during the warranty stage. Under RFRW-RC, the rebate removes manufacturers’ responsibility for continuing to ensure system reliability, while the charge is a support where manufacturers continue to ensure system reliability. The warranty cost of RFRW-RC is derived, and a random discrete free repair warranty (RDFRW) is presented by simplifying RFRW-RC. By mixing random age replacement last (RARL) and classic age replacement (CAR), a random hybrid age replacement (RHAR) is designed in order to ensure system reliability during the post-warranty stage. In such an RHAR, RARL is applied to extend the replacement time during the post-warranty stage in order to maximize the remaining life of the system through warranty, and CAR is used to lower the maintenance cost of the system through warranty. The cost rate of RHAR is modeled, and the cost rate of RDFRW is offered as well by discussing parameter values. The decision variable is optimized by minimizing the cost rate model. The properties of the presented models are explored from numerical perspectives.

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Preventive maintenance policies for a big data system with throughput rate

2023

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

Cited by 6 publications

References 33 publications

Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity

Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity

An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge

Preventive maintenance policies for a big data system with throughput rate

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