Research On Reliability Assessment Methods And Applications Based On Small Sampled Complex Information Sets

During the development course of arm equipments, different kinds on tests must be arranged to guarantee the reliability. For the limitation of time and money, tests sample might be very small. At the same time, the test information arrived often appears such characteristics as no failure, grouped, contaminated or missing, etc., belong to complex information test sets. Traditional statistical inference methods currently might not deal with this complexity properly. Therefore, the reliability assessment methods based on small sampled complex information test sets be studied systematically according to the characteristics and producing mechanisms of different complex information sets.(1)In the aspect of reliability assessment based on zero failure data, three methods were proposed. The MMLE-Bayes-Weibull method is proposed for the reliability assessment of Weibull products. By introducing environment factor and similarity factor, different kinds of prior zero data can be objectively fused. For the long life degradation products, in the condition of zero failure, through modeling of degradation path and introducing the concept of fuzzy failure, a kind of fuzzy reliability assessment method is proposed for long storage equipment. The Bayes reliability assessment method is proposed for k/n system with sequential statistics and the second likelihood estimation method(ML-II).(2)In the aspect of reliability assessment based on grouped test data, a Bayesian estimation method for the parameter of exponent distribution is proposed. Because it is difficult to determine the prior distribution of the parameter directly,we consider the prior distribution of the probability that failures occur in each interval,and use Dirichlet distribution as its prior distribution.The posterior estimation of the parameter is obtained by minimizing the loss function.(3)In the aspect of reliability assessment based on contaminated data, a Bayes method for exponential life model, which is contaminated with normal distribution data during Type II censoring, is proposed and. The hyper parameters in the prior distribution is estimated by Bootstrap methods.(4)In the aspect of reliability assessment based on missing data, three methods were proposed. A Bayes method, which can appropriately utilize information coming from multiple sources, is proposed to solve the problem of reliability assessment for Weibull distribution products with small sampled missing data in constant-stress accelerated tests. Firstly, the likelihood function of the missing data is arrived from probability atom method. At the same time, the prior distribution of the unknown parameters in the likelihood function is set up according to their physics mechanism. The hyper parameters in the prior distribution functions can be estimated by ML-II method. A reliability growth analysis method is proposed with small sampled missing data. The non-informative prior distribution is constructed by Box-Tiao method. The current reliability growth model are mostly set up for repairable system, otherwise, most arm equipment are non-repairable products, that is, if the products in tests failed, they can not be repaired to test again. A new Bayes reliability growth model is proposed for the non-repaired arm equipments with small sample. Firstly, the likelihood function of test data is arrived through asynchronous growth theory. Then Gamma-uniform prior is constructed whose parameters are estimated through the second maximum likelihood method. The reliability growth law for the arm equipment is concluded by Bayes methods. In the end, an example is given to illustrate the efficiency of the method.