Joint distribution of X and X(n) for a random sample from the standard normal distribution with applications to a variables sampling inspection procedure which guarantees acceptance of perfectly screened lots.
Julius, Jerome D.
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In this paper, tables of the joint distribution of the sample mean and the largest observation in a sample for a random sample from the standard normal distribution are presented for a variables sampling inspection procedure which guarantees acceptance of perfectly screened lots. The quality of each item in the lot is described by a single quality characteristic. It is assumed that this quality characteristic has a normal density function with known variances Tables of standard truncated normal distribution required to compute the tables of the joint distribution of X and X(n). are also presented. The two sets of tables are also used to show how operating characteristic curves may be computed. Sample size is shown to affect the existence of levels of significance. For small sample sizes (a < 10), certain large levels of significance do not exist for tests of hypothesis concerning truncated normal distributions.
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