利用上記錄值樣本對具有廣義指數分配的產品之壽命性能指標做績效評估

Performance Evaluation for Lifetime Performance Index of Products for the Generalized Exponential Distribution with Upper Record Values

李汶娟(Wen-Chuan Lee) ； 吳忠武(Jong-Wuu Wu) ； 洪清文(Ching-Wen Hong) ； 何侃錚(Kan-Cheng Ho) ； 林義欽(Yi-Chin Lin)

《品質學報》 20卷3期 (2013/06) Pp. 275-304

https://doi.org/10.6220/joq.2013.20(3).02

摘要

製程能力指標（Process Capability Indices, PCIs）是常被用來衡量控管製程產出的產品是否達到業者所需要求之有效工具。而壽命性能指標CL就常被用來當作測量產品性能的方法，其中L是下規格界限（lower specification limit）。通常製程能力指標都會假設產品品質特性（例如，壽命、抗耐力等等）來自常態分配。然而，那是一個不合理的假設。實際上，一般產品之壽命分配較常為指數分配或與其有關的非常態分配如廣義指數分配（generalized exponential distribution）、gamma分配或Weibull分配等等。另外，在某些現實情況下我們只關心下次發生產品壽命高於之前的紀錄時才需記錄。所以，在本論文中主要探討假設產品壽命來自於一個具有廣義指數分配之上記錄值（upper record values）且利用該分配之參數的最佳線性不偏估計量（Best Linear Unbiased Estimator, BLUE）來建構壽命性能指標CL之估計量並使用此估計量在已知的下規格界限L下來發展出一套對CL之假設檢定程序。因此，買家或製造商可以應用本文中的檢定程序來判斷產品之壽命是否達到所要求之水準。

關鍵字

壽命性能指標 ； 廣義指數分配 ； 上記錄值 ； 檢定程序

並列摘要

The process capability indices (PCIs) is an effective tool for assessing whether product quality meets the required level. The lifetime performance index (or larger-the-better process capability index) CL is frequently used as a means of measuring product performance, where L is the lower specification limit. Most process capability indices assumed that the product quality characteristic comes from normal distribution. Nevertheless, it is not a reasonable assumption. In practice, the lifetime of products may usually follow an exponential distribution or a non-normal distribution which includes the generalized exponential distribution, gamma distribution, weibull distribution, etc. In addition, some practical situations we only care about reality the next occurrence of the product life performance than the previous record only to be recorded. Hence, we propose the estimator of CL to develop a novel hypothesis testing procedure for the lifetime performance index CL based on the best linear unbiased estimator (BLUE) of the parameter for the generalized exponential distribution with the upper record values in the condition of known L. Hence, the purchasers or manufacturers can use the test procedures to determine whether the lifetime performance of products adheres to the required level.

並列關鍵字

lifetime performance index ； generalized exponential distribution ； upper record values ； testing procedure

參考文獻

Ahsanullah, M.(1995).Record Statistics.Commack, New York:Nova Science Publishers.

Arnold, B. C.,Balakrishnan, N.,Nagaraja, H. N.(1998).Records.New York:John Wiley.

Balakrishnan, N.,Cohen, C. A.(1991).Order Statistic and Inference: Estimation Methods.New York:Academic Press.

Boyles, R. A.(1991).The Taguchi capability index.Journal of Quality Technology.23(1),17-26.

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