JSM 2004 - Toronto

Abstract #301868

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Activity Number: 48
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #301868
Title: The Distribution of the Present Value of a Nonrenewing Pro Rata Warranty
Author(s): John I. McCool*+
Companies: Pennsylvania State University, Great Valley
Address: 30 E. Swedesford Rd., Malvern , PA, 19444,
Keywords: Weibull ; warranty ; present value ; life distribution ; pro rata
Abstract:

The value to the purchaser of a limited warranty such as given by tire manufacturers on certain premium grades, is regarded as a random variable. The customer is entitled to a credit or rebate, computed on a pro rata basis if the product fails to achieve a specified lifetime in usage units (e.g., miles). The present value of such a warranty depends on the consumer's usage rate U, the discount rate [alpha];, the warranty period W in usage units and the distribution of life in usage units (e.g., miles) and may determine whether it is worthwhile for the consumer to purchase such a warranty if it is not included in the purchase price or to incur the maintenance expenses required to maintain the validity of the warranty. Under the assumption that the time to failure follows a two parameter Weibull distribution, the distribution of present value is found numerically for selected cases and the relative economics of warranty value are examined as a function of usage rate, discount rate, the warranty period and the life distribution parameters.

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