On minimizing expected warranty costs in 1-dimension and 2-dimension with different repair options
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We study warranty models of one-dimension and two-dimensions with different options available to the manufacturer for repair-replacement upon product failure. Product failures during warranty period incur additional costs to the manufacturer and leads to customer dissatisfaction when suitable service action is not adopted. To forecast and minimize the expected cost of warranty servicing is of considerable interest to product manufacturers and decision makers. The results of this research will enable manufacturers, reliability engineers and warranty managers to make better decisions in developing suitable servicing strategies and towards significant cost savings in administering effective management of warranty programs. In one-dimensional model we study a non renewing combination warranty policy with initial base-warranty period (BWP) followed by pro-rata period (PRP). Product failures during BWP incur no cost to the customer, while the customer can purchase a new product at pro-rata price during PRP period. The manufacturer has three options available during BWP, namely minimal repair, general repair and replacement to address product failures and each option varies based on degree of repair, and the cost associated. We obtain optimal product price, pro-rata period, and sales volume for each type of repair replacement option employed, derive stationary points and necessary second conditions to minimize the manufacturers cost of warranty servicing. We numerically illustrate the results obtained when the lifetime distribution of the product follows: (i) Gamma order-2, and (ii) extended weibull distribution. In two-dimensional model we study a non- renewing, combination warranty policy defined by rectangular region, which is composed of three disjoint subregions. Product failures in each subregion incur variable costs based on the usage, age of the product, and repair strategy adopted. We assume pro-rated costs for servicing which is dependent on the age and the usage of the product at the time of failure. We consider the warranty duration limits set by the manufacturer for restricted and unrestricted product usage and compare the effects of two servicing strategies based on when the manufacturer can exercise replacement option. Using an estimated failure intensity and usage distribution we derive expressions for expected costs of warranty servicing based on conditioning arguments. We numerically compare the effect of restricted and unrestricted cases for both the servicing strategies to obtain minimal expected costs to the manufacturer. Finally, we conclude with a brief discussion about extensions to the models developed and future research directions.