Finding the Center of the Cost Distribution for Choosing a Metric

Summary

This chapter is an important one of this book. It is an introduction to the algorithms that have to be used for finding a specific model.

In this chapter we study the distribution of the cost without using any other variable; the purpose is to see how the center of this distribution can be found.

Generally speaking the distribution of a quantitative variable can be described (see Chapter 2) as a set of two things:

• 1. The value of the “center” of this distribution.

• 2. How the “residuals” (the differences between the values of the variable and the center just found) are scattered around this center.

Splitting a distribution into these two terms is extremely useful and is the basis of the work the cost analyst has to carry out. When trying to extract from the data a specific cost model for forecasting the cost of future products, the center of the distribution will lead to what can be called the cost-estimating relationship (or CER) from which the “nominal cost” of these future products will be computed.

The “residuals” are what is left from the data when the value of the center has been removed from the cost values.

This part deals only with the search of the center as the definition of the metric to be used is a prerequisite toward this end. Part IV will study the residuals.

The question of finding the center of a distribution is completely independent of the formula type that can be chosen by the cost analyst. The answer to it can be used whatever this type: this is the reason of its importance.

Choosing the algorithm which will be used for finding the center of a distribution is one of the most important decision that the cost analyst has to make (the second one being the formula type). For this reason the different algorithms which can be used will be explored in order for the cost analyst to understand the advantages and disadvantages of each. The reader will discover that no one solution is theoretically better than the other ones and imposes itself to the cost analyst.

The distributions which are studied here use one variable only. Consequently the “centers” are quantified with one value only. When we study the distribution involving two or more variables, the center cannot be one value anymore: we will introduce, in this Part III, the concept of the “dynamic center”. This concept will use all the developments made in this chapter.