The problem of estimating the precision （or variance） of a product under development testing is considered from a Bayesian approach m sets of precision trials are performed under conditions which lead to an ordering of precisions h1<h2<…<hm. The parameter of interest is hm

the final underlying precision of the product. The marginal posterior probability density function for hm is obtained when the conjugated type prior distribution without prior knowledge is assumed. An approximate solution is derived to meet the practical engineering needs

and the method is illustrated