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Space Program Schedule Change Probability Distributions

机译：太空计划时间表变更概率分布

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Many complex space and non-space programs are driven by performance requirements with cost and/or schedule being less dominant, if not dependent variables. The net result when comparing actual versus initial projections is cost and schedule change that grows (slips) during the course of a program. Several different samples of space and non-space data were examined to estimate descriptive statistics (e.g., mean, median, skewness, kurtosis) and determine what types of statistical distributions might represent schedule change data. The analyses performed also tested assertions of other researchers who postulated that space and non-space program schedule change can be represented by a normal distribution or an extreme value (Gumbel) distribution. A data sample of 28 NASA programs was examined to test the hypothesis claimed by other researchers that schedule change can be represented by a normal distribution. Both the skewness and kurtosis of the data and results from Anderson-Darling and Kolmogorov-Smirnov statistical tests show that this data is not normally distributed. A large sample of space and non-space programs (365 programs) was obtained and evaluated against 23 different types of continuous univariate distributions. Anderson-Darling and Kolmogorov-Smirnov test results show that all 23 distribution types (including normal and extreme value distributions) were rejected at the 0.05 level. The sample size was subsequently artificially reduced by only including every sixth value both from random and sorted representations of the data that also had values associated with on-time deliveries removed. Anderson-Darling and Kolmogorov-Smirnov test results show that the extreme value distribution could not be rejected at the 0.05 level. This potential contradiction resulted from the much smaller sample size versus the full sample (with or without on-time delivery values removed) which led to diminished statistical power of the Anderson-Darling and Kolmogorov-Smirnov tests; thus not rejecting the extreme value distribution at the 0.05 level. Consequently, sample sizes of roughly 200 or more data points may be necessary to provide a meaningful distribution fit of schedule change and potentially other data. For smaller, and particularly much smaller, sample sizes it is recommended that the data not be evaluated against candidate distribution types, but simply be converted into an ascending cumulative distribution function (CDF) and this function used as appropriate in subsequent analyses (e.g., Monte Carlo simulations).
机译：许多复杂的空间和非空间程序都是由性能要求驱动的，如果不是因变量，则成本和/或进度表的支配性较小。将实际预测与初始预测进行比较时，最终结果是成本和进度计划更改，这些更改在计划执行过程中会不断增加（延误）。检查了空间和非空间数据的几种不同样本以估计描述性统计数据（例如均值，中位数，偏度，峰度），并确定哪些类型的统计分布可能代表进度变更数据。进行的分析还检验了其他研究人员的断言，他们认为空间和非空间计划进度变化可以用正态分布或极值（Gumbel）分布表示。检查了28个NASA程序的数据样本，以检验其他研究人员声称的时间表更改可以由正态分布表示的假设。数据的偏度和峰度以及Anderson-Darling和Kolmogorov-Smirnov统计检验的结果均表明该数据不是正态分布。获得了大量的空间和非空间程序样本（365个程序），并针对23种不同类型的连续单变量分布进行了评估。 Anderson-Darling和Kolmogorov-Smirnov的测试结果表明，所有23种分布类型（包括正态分布和极值分布）均在0.05水平上被拒绝。随后通过仅包括来自数据的随机和排序表示的所有第六个值（也具有与按时交货相关联的值）来人为地减少了样本大小。 Anderson-Darling和Kolmogorov-Smirnov的测试结果表明，在0.05水平上不能拒绝极值分布。这种潜在的矛盾是由于样本量远小于全部样本（有或没有准时交货值被删除）而导致的，这导致了安德森-达林检验和科莫莫洛夫-斯米尔诺夫检验的统计能力下降;因此不会拒绝在0.05水平上的极值分布。因此，可能需要大约200个或更多数据点的样本大小，才能提供有意义的时间表变更和其他潜在数据的分布拟合。对于较小的样本，尤其是小得多的样本，建议不要针对候选分布类型评估数据，而应将其简单地转换为递增累积分布函数（CDF），并在后续分析中适当使用此函数（例如，蒙特Carlo模拟）。

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