Comparison of approximation methods for computing tolerance factors for a multivariate normal population

In this article, we compare several approximation methods for computing the tolerance factors of a multivariate normal population. These approximate m ethods are evaluated by comparing the Monte Carte estimates of the coverage probabilities with those of the specified ones. Numerical studies indicate that, in general, the tolerance factors based on an approximate method giv en by John, which is commonly used in the literature, are inaccurate when t he number of variates is greater than or equal to 2, bur another approximat ion (which is also due to John) with slight modification gives better resul ts. Using John's idea, we also suggest some new approximations, which give satisfactory results. Two of the new approximations emerge as satisfactory candidates for practical use. Our fairly extensive numerical results provid e guidelines regarding: the choice of the tolerance factor for practical ap plications.