Weibull 分配產品在逐步型I區間設限下之壽命績效指標之最佳實驗設計

Sampling design for the lifetime performance index of Weibull lifetime distribution under progressive type I interval censoring

吳祐誠(Yu-Cheng Wu)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2020年)

https://doi.org/10.6846/TKU.2020.00657

摘要

隨著科學技術日新月異的變化，許多電子產品對我們的日常生活越來越重要，降低產品成本也成為重要的研究方向。在實驗設計中製程能力指標(process capability indices, PCIs) 可用於測量產品質量，並提供有用的信息來評估製程的性能。
當產品的壽命假設服從Weibull分配時，在逐步型I區間設限下，計算出壽命績效指標C下標L之最大概似估計量並以其為檢定統計量發展出檢定程序。我們還考慮檢測次數m是否固定或終止時間T是否固定之下，給定顯著水準和檢定力下，決定最佳實驗的抽樣設計以達到最低實驗總成本。最後，藉由一個數值例子和一個模擬例子說明如何使用本研究所提出的最佳實驗設計之檢定程序以及評估方法。

關鍵字

逐步型I 區間設限 ； Weibull分配 ； 最大概似估計量 ； 製程能力指標 ； 檢定程序

並列摘要

With the ever-changing nature of technology and science, many electronic products are becoming more demanding for our daily life. Furthermore, for the customers, they will choose the products with longer life expectancy and lower failure rate. In addition, the manufacturer will tend to lower the cost of the product but the quality will hold or even better. For measuring the quality of products, Process capability indices (PCI) have provided very useful information to evaluate the performance and the capability of the process. As for the lifetime of products, we use C_L to assess the performance of the lifetime with Weibull distribution.
Our research is focusing on the evaluation of lifetime performance of products with Weibull distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample and it’s used to develop a hypothesis testing procedure. In the condition of either the number of inspections m is fixed or not or the termination time T is fixed or not, we proposed the algorithm to achieve the optimal experimental design to attain the minimum total experimental cost. Finally, we give one simulation example and one practical example to illustrate the use of the proposed experimental design to conduct the testing algorithmic procedure to determine whether the process is capable.

並列關鍵字

progressive type I interval censoring ； Weibull distribution ； maximum likelihood estimator ； process capability index ； testing procedure

參考文獻

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

[2] Caroni, C. (2002a), Modeling the reliability of ball bearings. Journal of Statistics Education, 10(3), pp. 1-8.

[3] Caroni, C. (2002b), The correct ”ball bearings” data. Lifetime Data Analysis, 8(4), pp.395-399.

[4] Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), A new measure of process capability: Cpm, Journal of Quality Technology, 20(3), pp. 162-175.

[5] Cohen, A. C. (1963), Progressively Censored Samples in Life Testing, Technometrics, 5(3), pp. 327–339.