Probabilistic design

E. B. Haugen, Probabilistic Approaches to Design, John Wiley Sons, Inc., New York, 1968. 

Figure 1.22 Hole in a plate analogy of probabilistic design...

It is essential to introduce probabilistic design methods into engineering design procedures. I feel that the UK will be faced with a severe skill gap. I also feel there is a lack of appreciation of the need and time scale to introduce the required procedures to engineers. .. the Japanese have identified probabilistic design as a key technical area. 

Probabilistic design methods have been shown to be important when the design cannot be tested to failure and when it is important to minimize weight and/or cost (Dieter, 1986). In companies where minimizing weight is crucial, for example such as those in the aerospace industry, probabilistic design techniques can be found. 

Non-complex and/or non-critical applications in mechanical design can also make use of probabilistic design techniques and justify a more in-depth approach if the benefits are related to practitioners and customers alike. Surveys have indicated that many products in the industrial sector have in the past been overdesigned (Kalpakjian, 1995). That is, they were either too bulky, were made of materials too high in quality, or were made with unwarranted precision for the intended use. Overdesign may result from uncertainties in design calculations or the concern of the designer and manufacturer over product safety in order to avoid user injury or... 

The development of the probabilistic design approach, as already touched on, includes elements of probability theory and statistics. The introductory statistical methods discussed in Appendix I provide a useful background for some of the more advanced topics covered next. Wherever possible, the application of the statistical methods is done so through the use of realistic examples, and in some cases with the aid of computer software. 

Figure 4.2 Comparison of the probabilistic and deterministic design approaches...

Statistical methods for probabilistic design 4.2.1 Modelling data using statistical distributions... 

It can be seen from Table 4.3 that there is no positive or foolproof way of determining the distributional parameters useful in probabilistic design, although the linear rectification method is an efficient approach (Siddal, 1983). The choice of ranking equation can also affect the accuracy of the calculated distribution parameters using the methods described. Reference should be made to the guidance notes given in this respect. 

The measures of dimensional variability from Conformability Analysis (CA) (as described in Chapters 2 and 3), specifically the Component Manufacturing Variability Risk, q, is useful in the allocation of tolerances and subsequent analysis of their distributions in probabilistic design. The value is determined from process capability maps for the manufacturing process and knowledge of the component s material and geometry compatibility with the process. In the specific case to the th component bilateral tolerance, it was shown in Chapter 3 that the standard deviation estimates were ... 

In the probabilistic design calculations, the value of Kt would be determined from the empirical models related to the nominal part dimensions, including the dimensional variation estimates from equations 4.19 or 4.20. Norton (1996) models Kt using power laws for many standard cases. Young (1989) uses fourth order polynomials. In either case, it is a relatively straightforward task to include Kt in the probabilistic model by determining the standard deviation through the variance equation. 

The use of computers is essential in probabilistic design (Siddal, 1983). However, research has shown that even the most complete computer supported analytical methods do not enable the designer to predict reliability with sufficiently low statistical risk (Fajdiga et al., 1996). Far more than try to decrease the statistical risk, which is probably impossible, it is hoped that the approach will make it possible to model a particular situation more completely, and from this provide the necessary redesign information which will generate a reliable design solution. 

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