Title Page
Contents
Abstract 12
Ⅰ. Introduction 14
1.1. Research Background and Purpose 14
1.2. Scope of the Research 17
Ⅱ. Literature Review 19
2.1. Classification of Failure Types in Accordance with Failure Rates 19
2.1.1. Infant Mortality 19
2.1.2. Random Failure 20
2.1.3. Wear-out Failure 21
2.2. Reliability Engineering Using Bayesian Inference 22
2.3. Stress-Time Relationship in Reliability Engineering 24
Ⅲ. Design of the Random Failure Test and Statistical Probability Estimation 26
3.1. Introduction 26
3.2. Phase I: Understanding Failure Mechanisms, and Test Design 28
3.3. Phase II: Estimating Failure Probability Based on Statistical Analysis 31
3.4. Design of the Random Failure Test and Estimating Failure Probability of Brake Discs 37
3.4.1. Random Failure Testing and Temperature Stress Results 38
3.4.2. Statistical Analysis 39
3.5. Discussion 42
Ⅳ. Estimation of Random Failure Probability Based on Bayesian Inference 43
4.1. Introduction 43
4.2. The Process of Estimating Random Failure Probability Using Bayesian Inference 45
4.2.1. Bayesian Inference 45
4.2.2. Estimating Random Failure Probability Based on Bayesian Inference Process 53
4.3. Numerical Experiments 58
4.3.1. Experimental Conditions 59
4.3.2. Analysis of the Results Depending on the Hyperparameters 68
4.4. Discussion 79
Ⅴ. Statistical Estimation for Random Failure Probability over Time 81
5.1. Introduction 81
5.2. Stochastic Process for Simulation 83
5.2.1. Poisson Process 84
5.2.2. Wiener Process 86
5.3. Statistical Estimation for Random Failure Probability over Time Process 89
5.4. Numerical Experiments 93
5.4.1. Experimental Conditions 94
5.4.2. Analysis of the Results Based on the Simulation Model 96
5.5. Discussion 104
Ⅵ. Conclusion 106
References 108
국문요지 117
〈Table 1〉 The trajectory models favoured by reliability engineers 32
〈Table 2〉 Description of probability distributions favoured by reliability engineers 35
〈Table 3〉 Test conditions of brake discs 38
〈Table 4〉 Experimental results 38
〈Table 5〉 The extrapolated temperature values based on the Gompertz model's predictions 40
〈Table 6〉 Random failure probability by brake disc temperature 41
〈Table 7〉 Common conjugate priors 46
〈Table 8〉 Conjugate priors in reliability engineering 47
〈Table 9〉 Estimated lognormal parameters on stress levels 59
〈Table 10〉 The experimental conditions 60
〈Table 11〉 Experimental conditions for the location parameter hyperparameters 66
〈Table 12〉 Homogeneity test for stress levels (the scale parameter) 67
〈Table 13〉 The hyperparameters of the scale parameter 67
〈Table 14〉 Comparison of RMSE ratios from maximum likelihood and Bayesian estimations 73
〈Table 15〉 Maximum temperature of single braking according to vehicle speeds 95
〈Table 16〉 Results of the statistical analysis performed on the open data 97
〈Table 17〉 A linear model of the surface temperature of a disc brake during sudden braking events 99
〈Table 18〉 Simulation model-based random failure probabilities of Incheon taxis due to hot judder 102
〈Figure 1〉 A comparison of wear-out and random failures 26
〈Figure 2〉 The two-phase process used to estimate the probability of random failure: Phase I 28
〈Figure 3〉 Determination of the independent and dependent variables 29
〈Figure 4〉 Differences between failure modes 30
〈Figure 5〉 Random failure test 30
〈Figure 6〉 Two-phase process used to estimate random failure probability: Phase II 31
〈Figure 7〉 Estimation of failure stress values 32
〈Figure 8〉 Typical structure of each regression model 33
〈Figure 9〉 Selection of a probability distribution 34
〈Figure 10〉 A brake disc 37
〈Figure 11〉 Representation of BTV models as a function of stress level 39
〈Figure 12〉 Failure plot and Anderson-Darling statistics for the estimated stresses 41
〈Figure 13〉 The procedure of estimating parameters in Bayesian inference 45
〈Figure 14〉 Estimating random failure probability based on the Bayesian inference process 54
〈Figure 15〉 Procedure for estimating random failure probability based on Bayesian inference 55
〈Figure 16〉 The tendency of the priors' informativeness 60
〈Figure 17〉 Results of estimated the lognormal distribution parameters at each iteration (burn-in) 62
〈Figure 18〉 Trace plots of successive values of μ, τ, and deviance generated in 10,000 updates from a Gibbs sampler 63
〈Figure 19〉 Autocorrelogram of the parameters and DIC 64
〈Figure 20〉 Comparison of RMSE across varying levels of prior error 70
〈Figure 21〉 Comparison of RMSE across varying numbers of specimens 77
〈Figure 22〉 Simulation of outdoor temperature based on the Wiener process 88
〈Figure 23〉 Statistical estimation for random failure probability over time process 89
〈Figure 24〉 A probability distribution serving as the parameter λ 96
〈Figure 25〉 A probability distribution of the speeds during sudden braking events 98
〈Figure 26〉 A linear model for initial speed of the vehicle 99
〈Figure 27〉 A framework for estimating random failure probabilities over time 100
〈Figure 28〉 Comparison of means and medians of random failure probabilities 103