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研究生:盧名慧
研究生(外文):Ming-HueiLu
論文名稱:考慮保固政策效應下基於市場故障資料之可靠度分析
論文名稱(外文):Reliability Analysis about Field Failure DataConsidering Warranty Strategy Effect
指導教授:鄭順林鄭順林引用關係
指導教授(外文):Shuen-Lin Jeng
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:40
中文關鍵詞:市場失效保固資料使用者第一次開機時間保固效應模型保固效應下的隨機啟用模型
外文關鍵詞:Field Failure Warranty DataFUB InformationWarranty Effect (WE) ModelWarranty Effect- Random Start (WE-RAST) Model
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保固為售貨公司對於購買產品顧客的一個擔保。在產品的保固期內,若此產品在正常的使用情況下,而導致產品不能使用或損壞,售貨公司必須無條件的將損壞的產品修理至正常甚至更換新的產品給顧客。保固維修的資料庫建立容易,很多公司建立此資料庫通常是想使用其訊息達到對於維修所需更換的產品元件備料預測。
在保固資料庫中存在著回報延遲與銷售延遲的問題,使得部份資料無法被觀察到以及觀察不到產品真實的失效時間。這樣的問題已經在過去的文獻中已使用褶積模型解決。在本研究中,因為新的使用者第一次開機時間(FUB)的資訊搜集,我們可以直接估得產品的失效時間。然而,新的FUB資訊卻造成了複雜的多重設限的問題。在保固資料庫中並非所有產品都可取得FUB資訊,故本研究分成兩組子集進行討論: FUB子集與非FUB子集。
本研究的主要挑戰是如何適當的採用新的資訊以及如何分別對兩個子集發展出新的、考慮保固政策效應下的失效機率模型。我們在本研究中對FUB子集,提出保固效應模型;而對非FUB子集,我們修訂隨機啟用模型得到一個新的保固效應下的隨機啟用模型。這兩個模型都有考慮到保固政策的效應,包含保固終止前期的維修增量與保固終止後的維修劇減兩種保固所造成的效應。最後,我們使用估得的失效機率來估計所需的備料以達成產品備料準備的目標。
Warranty is a guarantee between a manufacturer and a consumer which can be used to require the manufacturer to rectify failures that occurred in non-human factors within warranty period. Most companies maintain warranty databases for purposes of warranty costs forecasting.
There are report lag problem and sales lag problem in warranty database, which result in partially unobserved data and unobserved use time of the product. Such problems had been resolved by “Convolution Model at the past literature. In this study, the use time estimation can be calculated because of a new FUB ( First User Boot ) information. However it raises up a complicated multiple censored problem. Because not all products have FUB information in the warranty database, two subsets in this study had been considered separately: FUB subset and Non-FUB subset.
The major challenge in this study is from the new-type data in which we want to answer how to use the new information appropriately and how to develop new failure rate models considering the warranty strategy effect to each subset. We propose a new model, Warranty Effect (WE) Model for FUB subset, and by modifying the Random Start (RAST) Model, we get a new Warranty Effect- Random Start (WE-RAST) Model for Non-FUB subset. Both of the models are
considered the influence of warranty strategy, which leads to increments of the call help before the warranty deadline and a sharp reduction of call help after the warranty deadline. Finally, we use the predicted failure rate to estimate the required spare parts for the goal about material preparation.

1. INTRODUCTION......1
1.1 Background and Motivation......1
1.2 Literature Review......2
1.2.1 Age-Based Failure Time Analysis......2
1.2.2 Convolution Model Application......3
1.2.3 Warranty Claims Forecast Analysis......3
1.3 Overview......4
2. WARRANTY DATA EXPLORATION......5
2.1 Warranty Data Description......5
2.2 FUB-Failure-Time and On-Field-Time......9
2.3 Data Exploration......11
3. METHODOLOGY......14
3.1 Model Identification of Time Variable......14
3.1.1 Probability Plot......14
3.1.2 Histogram for Hazard Rate......16
3.2 WE Model for FUB subset......18
3.3 RAST Model and WE-RAST Model for Non-FUB subset......21
3.4 The Prediction for the Staggered Entry Data......24
4. ANALYSIS USING WE MODEL......26
4.1 Model Selection and Model Fitting......26
4.2 WE Model Prediction and Verification......28
5. ANALYSIS USING WE-RAST MODEL......31
5.1 Model Selection and Model Fitting......31
5.2 WE-RAST Model Prediction and Verification......33
6. CONCLUSIONS AND FUTURE STUDIES......37
6.1 Conclusions......37
6.2 Future Studies......38
Bibliography......39
Alam, M. M. and Suzuki, K. (2009), “Lifetime esimation using only failure information from warranty database, IEEE transactions on reliability, 58(4), 573-582.
Chen, Y. Y. and Jeng, S. L. (2010), “Inferences by using convolution models for field failure Warranty data with lag time problem, National Cheng Kung University Department of Statistics.
Escobar, L. A. and Meeker, W. Q. (1999), “Statistical prediction based on censored life data, Technometrics, 41(2), 113–124.
Hong, Y. and Meeker W. Q. (2010), “Field-failure and warranty prediction based on auxiliary use-rate information, Technometrics, May 2010, 52(2), 148-159.
Ion, R. A., Petkova, V. T. , Peeters, B. H. J. and Sander, P. C. (2007), “Field reliability prediction in consumer electronics using warranty data, Quality and Reliability
Engineering International 23, 401-414.
Kalbfleisch, J. D., Lawless, J. F., and Robinson, J. A. (1991), “Methods for the analysis and prediction of warranty claims, Technometrics, 33(2), 273–85.
Kalbfleisch, J. D. and Lawless, J. F. (1988), “Estimation of reliability from field performance studies (with discussion), Technometrics, 30(2), 365–88.
Kalbfleisch, J. D. and Lawless, J. F. (1996), “Statistical analysis of warranty claims data, in Blischke, W. R. and Murthy, D. N. P. (Eds), Product Warranty Handbook, Marcel Dekker, New York, NY, 231–59.
Lu, L. and Cook, C. M. A. (2010), “Prediction of reliability of an arbitrary system from a finite population, Quality Engineering, 23(1), 71-83.
Lawless, J. F. (1998), “Statistical analysis of product warranty data, International Statistical Review, 66(1), 41–60.
Lawless, J. F. and Kalbfleisch, J. D. (1992), “Some issues in the collection and analysis of field reliability data, in Klein, J. P. and Goel, P. K. (Eds), Survival Analysis: State of the Art, Kluwer Academic, Dordrecht, 141–152.
Meeker, W. Q. and Escobar, L. A. (1998), Statistical Methods for Reliability Data, New York: Wiley & Sons.
Robinson, J. A. and McDonald, G. C. (1991), “Issues related to field reliability and warranty data, in Liepins, G. E. and Uppuluri, V. R. R. (Eds), Data Quality Control:
Theory and Pragmatics, Marcel Dekker, New York, NY.
Suzuki, K. (1985a), “Nonparametric estimation of lifetime distribution from a record of failures and follow-ups, Journal of the American Statistical Association, 80(389), 68–72.
Suzuki, K. (1985b), “Estimation of lifetime parameters from incomplete field data, Technometrics, 27(3), 263–271.
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