Young H. Chun

Cost analysis of two-attribute warranty policies based on the product usage rate

In the so-called two-attribute warranty policy, two types of warranty criteria, such as the age and mileage of an automobile, are employed simultaneously to determine the eligibility of a warranty claim. The authors propose in the paper several decision models that estimate the expected total cost incurred under various types of two-attribute warranty policies. They also perform a sensitivity analysis to study the effects of several model parameters, such as the discount rate, the product usage rate, and the warranty terms, on the total warranty cost.

Sequential decisions under uncertainty in the R&D project selection problem

In most cases, the R&D project selection problem is concerned with how to evaluate and identify the best subset of projects under some resource constraints. In this paper, we consider the sequential decision problem of optimally sequencing a set of projects which must be undertaken sequentially over time. We derive the optimal ordering strategy for two special cases, (1) a series system of tasks in which the selection process is terminated as soon as one of the tasks is failed, and (2) a parallel system of alternatives in which the selection process continues until any of the alternatives is completed successfully. We further consider the precedence restriction in a series system of tasks which specifies that, for some technological or budgetary constraints, a certain task must be undertaken before another. In a parallel system of alternatives, we also investigate the availability condition under which a certain alternative will not be available if not selected within a certain period of time. >

Effect of quality loss functions on the economic design of process control charts

Abstract There has been considerable research on the economic design of Statistical Process Control (SPC) models, for example x charts. However, the effects of the nature of variability costs (cost due to process variation or, alternatively, the risk position of the firm) on the design parameters of such models have not been investigated. To examine the effects of variability cost, we develop a continuous shift model that plausibly assumes that a process mean stochastically undergoes numerous small, possibly undetectable shifts, some moderate size shifts, and a few larger shifts each having some cost. Using this continuous time model, we show in what manner the optimal design parameters of an x chart are significantly affected by the nature of the variability cost function. Moreover, contrary to the results of past research, we show that under certain conditions, there can be significant differences in expected costs and design parameters between continuous and single shift models.

Three Types of Producer's and Consumer's Risks in the Single Sampling Plan

The classical producers risk and the classical consumers risk are defined in acceptance sampling based on the assumption that the proportion defective of incoming lots is a constant. This assumption has been a focus of much of the criticism of accepta..

Dynamic programming formulation of the group interview problem with a general utility function

Abstract In many managerial decision situations such as buying an electronic appliance, several groups of alternatives are presented sequentially and an accept-or-reject decision is made immediately after evaluating the alternatives in each group. If each group contains only one alternative, this optimal selection problem is known as the secretary problem which has a long and rich history of research devoted to developing solution strategies. We propose a more generalized version of the secretary problem, called the group interview problem , in which each group contains more than one alternative and each group is presented and evaluated sequentially over time. Using a dynamic programming approach, we derive a backward recursive equation for solving the group interview problem in which a decision makers utility of selecting a certain choice is expressed as a general function. Depending on the specific form of this function, we derive optimal selection strategies for various types of group interview problems such as minimum rank, maximum utility, best choice, and one out of the p best choice problems.

Bayesian inspection model with the negative binomial prior in the presence of inspection errors

One of the basic assumptions in Bayesian inspection models is that we have some prior knowledge about the number of defects in a certain product or software system. The prior knowledge can be often described as a probability distribution (e.g., Poisson distribution). In the paper, we propose three conditions that should be put forth as desirable properties for a prior probability distribution of the number of defects in the product. We review various prior probability distributions and test if they meet those conditions. The negative binomial distribution is found to be the only one that satisfies all the desirable conditions. With the negative binomial prior, we analyze the effects of various parameters on the Bayesian estimate of the number of undetected errors still remaining in the product.

Estimating the number of undetected software errors via the correlated capture-recapture model

Abstract Sometimes a complex software system fails because of errors undiscovered in the design stage of the development process. Detecting these errors early in the process would eliminate many downstream problems. The so-called “capture–recapture” model, initially used by biologists to estimate the size of wildlife populations, has been widely used to estimate the number of software design errors. However, one simplifying assumption in capture–recapture models is that the inspections performed by various inspectors are statistically independent from each other. In the paper, we propose a novel method that is based on the correlation matrix of multiple inspectors. In a numerical analysis, we show that our method outperforms other traditional models that are based on the independence assumption.

Selecting the best choice in the full information group interview problem

Abstract We consider the problem of selecting the single best choice when several groups of choices are presented sequentially for evaluation. In the so-called group interview problem, we assume that the values of choices are random observations from a known distribution function and derive the optimal search strategy that maximizes the probability of selecting the best among all choices. Under the optimal search strategy derived by means of a dynamic programming technique, a decision maker simply selects the best choice in the group under consideration if its value is higher than the pre-specified decision value for that group. We also consider the optimal ordering strategy for the case where the decision maker is permitted to rearrange the sequence of groups for evaluation. We show that the optimal search and ordering strategies can be applied to many sequential decision problems such as the store location problem.

Bayesian inspection model for the production process subject to a random failure

Consider a sequence of items produced on a high-speed mass production line which is subject to a random failure. When an item in the sequence is inspected it is possible to obtain directional information about the exact timing of a process failure—before or after producing the inspected item. Using this directional information this paper proposes Bayesian inspection procedures that deal with three related problems: (i) how often to inspect items on the production line; (ii) how to conduct the search for more defective items; and (iii) when to stop the search process and salvage the remaining items. Based on various cost factors, the problem of optimal inspection interval, optimal search process and an optimal stopping rule is formulated as a profit-maximization model via a dynamic programming approach. For the production process with an unknown failure rate, Bayesian methods of estimating the process failure rate are proposed. The proposed Bayesian inspection procedures can be applied to a wide variety of high-speed mass production processes such as printing labels, filling containers or mixing ingredients.

Selecting the best choice in the weighted secretary problem

Abstract In the sequential evaluation and selection problem with n applicants, we assume that a decision maker has some prior information about each applicant so that unequal weights may be assigned to each applicant according to his or her likelihood of being the best among all applicants. Assuming that the pre-assigned weights are available in advance, we derive the optimal selection strategy that maximizes the probability of selecting the best among all applicants. For the case where the decision maker is permitted to rearrange the sequence in which applicants are evaluated, we further propose a simple heuristic procedure to the problem of optimally ordering the sequence of evaluations. Based on a pairwise comparison matrix and a goal programming procedure, we also propose a method that easily computes the weights in a practical situation.