The distribution of the present value of a pro rata warranty policy

This paper extends work on the evaluation of a pro rata warranty to include the computation of the distribution, and percentage points, of the present value of the warranty as a fraction of the original item cost. The evaluation is in terms of three dimensionless groups composed of 1) the discount rate used in the determination of present value, 2) the consumer's usage rate for the warranted item 3) the warranty period in usage units and 4) the two parameters of the Weibull distribution used to characterize the item life distribution in usage units. The mean, standard deviation, median and 90^th percentile of the present value fraction is tabulated for values of the dimensionless groups spanning the range met in practical applications. A numerical example of the use of the tables is given from the perspective of the consumer and the manufacturer. Significance: This paper provides the means to judge the average and range of variation of the present value of a warranty as the basis for a consumer to decide whether to purchase a warranty and a supplier to project warranty costs.