# Probabilistic design approach

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. [c.135]

Figure 4.14 Key variables in a probabilistic design approach |

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 [c.134]

Probabilistic design provides a transparent means of explaining to a business more about the safety aspects of engineering design decisions with a degree of clarity not provided by the factor of safety approach. The measures of performance determined using a probabilistic approach give the designers more confidence in their designs by providing better understanding of the variables involved and quantitative estimates for reliability. [c.251]

Product life-time prediction, cost and weight optimization have enormous implications on the business of engineering manufacture. Using large Factors of Safety in a deterministic design approach fails to provide the necessary understanding of the nature of manufacture, material properties, in-service loading and their variability. Probabilistic approaches offer much potential in this connection, but have yet to be taken up widely by manufacturing industry. In Chapter 4, a probabilistic design [c.416]

This case study discusses the design of a reciprocating mechanical press for the manufacture of can lids drawn from sheet steel material. The authors were involved in the early stages of the product development process to advise the company designing the press in choosing between a number of design alternatives with the goal of ensuring its reliability. The authors used a probabilistic approach to the problem to provide the necessary degree of clarity between the competing solutions. [c.244]

The press had been designed with a capacity to deliver 280 kN press force and to work at a production rate of 40 lids per minute. Calculations to determine the distribution of forming loads required indicated that the press capacity was adequate to form the family of steel lids to be produced on the machine. One of the major areas of interest in the design was the con-rod and pin (see Figure 4.66). The first option considered was based on a previous design where the con-rod was manufactured from cast iron with phosphor bronze bearings at the big and small ends. However, weaknesses in this approach necessitated the consideration of other options. The case study presents the analysis of the pin and con-rod using simple probabilistic techniques in an attempt to provide in-service reliable press operation. The way a weak link was introduced to ensure ease of maintenance and repair in the event [c.244]

An important aspect of the simple probabilistic approach used above was that it provided a transparent means of explaining to the company the reasons behind the design decisions. It gave a degree of clarity not provided by a deterministic approach and ultimately gave the engineers more confidence in their designs. [c.249]

Virtually all design parameters such as tolerances, material properties and service loads exhibit some statistical variability and uncertainty that influence the adequacy of the design. A key requirement in the probabilistic approach is detailed knowledge [c.249]

Deterministic design is still appealing because of its simplicity in form and application, but since factors of safety are not performance related measures, there is no way of indicating if the design is near optimum (Haugen, 1980). With increasing concern over minimizing the cost of failure, the probabilistic design approach will become more important (Dieter, 1986). Probabilistic design gives the designer a better feel of just how conservative or unconservative the design is (Ullman, 1992). In order to determine this, however, it is important to make decisions about the target reliability level (Ditlevsen, 1997). [c.33]

Figure 4.1 gives an indication that engineers in the 1950s were beginning to think differently about design with the introduction of a true margin of safety, and a probabilistic design approach was being advocated. It shows that the design problem was multifactored and variability based. With the increasing use of statistics in engineering around this time, the theories of probabilistic design and reliability were to become established methods in some sectors by the 1960s. [c.133]

Figure 4.2 shows the probabilistic design concept in comparison to the deterministic approach. Not fully understanding the variable nature of the stress and strength, the designer using the deterministic approach would select a suitable factor of safety which would provide adequate separation of the nominal stress and strength values (for argument s sake). Selecting too high a factor of safety results in overdesign too low and the number of failures could be catastrophically high. In reality, the interference between the actual stress and strength distributions dictates the performance of the product in service and this is the basis of the probabilistic design approach. The degree of interference and hence the failure probability depends on (Mahadevan, 1997) [c.135]

In this the final case study we have touched on a probabilistic approach in support of designing against fatigue failure, a topic which is actually outside the scope of the book. A fatigue analysis for the con-rod would need to take into account all factors affecting the fatigue life, such as stress concentrations and surface finish. However, it has indicated that a probabilistic design approach has a useful role in such a setting. Readers interested in more on stress concentrations and probabilistic fatigue design are directed to Carter (1986), Haugen (1980) and Mischke (1992). [c.249]

To be able to evaluate design reliability estimates using probabilistic methods, the designer needs much more information than for a deterministic evaluation (Fajdiga et al., 1996). It can be argued that probabilistic design can be used only when all the needed statistical data is available and it would be dangerous to design to a reliability target when the data is suspect (Shigley and Mischke, 1989). Because of the lack of statistical data for the strength of materials used and the applied loads in particular, design concepts based on the factor of safety will still dominate the design of some products (NASA, 1995 Zhu, 1993). However, the probabilistic approach allows us to perform a sensitivity analysis of the design with respect to the various design parameters to give an idea of the impact of the variability of dimensions, material strength and loads on performance, and this makes design optimization possible (Kapur and Lamberson, 1977). Probabilistic design is another way of thinking about the design problem which must surely be an improvement over using large factors of safety (Loll, 1987). [c.33]

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. [c.147]

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. [c.202]

Probabilistic methods have gained increased interest in engineering as judged from the growing community of reliability engineers and from the increasing number of conferences on the subject (Ditlevsen, 1997). Some practitioners in the UK, however, either seem to lose confidence with statistical and probabilistic methods or are just not aware of them. At present, only larger companies seem to be aware of their importance (Howell, 1999). Some advocates of a statistical approach to engineering design even claim that this is why large chunks of manufacturing have moved to countries like Japan who embrace the use of such techniques. A comment in 1995 by Margetson gives an indication of the situation related to the UK [c.33]

The deterministic approach is not very precise and the tendency is to use it very conservatively resulting in overdesigned components, high costs and sometimes ineffectiveness (Modarres, 1993). Carter (1986) notes that stress rupture was responsible for a sufficient number of failures for us to conclude that deterministic design does not always ensure intrinsic reliability, and that room for improvement still exists. Increasing demands for performance, resulting often in operation near limit conditions, has placed increasing emphasis on precision and realism (Haugen, 1980). There has been a great disenchantment with factors of safety for many years, mainly because they disregard the fact that material properties, the dimensions of the components and the externally applied loads are statistical in nature (Dieter, 1986). The deterministic approach is, therefore, not suitable for today s products where superior functionality and high customer satisfaction should be a design output. The need for more efficient, higher performance products is encouraging more applications of probabilistic methods (Smith, 1995). [c.133]

See pages that mention the term

**Probabilistic design approach**:

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Designing capable and reliable products (2000) -- [ c.0 ]