Probabilistic Design

Course Notes

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Probabilistic Design Course Notes

File format This page enables you to read the text of the Probabilistic Design course notes by clicking on the headings below. The files are in Portable Document Format (.pdf), and provided your browser is enabled with Adobe Acrobat Reader or your computer is running Mac OS X, you should be able to read them on screen and print them if you wish. The main text files were originally created in FrameMaker with the case studies, problems and solutions created in Mathematica version 4. The main text does not display the diagrams, since these were drawn as exercises by the class.

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Title Page  [62 KB]

Table of Contents  [40 KB]

1. Introduction  [61 KB]
Aim of the course. Focus. References.

2. Probabilistic Design  [230 KB]
Introduction. Types of probability distributions. Describing probability distributions. Graphical functions of a random variable. Analytical functions of a random variable. Moments. The normal distribution. Means from nominal values. Standard deviations from tolerances. The expectation operator. Linear functions. Reliability. Products of random variables. Positive integer powers. General functions. Summary of approximate formulae. General power functions.

Problems and solutions in Probabilistic Design  [235 KB]
Uniformly distributed design parameters. Sketching distributions. Sound output. Sphere volume. Alloy steel. Probability of a continuous random variable. Sketching a Normal distribution. Moments as Expectations. Expectation of a linear sum. First central moment. Central and non-central moments. Variance and skew. Mean values of a power. Mean second moment of area. Volume of a sphere. Inconsistency? Tolerance buildup. Springs in parallel. Counterweights. Algenon and Biggles. Machine support. Moon lander. Bolt strength reliability. Buoyancy force reliability. Bearing fit. Shaft failure. Fitting of car doors and windshields. Volume of a cube. Inconsistency? Mean of a function of one variable. Variance of a function of one variable. Mean of a function of two variables. Probabilistic means. Approximate formulae. Right-angled bracket. Applications of probabilistic design. The mean of a square. Volume of a cylinder. Second moment of area. Coefficients of variation. Experimental formula. First order approximation. Springs in series. The minimum diameter of a rod in tension.
The problems and solutions are written in Mathematica.

3. Robust Design  [93 KB]
Introduction. Terminology. The concept of robustness. Taguchi's quality loss function. First order analytical robust design. Example: Locating struts. Example: simple power model. Case study summary: Passive filter network.

Visualization of the Robust Design Process  [201 KB]
Mathematica is used to help visualize the geometry underpinning a robust design.

Case study: Passive Filter Network  [91 KB]
An analytical robust design in two quality variables: A mass-produced passive filter network is to be designed to maintain the filter cutoff frequency and galvanometer full-scale deflection as close as possible to their target values whilst using the least expensive components.
Mathematica is used to perform the symbolic and numeric computations.

Problems and solutions in Robust Design  [114 KB]
Sources of variation. Designing robust products. Terminology for robust design. The concept of robustness. First order robustness problem. Exploitation of non-linearity. Derivation of average quality loss. Example of average quality loss. Robustification methodology. Simple power model. Stiffness of a cantilever. Wooden cantilever. Helical spring.
The problems and solutions are written in Mathematica.

4. Simulation  [158 KB]
Introduction. The Monte Carlo method. Stiffness of a cantilever spring. Moment and simulation methods. Case study: Wiper bearing torque. Case study: Wrap-spring clutch.

Contact Details

John M Browne
http://grassmannalgebra.info
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