Statistical Inference For Dynamic Population In Equipments Test Evaluation

With the increasing complexity of weapons and sorts of mechatronic products, the dynamic changing process of products lifecycle properties has become more complicated, which brings diverse test evaluation means. Sorts of data (multistage and multi-source) should be synthesized to realize the proper modeling and analysis of products performance changing during development phase. In the domain of equipments test evaluation, the typical problems are multistage reliability growth test evaluation and multi-batch or multi-source weapons tactical and technical indices evaluation. Both problems show distinct features of dynamic population statistics, and the corresponding statistical inferences veracity will greatly affect the risk of equipments acceptance and usage. It has great theoretical significance and application value to carry out studies of dynamic population statistics in the domain of equipments test evaluation.For the dynamic population statistics problems in equipments test evaluation, the essential theoretical problems are systematically studied for the first time. In both important domains of multistage reliability growth evaluation and multi-batch or multi-source hit probability synthetic evaluation, concrete and detailed studies are given to four types of representative problems, and several innovative approaches are proposed. The leading contents and outcomes are as follows.1. The basic theory of dynamic population statistics in equipments test evaluation. After a systematical review of developments of dynamic population statistics, the essential features of dynamic population statistics are presented. By compare with other related subjects, the thesis grasps its basic connotation and several key theoretical problems. The preprocessing methods involved are analyzed, and three elementary approaches of dynamic population statistics are summarized and presented with discussion of their features and prospects: constraints based multi-population integrated estimation, linear model based dynamic population forecasting and Bayesian based multi-source prior information fusion.2. Evaluation approaches of multistage reliability growth test with delayed fix mode. The reliability changing rules of exponential life type products are analyzed firstly. The MCMC (Markov Chain Monte Carlo) method is introduced to the computation of the ordinal constrained Bayesian posterior, and it's easy to operate with high precision. Different acquisition ways of improvement factor and different conversion rules of adjacent stages failure rates are compared and discussed. In the improvement factor approach, a new conversion principle is put forward, which uses only the proportional relation and stochastic order relation and can restrain the arbitrary decision by human. Both approaches by improvement factor and ordinal constraint respectively are compared, and the general choosing rules are discussed. For the case of more stages, the linear model and Bayesian dynamic forecasting are introduced to realize the incursive estimation of failure rates.3. Evaluation approaches of multistage reliability growth test with hybrid fix modes (instant & delayed fix modes). Two models for such process are presented: MS-NHPP-I&II (Multi-Stage Non-homogeneous Poisson Process Type I&II), followed with their features, application domains and choosing rules. For MS-NHPP-I, the ordinal constraints of failure intensities are established at stage terminals. For MS-NHPP-II, ordinal constraints of failure intensities are established at stage conjunctions. The Bayesian posterior is computed by MCMC based on Metropolis-Hastings principle. For multiple equipments tested simultaneously, the proportional relations are established on the mean value function at a particular point. And then by improvement factor, the multistage analysis diagram is established. Finally, by analysis of the linear relation of stage parameters in both models, the linear model is established based on the proportional intensity assumption, followed with parameters estimations and model check approaches.4. Evaluation approaches of hit probability based on multi-batch test data. Firstly, the computations of missile hit probability are analyzed under complex conditions (cluster warhead, small sample size, target rotation, etc.) For the cluster warhead, a method of numerical integral mixed with statistical simulation is proposed. For small sample size, the altered Bootstrap and empirical Bayesian methods are presented for the bivariate normal variable. Based on the above, the distribution parameters variations are analyzed for the multi-batch test, and the ordinal constraints of the mean and variance parameters of both directions are established accordingly. By MCMC, the parameter posteriors can be obtained under complex constraints thus to realize the multi-batch test data fusion.5. Evaluation approaches of hit probability based on multi-source test data. The thesis defines the prior sample size constrained ML-II (Maximum Likelihood Type II) estimation of the field data and the corresponding marginal density, denoted respectively as SCML-II (prior sample Size Constrained ML-II) and SCMD (prior sample Size Constrained Marginal Density). A novel way of fusion estimation of normal distribution parameters is presented based on mixed posterior with modified weights. Based on it, the simulation credibility based test evaluation method is improved for smaller MSE (Mean Square Error) and stronger capacity to restrain from obliteration phenomenon. As a further extension, the SCML-II and SCMD of multivariate normal distribution parameters are put forward to solve the hit probability computation with bidirectional correlation. Finally, the conventional fusion structure of multi-source prior information is improved for better applicability by adding the non-informative prior to the mixed prior and using SCMD in the mixed posterior weights.