## Bayesian methods in reliability |

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adaptive analysis approximately assessment assumed assumption Bayes Bayesian approach Bayesian methods Bayesian statistical beta density Beta distribution calibration components Computer confidence interval consider credible interval curve data of Table data set defined degrees of belief denote Duane example expert judgements exponential failure rate faults give given hazard rate independent inferences inter-failure km*year labelling parameters likelihood function likelihood principle Littlewood LNHPP mathematical maximum likelihood estimate measure median Methods in Reliability MTBF non-Bayesian number of failures observed obtained parameter 9 particular plots Poisson distribution Poisson process posterior beliefs posterior density posterior distribution posterior mean prediction system predictor prequential likelihood prior beliefs prior density prior distribution probability density problem procedure random variable repairable systems sample seed variables sequence shown in Figure Smith section software reliability specified sufficient statistics Suppose theorem u-plot U.S. data uncertainty unknown parameters vague prior values