Weibull Parameters' Trend under Varying Production Lots

不同生產批量下韋伯參數的變化趨勢

10.29977/JCIIE.200705.0004

廖明癸(Ming-Kuei Liao)

韋伯參數 ； 生產批量 ； 韋伯機率紙 ； 免費維修保固 ； Weibull parameter ； production lots ； Weibull probability paper WPP ； free repair/replacement warranty FRW

工業工程學刊

24卷3期（2007 / 05 / 01）

219 - 224

英文

針對保固資料庫的資訊，本文研究資訊產品在不同生產批量下韋伯參數的變化狀況。以三參數韋伯分佈來模擬產品失效模式，利用韋伯機率紙繪圖解析形狀、尺度、位置參數值變化與生產批次的關聯性。以主機板產品為例，在免費維修保固的條件下，可以發現位置參數不為零，隨生產批量的增長，在平順的供應鍊下，其值會趨近於一定值，約為480小時。而形狀參數則會接近1。基本上，形狀與尺度參數則會隨批量的生產品質好壞而有所差異。不易因使用時間的差異而變動。最後針對韋伯各參數的取得，分析產品可靠度在不同生產批次下的變化，以本文為例，在1.5%與2.5%操作時間與MTBF比例下，可靠度分別會下降至0.95與0.90。

Based on warranty databases, this article is a study of how the variation of Weibull parameters in different production lots affects the reliability of electronic appliance. Three-parameter Weibull distribution is performed to simulate product failure mode and Weibull probability paper is used to define the shape, scale and location parameter for each production lot. Two computer motherboard cases are studied under free repair/replacement warranty condition. The results demonstrate the location parameter (γ) is not zero and approaches a constant of 480 hours, under a smoothly fulfillment process. Most of time the shape parameter (β) is close to 1.0. Both the shape and scale (η) parameters significantly reflect product durability. Finally, the reliability trend is affected by parameters set on varying production lots and will decline to 0.95 and 0.90 while operational time moves to 1.5% and 2.5% of MTBF respectively.

1. Attardi, L.,M. Guida,G. Pulcini(2005).A mixed-Weibull regression model for the analysis of automotive warranty data.Reliability Engineering & System Safety,87,265-273.
2. Kalbfleisch, J. D.,J. F. Lawless(1988).Estimation of reliability in field-performance studies.Technometrics,30,365-378.
3. Kleyner, A.,P. Sandborn(2005).A warranty forecasting model based on piecewise statistical distributions and stochastic simulation.Reliability Engineering & System Safety,88,207-214.
4. Liao, A.(2005).Evaluating motherboard reliability from early warranty databases.Warranty Chain Management (WCM) Conference,1-2.
5. Murthy, D. N. P.,I. Djamaludin(2002).New product warranty: a literature review.International Journal of Production Economics,79,231-260.
6. Oh, Y. S.,D. S. Bai(2001).Field data analysis with additional after-warranty failure data.Reliability Engineering & System Safety,72,1-8.
7. Wu, H.,W. Q. Meeker(2002).Early detection of reliability problems using information from warranty databases.Technometrics,44,120-133.
8. Zhang, T.,Y. Ren(2002).Failure data analysis by models involving 3 Weibull distributions.Proceedings of the Annual Reliability and Maintainability Symposium,28/44-31/50.