Analysis of two-dimensional warranty data considering global and local dependence of heterogeneous marginals

This paper conducts a two-dimensional warranty analysis on the data with heterogeneity in terms of both age and usage. Two models are developed to evaluate the severity of warranty claims. The first one uses a copula to describe the global dependence between the age and usage populations, whereas the second one further captures various local dependence in different warranty regions. Since the mixing proportions regarding heterogeneity are latent, the expectation maximization algorithm is proposed to estimate parameters and classify the warranty data. The likelihood ratio test is further utilized to determine the number of subpopulations. A comparison with two other models shows the superiority of the proposed one in terms of the Akaike information criterion. It is found that more than 85% of the claims are classified into normal failures, and local dependence structures might vary from a symmetric one to an asymmetric one. Meanwhile, as the sample size decreases, the heterogeneity of usage would vanish, and some local dependence structures would change.