Bayesian Optimum Warranty Region for Right Censored Two Dimensional Dependent Data

Abstract

Warranty policies play a crucial role in balancing customer satisfaction and cost of the manufacturer. Traditional one-dimensional warranty frameworks, based solely on either age or usage, often fail to capture the joint effect of product life factors. This article investigates two-dimensional warranty policies by combining Free Replacement Warranty, Pro-Rata Warranty, and Combination FRW-PRW Warranty schemes across both age and usage scales. A dissatisfaction cost function is proposed alongside the economic benefit and warranty cost functions, and the expected utility framework is employed to derive optimal warranty parameters. The expectation is taken with respect to the posterior predictive distribution of product lifetime and usage data, ensuring a data-driven approach. Finally, the methodology is validated using an open-source dataset, and a new two-dimensional starter motor dataset is introduced to demonstrate the practical advantages of adopting two-dimensional warranty policies.