Statistical Analysis Of The Fréchet Distribution Under The TFR Model Of The Step Plus Test

Accelerated life testing was proposed in the 1960 s and then introduced into China in the early 1970 s.Compared with the traditional life test,it effectively reduces the time and economic cost of the test,and is the first choice for enterprises and researchers.Up to now,accelerated life testing technology has been widely used in many fields in our country.The Fréchet distribution is one of the most important extreme value distributions,since it was proposed in the 1920 s,scholars at home and abroad have never stopped studying and applying the distribution.Now,Fréchet distribution can be seen in many industries.In this paper,we combine accelerated life step testing with Fréchet distribution to study the statistical properties of Fréchet distribution products under step testing TFR model.The main contents of this paper are as follows.(1)According to the definitions of TFR,TRV and CE models under step stress accelerated life testing,combined with the Fréchet distribution,the failure distributions of Fréchet distribution products under the three models of simple-step stress accelerated life testing are deduced respectively.(2)According to the three failure distributions in(1),the consistency and equivalence among TFR,TRV and CE models are analyzed,and it is concluded that the TRV model is consistent and equivalent to the CE model,while the TFR model is inconsistent and non-equivalent to both the TRV model and the CE model.(3)Based on the failure distribution of Fréchet distribution product under the TFR model of simple-step stress accelerated life testing,the maximum likelihood estimation of each parameter is solved,and finally the transcendental equations for the maximum likelihood estimates of three parameters are given,and the simulation example is analyzed by using software.(4)Based on the definition of TFR model under simple-step stress accelerated life testing,the failure distribution is derived for the Fréchet distribution product under the TFR model of multi-step stress accelerated life testing,and the transcendental equations for the maximum likelihood estimates of all parameter are given,finally,the simulation example is analyzed by using software in the case of three steps(that is,three stress level).