Determination of Optimum Warranty Region for Two Dimensional Dependent Data

TL;DR

This paper introduces a method to determine the optimal two-dimensional warranty region for products based on age and mileage, using a bivariate Gumbel copula and real-world data to maximize utility.

Contribution

It develops a novel approach combining copula modeling and utility maximization to optimize two-dimensional warranty policies.

Findings

Two-dimensional warranty cost function improves utility.

Optimal warranty region varies with product usage.

Method validated on real traction motor data.

Abstract

This paper presents a method for determining the optimal two-dimensional warranty region for age and mileage scales across all possible combinations of free replacement warranty (FRW), prorata warranty (PRW), and FRW-PRW combined policies. The operational time or lifetime and usage of the products are modeled using a bivariate Gumbel copula with Weibull as the marginal distribution. The optimal warranty region is derived by maximizing an expected utility function, which incorporates two cost components: the economic benefit function and the warranty cost function, specifically constructed for the two-dimensional warranty scenario. To obtain the optimal warranty region, a real-world dataset of traction motors, including age and mileage information, is analyzed. The results show that considering a two-dimensional warranty cost function yields the highest utility compared to all other scenarios.