Search results

SummaryThe inverse hypergeometric random variable is defined. Properties of the distribution, in particular the relationship to the hypergeometric, are discussed and a number of important applications are reviewed. Finally, an alternative definition which permits an easy extension to the multivariate case is given.

Variables sampling plans based upon continuous distributions are well known. The usual assumption is that a measurable characteristic associated with a product has a normal distribution, a case which has been treated extensively in the literature. Other continuous distributions, particularly the exponential, have also been used as models. In this paper we discuss variables sampling plans for situations in which the measurable characteristic has either a Poisson or a binomial distribution.

AbstractA review of univariate tolerance intervals is presented from an application‐oriented point of view. Both β‐content and β‐expectation intervals are defined and considered. Standard problems are discussed for the distribution‐free case and with various distributional assumptions (normal, gamma, Poisson) which occur most frequently in practice. The determination of sample size is emphasized. A number of examples are used to illustrate the types of problems which permit solutions with the excellent tables now available.

AbstractProcedures are described which yield single and double sample Dodge‐Romig [1] lot tolerance percent defective (LTPD) rectifying inspection plans. For the determination of such plans only a desk calculator and standard tables of the discrete probability distributions are required. Some advantages gained by using these procedures rather than the Dodge‐Romig table include: (a) The Consumer's Risk is not limited to 0.10. (b) More choices of LTPD are available. (c) Smaller average total inspection is achieved by using a plan designed for specific "process average" and lot size rather than a compromise plan designed to cover intervals on these two parameters.