Calculation of the cost of warranty policies as a function of estimated life distributions

TLDR

The paper examines free‑replacement and pro‑rata warranties, comparing their implications from both buyer and seller viewpoints. The study aims to compare the long‑run cost to buyers and profit to sellers between warranted and unwarranted items, requiring knowledge of item life‑distribution characteristics. The authors discuss parametric and nonparametric techniques for estimating life‑distribution characteristics from incomplete data, addressing both single and multiple failure‑mode scenarios. Illustrative solutions are presented using incomplete failure‑time data from an aircraft component.

Abstract

Abstract Two types of warranties are analyzed. These are the free‐replacement warranty, under which failed items are replaced free of charge until a specified total operating time has been achieved, and the pro rata warranty, under which items that fail prior to a specified time are replaced at pro rata cost to the buyer. Both the buyer's and seller's points of view are considered. The basis of the analysis is a comparison of warranted and unwarranted (otherwise identical) items with regard to long‐run cost to the buyer and long‐run profit to the seller. Application of the results requires knowledge of certain characteristics of the life distribution of the items in question. Parametric and nonparametric methods of estimation of these characteristics from incomplete data are discussed. Single and multiple failure‐mode situations are considered. Some solutions to the problem are illustrated using incomplete data on failure times of an aircraft component.