A note on calculating cost of two-dimensional warranty policy D.K. Manna a, * , Surajit Pal a , Sagnik Sinha b a SQC & OR Unit, Indian Statistical Institute, 110 Nelson Manickam Road, Chennai 600 029, India b Department of Mathematics, Jadavpur University, Kolkata 700 032, India Received 3 October 2006; received in revised form 5 October 2007; accepted 5 October 2007 Available online 14 October 2007 Abstract We study the derivation of warranty cost under rectangular two-dimensional policy for both repairable as well as non- repairable product. Typically, two approaches are adopted, namely, one-dimensional (1D) and two-dimensional (2D). We show the difference in results obtained from the formulae under the two approaches through several examples. Merits of the formulae are then analyzed to identify the correct ones. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: 1D/2D approach; Renewal function; Non-homogeneous Poisson process 1. Introduction Warranty is attracting significantly greater importance in the marketplace for consumer durables and auto- mobiles. Customers seek redress or compensation in the event of early failure of product, and the manufac- turers intend to have a larger market share. Towards this, warranty provides a common ground for both the parties. However, it is well known that warranty alone cannot address the issue without adequate product quality and reliability. This necessitates modeling and analysis of warranty policy in decision-making. In par- ticular, knowledge of warranty cost is extremely important. The description of a warranty policy involves a compensation scheme (repair, replacement, refund, etc.) that is being offered towards product failure within a specified period since the sale has taken place. Depending upon how this period is defined, policies are classified into one- and two-dimensional. One-dimensional policy is characterized by an interval (usually of age) as warranty period, with no limitation on usage of the product. A two-dimensional policy is represented by a region in two-dimensional plane, generally one dimension describing age and the other one usage. A typical example of two-dimensional policy for an automobile is as follows. The manufacturer agrees to repair or provide replacement for its failed parts free of cost for a max- imum period of 5 years or a maximum usage of 50,000 miles, whichever occurs first, from the time of sale. Following the nomenclature of warranty, we refer to this as rectangular two-dimensional policy (see 0360-8352/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.10.005 * Corresponding author. Tel.: +91 44 23740612. E-mail address: dkmanna@hotmail.com (D.K. Manna). Available online at www.sciencedirect.com Computers & Industrial Engineering 54 (2008) 1071–1077 www.elsevier.com/locate/dsw