Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity

• Published in: Mathematics (Basel) Vol. 11; no. 15; p. 3330
• Main Authors: Shang, Lijun, Liu, Baoliang, Gao, Kaiye, Yang, Li
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2023
• Subjects: Analysis; Automobile customizing; Categories; Consumers; Customization; Failure; Heterogeneity; Life cycle assessment; life cycle reliability; Maintenance; Mathematics; Methods; Preventive maintenance; Product reliability; random periodic replacement; Random variables; Reliability; Repair; task cycle; Time measurement; Warranties; Warranty; China
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11153330

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.