The Bayesian Equipment Reliability Statistical Demonstration Test Design Based On Experiment Loss

According to statistical theory, the equipment reliability statistical demonstration test design is a process that studies on how to find the test sample size or test time, and then establishes a feasible test plan based on the requirement of reliability hypothesis, risks and precision of reliability evaluation. A good test plan could help equipment test bureau spend the least resource for testing data describing the character of the equip-ment reliability, and estimate equipment reliability exactly with the least test risk for the benefits of equipment's producer and user. In this paper, based on the reliability test loss, using Bayesian method, the reliability statistical demonstration test design method was studied with the constraction on two types of risk and testing condition.The main contributions and innovation of the thesis are as follows:On the basis of Bayesian theory, decision inequation for sampling was deduced us-ing the loss function based on the principle of minimize the posterior expect loss. Con-sidering the cost which will be spent during reliability demonstration test (consists of initial test fee, cost of product, salary, and so on), and the expected loss caused by the risks in hypothesis test (consists of the producer's loss caused by the first risk and the user's loss caused by the second risk), the test loss function in reliability statistical demonstration test was established, and the Bayesian reliability statistical demonstration test design model based on test loss (BTDM) was carried out. The calculating method for the two types of risks based on average risk criteria and posterior risk criteria was discussed and comparatively analyzed based on the Bayesian method. The calculating formulas for the first risk and the second risk were given using the prior distribution of equipment reliability parameter and the likelihood function of the test data. To the problem of equipment reliability statistical demonstration, the common algorithm based on the Matlab software for BTDM was present.Reliability statistical demonstration test design for the equipment whose lifetime was normal distributed was modeled and analyzed. The hypothesis for mean lifetime was converted to the one for the expectation of normal distribution, and the Bayesian reliability statistical demonstration test design model for normal distribution (BTDM-N) was constructed. According to the Bayesian decision inequation, to the certain sample number, the calculating formula of equipment mean lifetime critical value was deduced, acceptance region and rejection region in the Bayesian reliability statistical demonstra-tion test plan for normal distribution were given. The calculating formulas for two types of risks in the BTDM-N were present based on two kinds of risk criteria, the relation-ship of two types of risks and sample number based on the different risk criteria was discussed through the simulation data, which were used for equipment test bureau's de-cision. The solving steps of the best sample number were present based on BTDM-N, the constructing and the calculating process for BTDM-N were illustrated using an ex-ample.The successful ratio was treated as the reliability test parameter for binomial prod-uct reliability statistical demonstration test design, and the Bayesian reliability statistical demonstration test design model for binomial distribution (BTDM-B) was constructed. To certain sample number, the functional relationship of posterior probability ratio and acceptance number was deduced based on the principle of minimize expect posterior loss, and the calculating method of the critical value of acceptance number was present through a example. The calculating formulas of two types of risks in the BTDM-B was given based on average risk criteria and posterior risk criteria, and two types of risks based on the different sample number(acceptance number) for the certain acceptance number(sample number) under the different risk criteria was laid out through a example. The searching iteration of BTDM-B was present with a simulation example using Mat-lab software.The failure ratio was treated as the parameter of the reliability test for exponential product reliability statistical demonstration test design, and the Bayesian reliability sta-tistical demonstration test design model for exponential distribution (BTDM-E) was constructed considering the constraint of the two types of risks, failure number and testing time. To certain failure number, the functional relationship of posterior probabil-ity ratio and testing time was deduced based on the Bayesian decision principle, and the calculating method of the critical value of testing time was given, The calculating for-mulas of two types of risks in BTDM-E based on the average risk criteria and the poste-rior risk criteria were deduced, and two types of risks based on the different failure number(testing time) for the certain testing time(failure number) under the different risk criteria was laid out through a example. The solution method of BTDM-E was illus-trated and validated follow a example based on the character of the exponential distrib-uted product.