Jen Tang

Design of Screening Procedures: A Review

It has been well accepted that dependence on inspection to correct quality problems is ineffective and costly, and hence screening (100% inspection) should not be used as a long-term solution for i...

Control Charts for Dependent and Independent Measurements Based on Bootstrap Methods

Abstract Shewhart charts are widely accepted as standard tools for monitoring manufacturing processes of univariate, independent “nearly” normal measurements. They are not as well developed beyond these types of data. We generalize the idea of Shewhart charts to cover other types of data commonly encountered in practice. More specifically, we develop some valid control charts for dependent data and for independent data that are not necessarily “nearly” normal. We derive the proposed charts from the moving blocks bootstrap and the standard bootstrap methods. Their constructions are completely nonparametric no distributional assumptions are required. Some simulated as well as real data examples are included they are very supportive of the proposed methods.

On the distribution of the product of independent beta random variables

In this paper, exact distribution of the product of independent beta random variables has been derived and its structural form is given together with recurrence relations for the coefficients of this representation. These recurrence relations yield a direct computational algorithm for computing the percentage points of many test criteria in multivariate statistical analysis.

Optimum step-stress accelerated degradation test for Wiener degradation process under constraints

Abstract To assess a products reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.

Statistical Process Control via the Subgroup Bootstrap

The most commonly used techniques in statistical process control are parametric, and so they require assumptions regarding the statistical properties of the underlying process. For example, Shewhart control charts assume that the observations are indepe..

Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap

This paper considers the problem of finding limits for a statistical process control (SPC) chart for the process mean, when the process distribution is unknown. The bootstrap method estimates these limits relying on Monte Carlo methods, which are subject to simulation errors. Therefore this paper develops a computationally efficient enumeration method for exact calculations of the control limits.

Incorporation Competence Sets of Decision Makers by Deduction Graphs

This paper proposes an optimization model of incorporating competence sets of group decision makers to maximize the total benefit of the whole group. Such an incorporation model is formulated as finding a deduction graph linked from the nodes of existing competencies to the nodes of desired competencies. Compared with other methods treating competence set problems (Yu and Zhang 1991, Li and Yu 1994, and Shi and Yu 1996), the proposed model can solve problems involving multiple decision makers; in addition it allows the network to be cyclic and to contain compound nodes.

Distribution of Aggregate Utility Using Stochastic Elements of Additive Multiattribute Utility Models

Conventionally, elements of a multiattribute utility model characterizing a decision makers preferences, such as attribute weights and attribute utilities, are treated as deterministic, which may be unrealistic because assessment of such elements can be imprecise and erroneous, or differ among a group of individuals. Moreover, attempting to make precise assessments can be time consuming and cognitively demanding. We propose to treat such elements as stochastic variables to account for inconsistency and imprecision in such assessments. Under these assumptions, we develop procedures for computing the probability distribution of aggregate utility for an additive multiattribute utility function (MAUF), based on the Edgeworth expansion. When the distributions of aggregate utility for all alternatives in a decision problem are known, stochastic dominance can then be invoked to filter inferior alternatives. We show that, under certain mild conditions, the aggregate utility distribution approaches normality as the number of attributes increases. Thus, only a few terms from the Edgeworth expansion with a standard normal density as the base function will be sufficient for approximating an aggregate utility distribution in practice. Moreover, the more symmetric the attribute utility distributions, the fewer the attributes to achieve normality. The Edgeworth expansion thus can provide a basis for a computationally viable approach for representing an aggregate utility distribution with imprecisely specified attribute weights and utilities assessments (or differing weights and utilities across individuals). Practical guidelines for using the Edgeworth approximation are given. The proposed methodology is illustrated using a vendor selection problem.

Step-stress accelerated life tests: a proportional hazards–based non-parametric model

Using data from a simple step-stress accelerated life test procedure, a non-parametric proportional hazards model is proposed for obtaining upper confidence bounds for the cumulative failure probability of a product under normal use conditions. The approach is non-parametric in the sense that most of the functions involved in the model do not assume any specific forms, except for certain verifiable conditions. Test statistics are introduced to verify assumptions about the model and to test the goodness of fit of the proposed model to the data. A numerical example, using data simulated from the lifetime distribution of an existing parametric study on metal-oxide semiconductor capacitors, is used to illustrate the proposed methods. Discussions on how to determine the optimal stress levels and sample size are also given.

Univariate X control charts for individual characteristics in a multinormal model

The early work on multivariate statistical process control was built upon Hotellings T2 control chart which was developed to simultaneously monitor the means of correlated quality variables. This chart, however, has a drawback, namely, the problem of identifying the responsible variable(s) when an out-of-control signal occurs. One alternative is to use a separate X¯ control chart for each individual characteristic with equal risks, based on Bonferroni inequality. In this study, we show that, from an economic perspective, it may be desirable to have unequal type I risks for the individual charts, because of different inspection and restoration costs associated with each variable. We obtain their risk ratios, which are measures of relative importance of the variables monitored. Then, based on these risk ratios, we develop computer algorithms for finding the exact control limits for individual variables from a multinormal distribution, in the sense that the overall type I risk of the charts is equal to the desired value. Numerical studies show that the proposed methods give optimal or near-optimal results from an economic as well as statistical point of view.