A probability inequality for ranges and its application to maximum range test procedures

Summary It is proved that for any fixed argument the sequence (P _k) of the distribution functions of the ranges ofk i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of “log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all pairwise comparisons (Royen 1988, 1989a, 1989b). Under the above assumptions the application of this algorithm can be extended e.g. to pairwise comparisons of variances.     

Bestimmung kostenoptimaler Parameter für den kontinuierlichen Stichprobenplan vonDodge

Summary Dodge's sampling plan for a continuous production process is determined by two constantsi andk. Under some assumptions about the statistical properties of the production process the average loss due to the costs for inspection and for replacing defective units by good ones is described by a loss function. It is shown that there are always constantsi andk which minimize the loss function in a special sense. Tables of these optimum parameters are computed.     

Abstracts

Quality & Quantity -     

The optimal growth of the firm in a growing environment

The paper presents a growth model based on three essential assumptions: perfect knowledge of the future, descreasing returns on investment in a stagnant economy, appearance of new investment possibilities with the growth of the economy. Two cases are considered: the self-financing growth and the borrowing situation in the context of two management policies, the maximization of the discounted flow of dividends and the maximization of the growth rate.