Aim\ Solving a very important but easily ignored fact in life testing is pointed out

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the life date analysis of the life testing with the original and the replacement items having the same two parameter exponential ditribution is quite different from that of the life testing with the replacement items having a one parameter exponential distribution. Methods Based on the theory of renewal process the maximum likelihood estimators of parameters of the former are given. Results\ The maximum likelihood estimators of parameters based on the theory of renewal process is valid. Conclusion\ The theory of renewal process can solve the difference of the life date analysis of the life testing from the original and the replacement items having the same two parameter exponential ditribution is quite different from that of the life testing with the replacement items having a one parameter exponential ditribution.