Many attributes contribute to product failures that result in warranty claims. In particular, there are situations where several attributes are used together as criteria for judging the warranty eligibility of a failed product. For example, automobiles warranty coverage has both age and mileage limits. The warranty policy characterized by a region in a two-dimensional plane with one axis representing product age and the other axis representing product usage is known as the "two-attribute" warranty policy. A number of procedures have been developed for analyzing the two-dimensional warranty policy. These procedures use many crisp data obtained from strictly controlled reliability tests. However, in real situations, these requirements might not be fulfilled. In extreme cases, the warranty claims data come from users whose reports are expressed in a vague way. This may be due to subjective and imprecise perception of failures by a user, imprecise warranty data record, or imprecise rate of usage record. This paper suggests fuzziness as an alternative to randomness for describing the two-dimensional warranty uncertainty. A new sets-as-points geometric view of fuzzy warranty sets is developed in this study. This view can reduce many errors of estimation and prediction of the cost associated with a variety of warranty policies including the "two-attribute" warranties and some reliability improvement warranties.
Identifying newly approved medications in Medicare claims data: a case study using tocilizumab
