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IEEE Std 610.12-1990. 1990. IEEE Standard Glossary of Modeling and Simulation Terminology. Institute of Electrical and Electronic Engineers (IEEE). New York, NY. Kossiakoff, Alexander, and Sweet, William N. 2003. Systems Engineering Principles and Practice, New York: Wiley-InterScience.
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ASD-100. 2004. National Airspace System System Engineering Manual, ATO Operations Planning. Washington, DC: Federal Aviation Administration (FAA).
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Statistical In uences on System Design
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For many engineers, system design evolves around abstract phrases such as bound environmental data and receive data. The challenge is: HOW do you quantify and bound the conditions for a speci c parameter Then, how does an SE determine conditions such as: 1. Acceptable signal and noise (S/N) ratios 2. Computational errors in processing the data 3. Time variations required to process system data The reality is that the hypothetical boundary condition problems engineers studied in college aren t so ideal. Additionally, when a system or product is developed, multiple copies may produce varying degrees of responses to a set of controlled inputs. So, how do SEs deal with the challenges of these uncertainties Systems and products have varying degrees of stability, performance, and uncertainty that are in uenced by their unique form, t, and function performance characteristics. Depending on the price the User is willing to pay, we can improve and match material characteristics and processes used to produce the SE systems and products. If we analyze a system s or product s performance characteristics over a controlled range of inputs and conditions, we can statistically state the variance in terms of standard deviation. This chapter provides an introductory overview of how statistical methods can be applied to system design to improve capability performance. As a prerequisite to this discussion, you should have basic familiarity with statistical methods and their applications.
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1. 2. 3. 4. 5. 6. How do you characterize random variations in system inputs suf ciently to bound the range How do SEs establish criteria for acceptable system inputs and outputs What is a design range How are upper and lower tolerance limits established for a design range How do SEs establish criteria for CAUTION and WARNING indicators What development methods can be employed to improve our understanding of the variability of engineering input data
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System Analysis, Design, and Development, by Charles S. Wasson Copyright 2006 by John Wiley & Sons, Inc.
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48.2 Understanding the Variability of the Engineering Data
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7. What is circular error probability (CEP) 8. What is meant by the degree of correlation
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Circular Error Probability (CEP) The Gaussian probability density function (normal distribution) referenced to a central point with concentric rings representing the standard deviations of data dispersion. Cumulative Error A measure of the total cumulative errors inherent within and created by a system or product when processing statistically variant inputs to produce a standard output or outcome. Logarithmic Distribution (Lognormal) An asymmetrical, graphical plot of the Poisson probability density function depicting the dispersion and frequency of independent data occurrences about a mean that is skewed from a median of the data distribution. Normal Distribution A graphical plot of the Gaussian probability density function depicting the symmetrical dispersion and frequency of independent data occurrences about a central mean. Variance (Statistical) A measure of the degree of spread among a set of values; a measure of the tendency of individual values to vary from the mean value. It is computed by subtracting the mean value from each value, squaring each of these differences, summing these results, and dividing this sum by the number of values in order to obtain the arithmetic mean of these squares. (Source: DSMC T&E Mgt. Guide, DoD Glossary of Test Terminology, p. B-21)
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In an ideal world, engineering data are precisely linear or identically match predictive values with zero error margins. In the real world, however, variations in mass properties and characteristics; attenuation, propagation, and transmission delays; and human responses are among the uncertainties that must be accounted for in engineering calculations. In general, the data are dispersed about the mean of the frequency distribution.
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