Titlebook: Standardization: Mathematical Methods in Assortment Determination; C. Bongers Book 1980 Springer Science+Business Media Dordrecht 1980 Mat

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https://doi.org/10.1007/978-94-017-6403-2Mathematica; mathematical method; mathematics; standardization

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The Construction of the Size Pattern and the Determination of the Number of Sizes When StandardizinIn this chapter we shall derive the conditions the size pattern has to satisfy in order to be optimal. In the literature about the subject these conditions are called the “recursion formulae.” This term also shall be used by us; later in this chapter the meaning of the word “recursion” in this context will be explained.

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The Recursion Formulae for the Normal Distribution,The probability density function of the normal distribution has the form

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The Estimation of the Parameters of a Probability Density Function Using a Table of Observed FrequeIn the preceding chapters, the probability density function of the required sizes was assumed to be known. In practical situations, however, this will in general not be the case. Before calculating the optimal size pattern, we then first have to specify a density function, on the basis of a sample, and next its parameters must be estimated.

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Further Analysis of Optimal Size Patterns,In this chapter three subjects are discussed which are related to the choice of an optimal size pattern. In the first place we will consider what consequences—in terms of the conditional expected adaptation losses—this choice may have for the various subpopulations. Here we use a technique which is known as “analysis of variance.”

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The Grid Restriction,The grid restriction is the first of the three restrictions we will introduce. As its name already suggests the restriction requires that the size pattern forms a grid of the type indicated by Fig. 14.1. In the figure the sizes are located at the intersection points of the horizontal and vertical lines. The grid thus contains 20 sizes.

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C. Bongersas developed particularly rapidly in the last decade. These developments have been stimulated by a wide range of interests and have encompassed a broad spectrum of research chemists. One may now safely claim that polyquinanes are readily available molecules. The more complex members of this class, p