Browsing by Author "Shiau, JJH"

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A Bayesian procedure for process capability assessment
(1999-09-01)
Shiau, JJH
;
Chiang, CT
;
Hung, HN
;
統計學研究所
;
Institute of Statistics
The usual practice of judging process capability by evaluating point estimates of some process capability indices has a flaw that there is no assessment on the error distributions of these estimates. However, the distributions of these estimates are usually so complicated that it is very difficult to obtain good interval estimates. In this paper we adopt a Bayesian approach to obtain an interval estimation, particularly for the index C(pm). The posterior probability p that the process under investigation is capable is derived; then the credible interval, a Bayesian analogue of the classical confidence interval, can be obtained. We claim that the process is capable if all the points in the credible interval are greater than the pre-specified capability level omega, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the minimum values of (C) over cap(pm)/omega for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the process mean equals the target value for C(pm) and equals the midpoint of the two specification limits for C(pk). the procedure is even simpler; only chi-square tables are needed. Copyright (C) 1999 John Wiley & Sons, Ltd.
A multivariate parallelogram and its application to multivariate trimmed means
(2003-09-01)
Shiau, JJH
;
Chen, LA
;
統計學研究所
;
Institute of Statistics
This paper introduces a multivariate parallelogram that can play the role of the univariate quantile in the location model, and uses it to define a multivariate trimmed mean. It assesses the asymptotic efficiency of the proposed multivariate trimmed mean by its asymptotic variance and by Monte Carlo simulation.
A new algorithm for 5-band Toeplitz matrix inversion with application to GCV smoothing spline computation
(1999-12-15)
Shiau, JJH
;
統計學研究所
;
Institute of Statistics
A new algorithm is developed for computing any entry of the inverse of a 5-band Toeplitz matrix. After a linear-time overhead, each entry can be computed in constant time. As an application of this algorithm, we present a way to compute the generalized cross validated smoothing spline in linear time for the equally spaced data case. (C) 1999 Elsevier Science B.V. All rights reserved.
A note on Bayesian estimation of process capability indices
(1999-11-15)
Shiau, JJH
;
Hung, HN
;
Chiang, CT
;
統計學研究所
;
Institute of Statistics
Process capability indices are useful for assessing the capability of manufacturing processes. Most traditional methods are obtained from the frequentist point of view. We view the problem fi om the Bayes and empirical Bayes approaches by using non-informative and conjugate priors, respectively. (C) 1999 Elsevier Science B.V. All rights reserved.
An empirical Bayes process monitoring technique for polytomous data
(2005-02-01)
Shiau, JJH
;
Chen, CR
;
Feltz, CJ
;
統計學研究所
;
Institute of Statistics
When a product item is tested, usually one has more information than just pass or fail. Often there are categories of failure modes. The purpose of this paper is to develop a method to monitor the fractions of the tested items falling into different categories of pass/fail modes. Using the multinomial model with Dirichlet prior, we describe the theory underlying an empirical Bayes approach to monitoring polytomous data generated in manufacturing processes. A pseudo maximum likelihood estimator (PMLE) and the method-of-moments estimator (MME) of the hyperparameters of the prior distribution are considered and compared by a simulation study. It is found that the PMLE performs slightly better than the MME. A monitoring scheme based on the marginal distributions of the observed pass/fail fractions is proposed. The average run length behavior of the proposed monitoring scheme is investigated. Finally, an example to illustrate the use of the technique is given. Copyright (C) 2004 John Wiley Sons, Ltd.
Analyzing accelerated degradation data by nonparametric regression
(1999-06-01)
Shiau, JJH
;
Lin, HH
;
統計學研究所
;
Institute of Statistics
This paper presents a nonparametric regression accelerated life-stress (NPRALS) model for accelerated degradation data wherein the data consist of groups of degrading curve data. In contrast to the usual parametric modeling, a nonparametric regression model relaxes assumptions on the form of the regression functions and lets data speak for themselves in searching for a suitable model for data. NPRALS assumes that various stress levels affect only the degradation rate, but not the shape of the degradation curve. An algorithm is presented for estimating the components of NPRALS. By investigating the relationship between the acceleration factors and the stress levels, the mean time to failure estimate of the product under the usual use condition is obtained. The procedure is applied to a set of data obtained from an accelerated degradation test for a light emitting diode product. The results look very promising. The performance of NPRALS is further checked by a simulated example and found satisfactory. We anticipate that NPRALS can be applied to other applications as well.
Statistical process monitoring using an empirical Bayes multivariate process control chart
(2001-03-01)
Feltz, CJ
;
Shiau, JJH
;
統計學研究所
;
Institute of Statistics
In this paper, we describe the theory underlying an empirical Bayesian approach to monitoring two or more process characteristics simultaneously. If the, data is continuous and multivariate in nature, often the multivariate normal distribution can be used to model the process. Then, using Bayesian theory: we develop techniques to implement empirical Bayes process monitoring of the multivariable process. Lastly, an example is given to illustrate the use of our techniques. Copyright (C) 2001 John Wiley & Sons, Ltd.