Top Level Spacecraft Cost Distribution Study
MacKenzie, D.; Welch, N; Robinson, M
Wyle Inc.

Previous studies have examined the shapes of the probability distributions of top level cost predictions obtained by summing up lower-level predicted costs. These cost sums are typically skewed to the right, towards higher costs. This study focused on comparing the suitability of normal vs. lognormal distributions as top level cost distributions for both spacecraft development and production. Monte Carlo simulations were performed on sums of lognormally-distributed costs, where each cost represented either the development cost or the production cost of typical spacecraft "boxes". The lognormal distribution provided lower errors than the normal distribution in the area of most concern to decision-makers - that above the 65th percentile of cost.

Each cost variable in the simulations was identically correlated with all other cost variables at levels representative of spacecraft development and production environments. Specifically, the correlation coefficients were identical across the non-diagonal elements of the cost-to-cost correlation matrix. The cost distribution variances (standard deviations) were also all identical and typical of space hardware development and production costs.

The primary measures of goodness for comparing the suitability of normal vs. lognormal distributions were the errors of the best fit distributions (normal or lognormal) to the samples of the cost sums, at the 70th, 80th 85th, 90th and 95th percentiles. These errors were plotted as functions of the number of cost elements (boxes) making up the cost sums. They were also plotted as functions of the distribution percentiles.

Besides addressing cases where all of the box costs had the same mean cost, two other cases with non-identical mean box costs were analyzed. These cases are more realistic than the uniform cost cases, since there are often several box costs which are well above the average cost of all boxes in an estimate. The two cases differed primarily in the sizes of the first few box costs, as compared to the total costs for all boxes. The impact of the non-uniformity of the box costs was also assessed using the percentile errors.

The distributions of sums of box costs with highly skewed triangular distributions were also studied as an excursion - even though lognormal distributions have been shown in previous Wyle studies to be more appropriate for spacecraft box costs. Once again, the percentile errors for normal and lognormal best fits to the samples of the cost sums were compared.

The results of this study provide a solid basis for selecting the lognormal distribution over the normal distribution for top level spacecraft costs - for both development and production.

This research was jointly sponsored by Wyle and the National Reconnaissance Office Cost Group (NCG). However, the views expressed in this article are those of the authors and do not necessarily reflect the official policy or position of the NCG or any other organization of the U.S. government.