Distributions & Simulation Overview

The purpose of the Distributions & Simulation analysis is to provide a general tool for performing simulation studies. Specifically, this module will enable users to perform “experiments” (sometimes also called modern design of experiments, see Giunta, Wojtkiewicz, Eldred 2003) by simulating multivariate design (or “input”) variables from specific distributions, and (rank-order) covariances that define the space of interest. These methods have become popular in various domains, including:

1. Risk modeling

2. Computer experiments and modern DOE

3. Multivariate process monitoring, and process capability analysis (to determine DPPM [Defective Parts Per Million], and – through inverses computations of Cpk and Cp from DPPM – the equivalent process capability of the respective multivariate process.

4. Reliability engineering, to determine the reliability of complex system through simulation.

5. Power analysis, to determine the statistical power of a particular design, and intended analytic approach.

6. Closed loop control system, stochastic optimization

This tool is useful for engineering, reliability engineering, and multivariate process control and monitoring. It is capable of applying various sampling methodologies from multivariate non-normal continuous and discrete distributions to enable applications that require detailed and customized risk analysis.

Distribution summary statistics include the Kolmogorov-Smirnov (KS) statistic and the Anderson-Darling statistic.  The KS statistic and p-values reported are based on those tabulated by Massey (1951). The critical values for the Anderson-Darling statistic have been tabulated (see, for example, Dodson, 1994, Table 4.4) for sample sizes between 10 and 40; however, the critical values (and p-values) reported in PROCEED and Distributions & Simulations are calculated via an approximation method (Marsaglia, 2004).