βExpectation and β-content tolerance intervals for dependent observations

Methods of constructing exact tolerance intervals (β-expectation and β-content) for independent observations are well known. For the case of dependent observations, obtaining exact results is not possible. In this article we provide an approximate method of constructing β-expectation tolerance intervals via a Taylor series expansion. Examples of independent observations are considered to compare the intervals constructed with those obtained by the exact method. For the case of non-stationary type processes we have proposed a method of constructing approximate β-content tolerance intervals. Once again an example is given to illustrate the results.