Date of Award

Spring 2011

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Manish Chandra Bhattacharjee

Second Advisor

Layek Abdel-Malek

Third Advisor

Sunil Kumar Dhar

Fourth Advisor

Sundarraman Subramanian

Fifth Advisor

Wenge Guo


Providing a warranty as a part of a product's sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization of such servicing strategies is thus a topic of great research interest in many fields.

In this dissertation, several warranty servicing strategies in two-dimensional warranty regimes, typically defined by a rectangle in the age-usage plane, have been proposed, analyzed and numerically illustrated. Two different approaches of modeling such usage sensitive warranty strategies are considered in the spirit of Jack, Iskandar and Murthy (2009) and Iskandar (2005). An `Accelerated Failure Time' (AFT) formulation is employed to model product degradation resulting due to excessive usage rate of consumers.

The focus of this research is on the analysis of warranty costs borne by the manufacturer (or seller or third party warranty providers) subject to various factors such as product's sale price, consumer's usage rate, types and costs of repair actions. By taking into account the impact of the rate of use of an item on its lifetime, a central focus of our research is on warranty cost models that are sensitive to the usage rate. Specifically, except the model in Chapter 4 where the rate at which an item is used is considered to be a random variable; all other warranty servicing policies that we consider, have usage rate as a fixed parameter, and hence are policies conditional on the rate of use. Such an approach allows us to examine the impact of a consumer's usage rate on the expected warranty costs. For the purpose of designing warranties, exploring such sensitivity analysis may in fact suggest putting an upper limit on the rate of use within the warranty contract, as for example in case of new or leased vehicle warranties.

A Bayesian approach of modeling 2-D Pro-rated warranty (PRW) with preventive maintenance is considered and explored in the spirit of Huang and Fang (2008). A decision regarding the optimal PRW proportion (paid by the manufacturer to repair failed item) and optimal warranty period that maximizes the expected profit of the rm under different usage rates of the consumers is explored in this research. A Bayesian updating process used in this context combines expert opinions with market data to improve the accuracy of the parameter estimates. The expected profit model investigated here captures the impact of juggling decision variables of 2-D pro-rated warranty and investigates the sensitivity of the total expected profit to the extent of mis-specification in prior information.

Included in

Mathematics Commons