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系統識別號 U0026-2007201323375100
論文名稱(中文) 建構使用中產品失效率預測區間以保固政策效應下市場故障資料為例
論文名稱(英文) Prediction Intervals for Future Failure Rates of In-service Products Based on Field Failure Data with Warranty Strategy Effects
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 101
學期 2
出版年 102
研究生(中文) 宋碧樺
研究生(英文) Pi-Hua Sung
學號 R26004019
學位類別 碩士
語文別 英文
論文頁數 83頁
口試委員 指導教授-鄭順林
口試委員-陳瑞彬
口試委員-張升懋
中文關鍵字 貝式  自助法  樣本內預測  保固資料  保固效應模型 
英文關鍵字 Bayesian  Bootstrap  within-sample prediction  warranty data  warranty strategy effect model 
學科別分類
中文摘要 本研究最主要的目的是針對產品未來失效機率建構預測區間。這些失效機率的預測區間可以提供決策者決定備料數量的參考。做為積極的決策可以參考本研究中所建議的累積失效機率上限,而保守的決策亦可參考累積失效機率下限。如果他們可以較準確地預測產品未來失效個數,那麼他們可以保存倉庫裡的產品數量,同時也可以降低庫存成本。否則,嚴重的預測誤差會給公司帶來龐大的財務負擔。我們使用累積失效機率來監控產品的表現,並透過區間來量化可能的預測誤差。

因為新的"使用者第一次開機時間" (FUB) 的資訊收集,造成我們的資料產生了動態多重右設限以及消費者行為效應,這也是本研究最主要的挑戰。本研究最主要的貢獻是我們結合了保固效應模型,針對使用中的產品,透過自助法以及貝式方法建構預測區間。首先,我們針對提出的方法進行模擬來評估各種區間表現的優劣。接著,我們將我們提出的方法應用在個人電腦保固資料庫上。最後,我們比較自助法以及貝式方法所建構的預測區間,提出各方法的優缺點。最後,我們建議如果沒有先前的資料訊息,使用自助法來建構預測區間。如果已經有過去的資料,我們建議使用貝式方法。有了過去的訊息,我們可以比較合理地選擇模型參數的先驗分布,並透過先驗分布來改善我們的預測結果。
英文摘要 In this study, the main goal is developing prediction intervals for future failure rate of in-service products. According to these prediction intervals, decision maker may utilize the bounds of prediction intervals to decide how many spare parts are needed. If they can precisely predict the future number of defects, they may be able to keep an appropriate stock level and reduce the inventory cost. Serious prediction error will cause great financial damage for companies. We use cumulative failure rate to monitor the performance of components of the products. The possible prediction error is evaluated by an interval.

Due to the newly collected First User Boot (FUB) information occurred, a dynamic multiple censored problem and the effects of customer behaviors occur in our data. The contribution of our work is that we construct rediction intervals with Warranty Effect (WE) model for within-sample problem through bootstrap and Bayesian approaches. We first use simulation experiments to evaluate the performance of each prediction intervals. Second, a guideline for applying our proposed methodologies will be performed, using personal computer warranty data for illustration. Finally, we compare the bootstrap analysis results with Bayesian's and conclude the pros and cons for both bootstrap and Bayesian approaches.

We finally conclude that if no previous data is available, we suggest using data-driven approach, bootstrap manner, to obtain corresponding prediction intervals. If there is more obtainable data, we recommend using Bayesian approach. With more obtainable data, we can rationally choose proper prior distributions for model parameters. And with these prior knowledge, we can improve our predictive results.
論文目次 1. Introduction............................................1
1.1 Background and Motivation..............................1
1.2 Literature Review......................................3
1.2.1 Model Building for Lifetime Data of Warranty Database3
1.2.2 Within-sample Forecasts of Future Failure Number.....4
1.3 Overview...............................................6

2. Methodology.............................................7
2.1 Statistical Lifetime Model and Likelihood Function.....7
2.2 Bayesian Scheme for Within-sample Prediction...........9
2.2.1 Prior and Posterior Distribution.....................9
2.2.2 MCMC Algorithm and Bayes stimator...................11
2.2.3 Bayesian Within-sample Prediction Interval..........13
2.3 Bootstrap-based Scheme for Within-sample Prediction...14
2.3.1 Overview of Bootstrap Methods.......................14
2.3.2 Bootstrap-based Within-sample Prediction Interval...18

3. Simulation Study.......................................20
3.1 Bayesian Framework....................................21
3.1.1 Single Right Censored Data..........................23
3.1.2 Multiple Right Censored Data........................28
3.2 Bootstrap-based Framework.............................39
3.2.1 Evaluating Coverage Probabilities of
Bootstrap-based Prediction Intervals................39
3.2.2 Single Right Censored Data..........................44
3.2.3 Multiple Right Censored Data........................50

4. Application............................................56
4.1 Personal Computer Warranty Data Description...........56
4.2 Data Exploration......................................57
4.3 Model Selection and Model Fitting.....................59
4.4 Within-sample Prediction with WE Model................62
4.4.1 Bootstrap Approach..................................66
4.4.2 Bayesian Approach...................................69
4.4.3 Comparison of Bootstrap-based and Bayesian
Approaches..........................................73

5. Conclusions and Future Work............................76
5.1 Conclusions...........................................76
5.2 Future Work...........................................77

Bibliography..............................................79
Appendix..................................................82
Appendix A. Definition and Theorem........................82
參考文獻 Abdel-Aty, Yahia (2012), “Bayesian prediction of future number of failures based on finite mixture of general class of distributions”, Statistics, 46(1), 111–122.

Albert, Jim (2007), Bayesian computation with R, Springer.

Cha, Ji Hwan and Giorgio, Massimiliano (2012), “A note on the failure rates in finite mixed populations”, Journal of Applied Probability, 49(2), 405–415.

Chen, Yen-Yu (2010), “Inferences by using convolution models for field failure warranty data with lag time problem”, Master’s thesis, National Cheng Kung University.

Chib, Siddhartha (2008), “Markov chain”, Technical report, Humboldt Universitat zu Berlin.

Condra, Lloyd W. (2001), Reliability improvement with design of experiments, volume 59, CRC Press.

Ebrahimi, Nader (2009), “Bayesian framework for prediction of future number of failures from a single group of units in the field”, Reliability Engineering & System Safety, 94(3), 773–775.

Friedman, Jerome, Hastie, Trevor, and Tibshirani, Robert (2009), The Elements of Statistical Learning : Data Mining, Inference, and Prediction, Springer Series in Statistics, New York, NY: Springer-Verlag New York, monograph Wageningen UR Library.

Gelman, Andrew, Carlin, John B., Stern, Hal S., and Rubin, Donald B. (2003), Bayesian data analysis, Chapman & Hall/CRC.

Hamada, Michael S., Wilson, Alyson, Reese, C. Shane, and Martz, Harry (2008), Bayesian reliability, Springer.

Hong, Yili, Meeker, William Q., and McCalley, James D. (2009), “Prediction of remaining life of power transformers based on left truncated and right censored lifetime data”, The Annals of Applied Statistics, 3(2), 857–879.

Jack, Nat and Van der Duyn Schouten, Frank (2000), “Optimal repair - replace strategies for a warranted product”, International Journal of Production Economics, 67(1), 95–100.

Jin, Zhezhen, Ying, Zhiliang, and Wei, Lee-Jen (2001), “A simple resampling method by perturbing the minimand”, Biometrika, 88(2), 381–390.

Kundu, Debasis (2008), “Bayesian inference and life testing plan for the weibull distribution in presence of progressive censoring”, Technometrics, 50(2), 144–154.

Lu, Lu and Anderson-Cook, Christine M. (2010), “Prediction of reliability of an arbitrary system from a finite population”, Quality Engineering, 23(1), 71–83.

Lu, Ming-Huei (2012), “Reliability analysis about field failure data considering warranty strategy effect”, Master’s thesis, National Cheng Kung University.

Meeker, William Q. and Escobar, Luis A. (1998), Statistical methods for reliability data, volume 78, Wiley New York.

Newton, Michael A. and Raftery, Adrian E. (1994), Approximate bayesian inference with the weighted likelihood bootstrap”, Journal of the Royal Statistical Society. Series B (Methodological), 3–48.

Nordman, Daniel J. and Meeker, William Q. (2002), “Weibull prediction intervals for a future number of failures”, Technometrics, 44(1), 15–23.

Pradhan, Biswabrata and Kundu, Debasis (2011), “Bayes estimation and prediction of the two-parameter gamma distribution”, Journal of Statistical Computation and Simulation, 81(9), 1187–1198.

Rai, Bharatendra and Singh, Nanua (2006), “Customer-rush near warranty expiration limit, and nonparametric hazard rate estimation from known mileage accumulation rates”, Reliability, IEEE Transactions on, 55(3), 480–489.

Robert, Christian and Casella, George (2009), Introducing Monte Carlo Methods with R, Springer.

Sancetta, Alessio (2012), “Universality of bayesian predictions”, Bayesian Analysis, 7(1), 1–36.

Somboonsavatdee, Anupap (2007), “Contributions to reliability and lifetime data analysis”, Ph.D. thesis, The University of Michigan.
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