指數產品的品質績效評估研究

在高度競爭的產業時代，產品品質優劣是企業生存的命脈，例如製造業最重要的課題之一，就是如何有效地提昇產品的品質、壽命與合格率，以達到經濟效益。因此有許多文獻探討關於評估品質績效之方法，其中製程能力指標就是一個有效且方便的品質績效評估工具。而製程能力愈佳，代表該製程所提供的產品品質等級愈高，產品的合格率也就愈高，由此製程所提供的產品其品質績效也愈好。有關品質績效的文獻大多假設產品的品質特性服從常態分配，然而實際上產品的品質特性(例如：電壓、黏性、持久性、耐用性等等)並不一定服從常態分配。根據一些統計學家及品管工程師的研究指出，產品的壽命往往服從指數分配、韋伯分配和伽瑪分配等等，而非常態分配。因此，本研究探討當產品壽命服從指數分配或韋伯分配時，如何建構壽命績效指標(lifetime performance index)的估計量，進而提出壽命績效指標的假設檢定程序。為了使壽命績效指標能夠更合理且更準確的應用於產品壽命的績效評估，本文提出壽命績效指標的假設檢定程序，包括幾個主題，於第二章考慮產品壽命服從指數分配的情況下，以型II右設限樣本建構壽命績效指標的最大概似估計量與均勻最小變異數不偏估計量，並透過這些估計量發展出一個新的假設檢定程序來評估產品的壽命績效。第三章延續第二章的研究，利用上記錄值樣本建構壽命績效指標的均勻最小變異數不偏估計量，進而發展出一套新的假設檢定程序來評估產品的壽命績效是否達到顧客要求的水準。由於指數分配是韋伯分配的特例之ㄧ，因此更進一步說明產品壽命在韋伯分配下，如何建構產品的壽命績效指標之均勻最小變異數不偏估計量，並藉由此估計量發展出新的假設檢定程序來評估產品的壽命績效。最後，第四章則提出本研究的結論及未來研究的建議。此外，本研究也以數值範例來說明如何應用本文所提出之檢定程序來評估產品壽命之績效。

關鍵字

製程能力指標；設限樣本；上記錄值；最大概似估計量；均勻最小變異數不偏估計量；蒙地卡羅模擬

並列摘要

For the manufacturers and service industry, they not only need to produce or supply customers the products meet with the specification, but also have to satisfy them by enhancing process capability through regulation and improvement. Process capability indices(PCIs) are used as a means of measuring process potential and performance. The better process capability, the higher level of product quality it is, and the conforming rate. Until now, the literatures of quality performance mostly assumed the quality characteristics of product with the Normal distribution. However, the lifetime of products generally may possess an exponential, Weibull or gamma distribution and so on. Under a exponential distribution, this study constructs a maximum likelihood estimator (MLE) and an uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index. Then the MLE and UMVUE of the lifetime performance index are utilized to develop the new hypothesis testing procedure. To more reasonably and accurately utilize the lifetime performance index in assessing the lifetime performance of products, this study constructs a new hypothesis testing procedure. This thesis mainly focuses on some topics. There are three topics included in this study. In Chapter 2, under the exponential distribution, this study constructs MLE and UMVUE of the lifetime performance index based on the type II right censored sample. Then, the MLE and UMVUE of the lifetime performance index are utilized to develop the new hypothesis testing procedure. In Chapter 3, we extend Chapter 2’s idea to construct the UMVUE of the lifetime performance index based on the upper record values. Then the UMVUE of the lifetime performance index is utilized to develop the new hypothesis testing procedure. In addition, the Weibull distribution includes the exponential distribution as the special case. Hence, under the Weibull distribution, this study constructs the UMVUE of the lifetime performance index based on the upper record values. Then the UMVUE of the lifetime performance index is utilized to develop the new hypothesis testing procedure. Moreover, a practical example is illustrated to employ the testing procedure to determine whether the process is capable. Finally, the concluding remarks and future research directions are made in Chapter 4.

並列關鍵字

Process capability index ； censored sample ； upper record values ； maximum likelihood estimator ； UMVUE ； Monte Carlo simulation

參考文獻

1.吳忠武、李汶娟、侯宏政(2007)，「Rayleigh壽命商品之績效評估」，計量管理期刊，vol. 4, no. 2, 147-160。

16. Hogg, R. V., McKean, J. W. and Craig, A. T. (2005), Introduction to Mathematical Statistics, Sixth Edition, Pearson Prentice Hall, Pearson Education, Inc.

2. Anderson, D. R., Sweeney, D. J. and Williams, T. A. (1990), Statistics for Business and Economics, West Publishing Company, Saint Paul, MN.

4. Boyles, R. A. (1991), The Taguchi capability index, Journal of Quality Technology, 23, 17-26.

5. Chan, L. K., Chang, S. W. and Spiring, F. A. (1988), A new measure of process capability Cpm, Journal of Quality Technology, 20(3), 162-175.

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指數產品的品質績效評估研究

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