加速壽命測試下利用不同設限方式推估可靠度模式比較

Estimations of reliability models in accelerated life tests under various types of censored data

楊政廷(Cheng-Ting Yang)

指導教授 ： 黃怡婷

國立臺北大學/商學院/統計學系/碩士(2009年)

摘要

隨著科技的發展，積體電路產品的可靠度也愈來愈高。傳統上以正常環境下大量且持續測試產品壽命之方法受到了相當大的挑戰—測試時間內無法獲取產品壽命資料。因此，不同的資料型態 (如型一設限、型二設限)及不同的加速壽命測試方式亦應運而生。
針對不同的資料型態及加速壽命實驗方法已發展許多不同的估計方法。統計上對於不同的資料型態及壽命分佈，過去的研究著重在於各分佈的參數估計及估計方法間的比較。常用的壽命分佈有指數分佈、韋伯分佈、常態分佈、對數常態分佈等。
在實務考量的操作方式下，加速壽命之資料型態，除一般常用的完整資料 (Complete Data)、型一設限 (Type I Censored Data) 外，須加入區間設限 (Interval Censored Data) 之資料型態。本論文討論在三種資料型態及四種壽命分配下，參數估計的表現。以軟體R將上述各機率分佈在不同資料型態上產品壽命估計繁雜的計算予以模組化進行壽命估計之討論，同時與目前台灣積體電路設計業界對於產品之可靠度估計方式進行比較，並提出實驗操作上之建議及現行方法之限制。

關鍵字

最大概似估計法 ； 指數分佈 ； 韋伯分佈 ； 常態分佈 ； 對數常態分佈 ； 伽瑪分佈 ； 完整資料 ； 型一設限 ； 區間設限

並列摘要

The reliability of integrated circuit improves dramatically, as the semiconductor technology progresses. Traditional reliability testing methods based on a large sample size running long-term test face great challenge since it is no longer possible to obtain lifetime data in a fixed time interval. As a result, many lifetime data may be censored. Many estimations have to be adjusted to analyze censored lifetime data.
There are three types of censored data including Type I censoring, Type II censoring and interval censoring. Many estimations have been developed to estimate the distribution of lifetime under different types of censoring. Furthermore, many of these estimations are proposed under various parametric models. The most commonly used lifetime distributions include exponential distribution, Weibull distribution, normal distribution and lognormal distribution.
The accelerated lifetime can be observed completely, but it can be also censored. The type of censoring includes not only Type I censoring, but also interval censoring. However, in practice, to simplify the process, the estimate of the mean lifetime is obtained under complete data. Thus, the main purpose of this thesis is to fully understand the effect of different censored types and the sensitivity of the parametric assumption. The point and interval estimator of mean lifetime are derived under three different parametric assumption and three different censoring types. The performance of these estimators under various parametric settings are evaluated using Monte Carlo simulation. A real case study is also discussed.

並列關鍵字

Interval censoring ； Maximum likelihood method ； Parametric model ； Reliability ； Type I censoring

參考文獻

[1] Cohen, A. C. (1991). “Truncated and Censored Samples : Theory and Applications”, Dekker, New York.

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[6] JEDEC JEP 122D, (2008). “Failure Mechanisms and Models for Semiconductor Device”, Solid State Technology Association, USA.

[8] Nabendu, P., Chun, J., and Wooi, K.L.(2006). “Handbook of Exponential and Related Distributions for Engineers and Scientists”, Champman & Hall, New York.

[9]　Odell, P. M., Anderson, K. M. and D’Agostino, R. B. (1992). “Maximum Likelihood Estimation for Interval-Censored Data Using a Weibull-Based Accelerated Failure Time Data”, Biometrics, 48, No.3 951-959