Hierarchical Bayesian Estimation Of Failure Probability Of Normal Distribution

With the development of technology, more and more products with high reliability appear. We call these data "zero-failure data". The research on the zero-failure data get more and more important as it appear in the recent years.Using convexity-concavity of the normal distribution function,we get hierarchical Bayesian estimations of failure probability from p₁ to p_k and from p_k to p₁:It is estimated value of p_i for average value of two estimated value of p_i. And calculation is performed to practical problem.