Analysis And Experimental Design Of Degradation Data Based On The Tweedie Exponential Dispersion Process

The reliability modeling method based on product performance degradation data can effectively evaluate the reliability characteristics of highly reliable products.With the progress of production technology and the improvement of material properties,it is almost impossible for products with high reliability and long life to fail in a relatively short time.Under normal working stress,the degradation rate of product performance characteristics is often slow,and the performance degradation information obtained in a relatively short time is often less.The accelerated degradation test can accelerate the degradation of product performance characteristics by improving the stress level,so as to obtain as much degradation information as possible within a specified time,and then can extrapolate the reliability information under normal service conditions more accurately.It is an important test technology to solve the reliability evaluation problems of high reliability and long life products.In order to ensure the evaluation accuracy of reliability index and maximize the efficiency and cost ratio of the test,the optimization design theory and method of accelerated degradation test has become a research hotspot.The Tweedie exponential dispersion process has the advantages of good generalization and wide application range,and the common Wiener process,gamma process and inverse Gaussian process are its special cases.The Tweedie exponential dispersion process has a better fitting effect on the data and can more effectively describe the law of data degradation.However,the optimal design of accelerated degradation test based on Tweedie exponential dispersion process is still an urgent problem to be studied.The specific research content of this paper includes the following aspects:(1)First,the degradation process of the product is assumed to follow the Tweedie exponential dispersion process,and on the basis of a series of assumptions,the degradation model and its likelihood function of the product in the constant-stress accelerated degradation test are derived.Then,the optimal test design of the two optimization problems(D-optimality,V-optimality)is discussed respectively.Through theoretical proof,the optimal test plan of the constant-stress accelerated degradation test at multiple stress levels is as follows: the simple constant-stress accelerated degradation test of the minimum stress level and the maximum stress level are used only,and the sample distribution proportions under the minimum and maximum stress levels are derived.At the same time,the influence of the stress level on the objective function of the optimization problem is considered.It is concluded that the lower stress level should be arranged as small as possible and the higher stress level should be arranged as large as possible.Finally,a numerical example is used to compare with other constant-stress accelerated degradation test schemes to verify the efficiency of the proposed optimal scheme,and the theoretical results are further verified by simulation.(2)The optimal experimental design of step-stress accelerated degradation test based on Tweedie exponential dispersion process is theoretically presented.Firstly,based on a series of experimental hypotheses,a step-stress accelerated degradation test degradation model is established according to the incremental stationarity of Tweedie exponential dispersion process,and the likelihood function of the parameters in the model is given.Then,the optimal test design based on D-optimality and V-optimalityis discussed respectively.It is proved that the optimal step-stress accelerated degradation test plan is a simple step-stress accelerated degradation test plan which only uses the minimum and maximum stress levels,and the specific expression of the optimal step-stress accelerated degradation test plan is derived.In other words,the distribution ratio of sample detection times under minimum and maximum stress levels is theoretically given.Finally,the theoretical results are verified by a set of case data and simulation data.(3)The Bayesian optimization design of accelerated degradation test based on Tweedie exponential dispersion process is discussed.Firstly,the theoretical framework of Bayesian optimization design for accelerated degradation tests is given.Then the total test cost does not exceed the preset width value as the constraint condition,D-optimality and V-optimality as the optimization criteria,to determine the optimal sample size,detection interval and sample distribution under various stresses in the accelerated degradation test.Finally,a numerical example and simulation were used to illustrate the proposed model and method,verify the feasibility of the proposed method,further analyze the sensitivity of the optimal design to the prior distribution of parameters,and compare and analyze the traditional optimization design and Bayesian optimization design of the accelerated degradation test.