Data analysis and simulation for warranties and golf handicaps

Dissertation

Spring 5-31-2014

Degree Name

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

Department

Mathematical Sciences

David James Horntrop

Thomas Spencer

Wenge Guo

Abstract

In this dissertation, we discuss the application of data analysis and numerical simulation in order to gain insight into problems related to warranty cost management and the effectiveness of the golf handicap system. Despite the commonalities of the approaches, we will discuss these problems in turn.

For many moderately high value items with a substantial sales volume (such as automobiles), a warranty is used as an important element of marketing products as a better warranty typically signals higher product quality to customers. Much recent research on modeling and optimization of servicing costs for Non-Renewing Free Replacement Warranties (NR-FRW) assumes that the consumers’ usage profile is known. Such an assumption is unrealistic for many consumer durables. In such cases, it would be pragmatic to assume that the usage rate should be modeled by a probability distribution. This research seeks to model and minimize the expected costs of servicing strategies for NR-FRW; this is accomplished using a numerical technique known as simulated annealing while considering a variety of usage rate distributions. The relationship between the usage rate distribution and product life-length is modeled using the Accelerated Failure Time (AFT) formulation. We use a copula based approach to capture the adverse impact of increasing product usage rate on its time-to-failure. We obtain a unique copula based on the marginal distributions of both the usage rate and the product life-length, which we call the AFT Copula. The underlying dependency of our copula is evaluated using non-parametric measures of association. The Mean Time to First Failure (MTTF) indicates which usage rate distributions most likely correspond to highly reliable products. We found that certain warranty servicing strategies were more cost efficient than other commonly used approaches. We use data analysis techniques on a traction motor data set to study the practicality of our approach. The results obtained from this data are in qualitative agreement with our previous results.

The ability of a golfer is measured by a player’s handicap which is an estimate of his/her potential based on previously played games. The handicap system is administered by the United States Golf Association (USGA); it is designed to enable players of differing abilities to compete against each other on an equitable basis. Most previous studies in golf have focused on analyzing golf scores. The goal of this research is to study the effectiveness of the current handicapping system. We use the AT&T Golf Tournament League data set for our study; this data set contains scores and handicaps of golfers from almost 100 different tournaments. In this study, we use data analysis methods including filtering to remove outliers and goodness of fit tests to determine the most appropriate distribution for the golf scores. Because each handicap requires a separate fit, we develop a technique of minimizing the average ranks of the candidate distributions in order to obtain the single best distribution for all handicaps. For this data set, the generalized extreme value distribution is the most appropriate. In order to investigate the effectiveness of the handicap system, we conduct simulations of competitions between golfers with varying handicaps based on the empirical and fitted data for golf scores. These simulations indicate that a player with a lower handicap has an advantage over a player with a higher handicap.

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