The development of a complex electronic system may be divided into several stages. Let λ1 be the failure rate of the system in the i-th stage. In many situations

the reliability of the system increases stage by stage

i. e. λ1>λ2>…> λm. we choose the prior distributions of λ’s to be such that the Bayes confidence interval of A followed from the posterior density function is equivalent to the result of the classical statistics. Let f1 （τ1|λ1） be the conditional probability function

where τ1 is the total life time in the i-th stage

then the posterior density function isthe marginal posterior density function of Am iswhere is

the space formed by is the domain of λj

and is the subspace of 0. The r-confidence interval of λm is（o

λm…）

whereIn classical statistics

we can only use rm to calculate the r-confidence interval for Am

because the statistics r

（i = 1

2

…

m-1） belong to another population. But now we can use the formulas derived in this paper to calculate the r-confidence interval for Am not only by using rm

but also by using τ1

τ2

…

rm-1. The size of the sample of the m-th stage using this method will be smaller than the sample of the m-th stage using the classical statistics.