Bayesian Reliability Analysis With Evolving, Insufficient, and Subjective Data Sets

A primary concern in product design is ensuring high system reliability amidst various uncertainties throughout a product life-cycle. To achieve high reliability, uncertainty data for complex product systems must be adequately collected, analyzed, and managed throughout the product life-cycle. However, despite years of research, system reliability assessment is still difficult, mainly due to the challenges of evolving, insufficient, and subjective data sets. Therefore, the objective of this research is to establish a new paradigm of reliability prediction that enables the use of evolving, insufficient, and subjective data sets (from expert knowledge, customer survey, system inspection & testing, and field data) over the entire product life-cycle. This research will integrate probability encoding methods to a Bayesian updating mechanism. It is referred to as Bayesian Information Toolkit (BIT). Likewise, Bayesian Reliability Toolkit (BRT) will be created by incorporating reliability analysis to the Bayesian updating mechanism. In this research, both BIT and BRT will be integrated to predict reliability even with evolving, insufficient, and subjective data sets. It is shown that the proposed Bayesian reliability analysis can predict the reliability of door closing performance in a vehicle body-door subsystem where the relevant data sets availability are limited, subjective, and evolving.

[1]  Guo-Ying Li,et al.  ON BAYESIAN ANALYSIS OF BINOMIAL RELIABILITY GROWTH , 2002 .

[2]  Panos Y. Papalambros,et al.  A Bayesian Approach to Reliability-Based Optimization With Incomplete Information , 2006, DAC 2006.

[3]  B. Youn,et al.  Complementary Intersection Method for System Reliability Analysis , 2009 .

[4]  Norman A. Johnson,et al.  Detecting Positive Selection , 2007 .

[5]  B. Youn,et al.  Bayesian reliability-based design optimization using eigenvector dimension reduction (EDR) method , 2008 .

[6]  Rajkumar Roy,et al.  Recent advances in engineering design optimisation: Challenges and future trends , 2008 .

[7]  Ramkumar Rajagopal Bayesian Methods for Robustness in Process Optimization , 2004 .

[8]  Philippe Weber,et al.  Complex system reliability modelling with Dynamic Object Oriented Bayesian Networks (DOOBN) , 2006, Reliab. Eng. Syst. Saf..

[9]  David C. Yu,et al.  Bayesian network model for reliability assessment of power systems , 1999 .

[10]  Jun Zhou,et al.  A Sequential Algorithm for Possibility-Based Design Optimization , 2008 .

[11]  Shaofeng Liu,et al.  Engineering design: perspectives, challenges, and recent advances , 2009 .

[12]  Carl-Axel S. Staël von Holstein,et al.  Exceptional Paper---Probability Encoding in Decision Analysis , 1975 .

[13]  Volker Schulz,et al.  Problem Formulations and Treatment of Uncertainties in Aerodynamic Design , 2009 .

[14]  Mark P. McDonald,et al.  Reliability-Based Optimization With Discrete and Continuous Decision and Random Variables , 2008 .

[15]  Z. Mourelatos,et al.  A Design Optimization Method Using Evidence Theory , 2006, DAC 2005.

[16]  Harry F. Martz,et al.  Bayesian reliability analysis of series systems of binomial subsystems and components , 1988 .

[17]  Kyung K. Choi,et al.  Selecting probabilistic approaches for reliability-based design optimization , 2004 .

[18]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[19]  B. Youn,et al.  Inverse Possibility Analysis Method for Possibility-Based Design Optimization , 2006 .

[20]  Kyung K. Choi,et al.  Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation , 2008 .

[21]  B. Youn,et al.  Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis , 2008 .

[22]  Z. Mourelatos,et al.  Probabilistic analysis of an automotive body-door system , 2004 .

[23]  Fumika Ouchi,et al.  A literature review on the use of expert opinion in probabilistic risk analysis , 2004 .

[24]  R. L. Winkler The Assessment of Prior Distributions in Bayesian Analysis , 1967 .

[25]  John Quigley,et al.  Measuring the effectiveness of reliability growth testing , 1999 .

[26]  Simaan M. AbouRizk,et al.  Simulation input updating using Bayesian techniques , 2004, Proceedings of the 2004 Winter Simulation Conference, 2004..

[27]  Hong-Zhong Huang,et al.  Bayesian reliability analysis for fuzzy lifetime data , 2006, Fuzzy Sets Syst..

[28]  Kari Sentz,et al.  Combination of Evidence in Dempster-Shafer Theory , 2002 .

[29]  P. K. Kannan,et al.  Incorporating Subjective Characteristics in Product Design and Evaluations , 2007 .

[30]  B. Youn,et al.  Possibility-Based Design Optimization Method for Design Problems With Both Statistical and Fuzzy Input Data , 2006 .

[31]  K. Choi,et al.  An inverse analysis method for design optimization with both statistical and fuzzy uncertainties , 2008, DAC 2006.

[32]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[33]  Hongzhong Huang,et al.  Design Optimization With Discrete and Continuous Variables of Aleatory and Epistemic Uncertainties , 2009 .

[34]  Kyung K. Choi,et al.  Hybrid Analysis Method for Reliability-Based Design Optimization , 2003 .

[35]  Jon C. Helton,et al.  Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty , 2006, Reliab. Eng. Syst. Saf..

[36]  Kyung K. Choi,et al.  A mixed design approach for probabilistic structural durability , 1997 .

[37]  T. P. Ryan,et al.  System Reliability Theory: Models, Statistical Methods, and Applications, Second Edition , 2005 .

[38]  H. Martz Bayesian reliability analysis , 1982 .

[39]  Martin Newby,et al.  Bayesian reliability analysis with imprecise prior probabilities , 1992 .

[40]  Jon C. Helton,et al.  Challenge Problems : Uncertainty in System Response Given Uncertain Parameters ( DRAFT : November 29 , 2001 ) , 2001 .

[41]  Robert L. Winkler,et al.  Combining Probability Distributions From Experts in Risk Analysis , 1999 .

[42]  David V. Budescu,et al.  Encoding subjective probabilities: A psychological and psychometric review , 1983 .

[43]  Lev V. Utkin,et al.  A general formal approach for fuzzy reliability analysis in the possibility context , 1996, Fuzzy Sets Syst..

[44]  J. Beck,et al.  Bayesian Updating of Structural Models and Reliability using Markov Chain Monte Carlo Simulation , 2002 .

[45]  Sohrab Asgarpoor,et al.  Fuzzy-based approaches to substation reliability evaluation , 2004 .

[46]  Singiresu S Rao,et al.  Reliability-Based Design , 1992 .

[47]  Ramana V. Grandhi,et al.  Uncertainty Quantification of Structural Response Using Evidence Theory , 2002 .

[48]  Kyung K. Choi,et al.  Integration of Possibility-Based Optimization and Robust Design for Epistemic Uncertainty , 2007 .

[49]  John Dalsgaard Sørensen,et al.  Reliability-Based Optimization in Structural Engineering , 1994 .

[50]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[51]  Hae-Jin Choi,et al.  A Metamodeling Approach for Uncertainty Analysis of Nondeterministic Systems , 2009 .