Probabilistic design is a discipline within engineering design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects are related to quality and reliability. Thus, probabilistic design is a tool that is mostly used in areas that are concerned with quality and reliability. For example, product design, quality control, systems engineering, machine design,

civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...

(particularly useful in limit state design) and manufacturing. It differs from the classical approach to design by assuming a small probability of failure instead of using the safety factor.

Designer's perspective

When using a probabilistic approach to design, the designer no longer thinks of each variable as a single value or number. Instead, each variable is viewed as a

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...

. From this perspective, probabilistic design predicts the flow of variability (or distributions) through a system. By considering this flow, a designer can make adjustments to reduce the flow of random variability, and improve quality. Proponents of the approach contend that many quality problems can be predicted and rectified during the early design stages and at a much reduced cost.

The objective of probabilistic design

Typically, the goal of probabilistic design is to identify the design that will exhibit the smallest effects of random variability. This could be the one design option out of several that is found to be most robust. Alternatively, it could be the only design option available, but with the optimum combination of input variables and parameters. This second approach is sometimes referred to as

robustification Robustification is a form of optimisation whereby a system is made less sensitive to the effects of random variability, or noise, that is present in that system's input variables and parameters. The process is typically associated with engineerin ...

, parameter design or design for six sigma

Methods used

Essentially, probabilistic design focuses upon the prediction of the effects of random variability. Some methods that are used to predict the random variability of an output include: *the

Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...

(including Latin hypercubes); *

propagation of error In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of exp ...

; *

design of experiments The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

(DOE) * the method of moments *

Statistical interference When two probability distributions overlap, statistical interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much. This technique can be used for dimensioning ...

* quality function deployment *

Failure mode and effects analysis Failure mode and effects analysis (FMEA; often written with "failure modes" in plural) is the process of reviewing as many components, assemblies, and subsystems as possible to identify potential failure modes in a system and their causes and effe ...

Footnotes

References

* Ang and Tang (2006) ''Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering.'' John Wiley & Sons. * Ash (1993) ''The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists'' (''and Everyone Else''). Wiley-IEEE Press. * Clausing (1994) ''Total Quality Development: A Step-By-Step Guide to World-Class Concurrent Engineering.'' American Society of Mechanical Engineers. * Haugen (1980) ''Probabilistic mechanical design.'' Wiley. * Papoulis (2002) ''Probability, Random Variables and Stochastic Process.'' McGraw-Hill Publishing Co. * Siddall (1982) ''Optimal Engineering Design.'' CRC. * Dodson, B., Hammett, P., and Klerx, R. (2014) ''Probabilistic Design for Optimization and Robustness for Engineers'' John Wiley & Sons, Inc. * Cederbaum G., Elishakoff I., Aboudi J. and Librescu L., Random Vibration and Reliability of Composite Structures, Technomic, Lancaster, 1992, XIII + pp. 191; * Elishakoff I., Lin Y.K. and Zhu L.P. , Probabilistic and Convex Modeling of Acoustically Excited Structures, Elsevier Science Publishers, Amsterdam, 1994, VIII + pp. 296; * Elishakoff I., Probabilistic Methods in the Theory of Structures: Random Strength of Materials, Random Vibration, and Buckling, World Scientific, Singapore, , 2017

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