## 16 Designing for reliability

The pursuit of product quality over the last few decades has been intense in many companies around the world, but in many sectors of industry, reliability is considered to be the most important quality attribute of the product (Kehoe, 1996). As consumers become more aware than ever of quality, their expectations for reliability are also increasing. Even equipment without obvious safety concerns can have important reliability implications. Most products can, therefore, benefit from the use of sound reliability techniques (Burns, 1994). Reliability prediction, in turn, has the benefit that it gives a quantifiable estimate of the likely reliability that can be assessed to see if this is appropriate for the market (Stephenson and Wallace, 1996).

Reliability prediction is undoubtedly an important aspect of the product design process, not only to quantify the design in terms of reliability, but also to determine the critical design parameters that go to produce a reliable product. To this end, it is necessary to have a mathematical, quantitative measure of reliability defined by probability (Leitch, 1995). It is, however, a controversial aspect of reliability engineering in terms of accuracy and validity because it relies on detailed knowledge about sometimes unknown design parameters (Burns, 1994; Carter, 1986; O'Connor, 1995). In addition, the practical 'engineering' of reliability in the product is still seen as a science to many designers and evaluating concept designs for reliability is especially difficult for inexperienced staff (Broadbent, 1993). A fundamental reason for this is the supporting use of statistics and probability theory. Designers and engineers have consistently turned a blind eye to the advantages of using these methods; however, they can be trained to use them without being rigorously schooled in their mathematical foundation (Morrison, 1997). Reliability prediction will remain a controversial technique until the statistical methods for quantifying design parameters becomes embedded in everyday engineering practice. Using statistically based design techniques will not solve the whole problem, although it will be much closer to the desired end result (Carter, 1997).

The reliability of a product is the measure of its ability to perform its intended function without failure for a specified time in a particular environment. Reliability engineering has developed into two principal areas: part and system. Part reliability is concerned with the failure characteristics of the individual part to make inferences about the part population. This area is the focus of Chapter 4 of the book and dominates reliability analysis. System reliability is concerned with the failure characteristics of a group of typically different parts assembled as a system (Sadlon, 1993).

There are currently three main approaches used in the pursuit of a reliable product (Stephenson and Wallace, 1996):

• Reliability prediction (includes probabilistic design)

• Design techniques (for example, FMEA or Fault Tree Analysis (FTA))

• Pre-production reliability testing (prototyping).

Reliability prediction techniques are a controversial but effective approach to designing for reliability, as discussed later. FTA (Bignell and Fortune, 1984; Straker, 1995) and FMEA are established techniques that aim to determine the potential causes and effects of failures in components and systems. Although subjective in nature, they are useful at the system level where many interactions of components take place. Finally, prototype testing is a pre-production exercise performed on a few model products tested to determine if they meet the specification requirements. All three approaches have their value in the product development process, although the aim of the first two must surely be to reduce the third, prototype testing, which can be an expensive undertaking. However, you could never remove the necessity for some kind of prototype testing, especially where the aim is to verify the integration of parts and subassemblies. From the above, it would seem that designing for reliability depends on both quantitative results and qualitative processes (Ben-Haim, 1994). However, the collection of reliability tasks might look intimidating causing one to wonder if the benefit gained by performing all is worth the effort (Burns, 1994).

Virtually all design parameters such as dimensional characteristics, material properties and service loads exhibit some statistical variability and uncertainty that influence the adequacy of the design (Rice, 1997). Variability may arise from material quality, adverse part geometry and environmental factors (Weber and Penny, 1991). Historically, the designer has catered for these variabilities by using large factors of safety in a deterministic design approach. In probabilistic design, statistical methods are used to investigate the combination and interaction of these parameters, having characterized distributions, to estimate the probability of failure. A key requirement is detailed knowledge about the distributions involved to enable plausible results to be produced. The amount of information available at these early stages is limited, and the designer makes experienced judgements where information is lacking. This is why the deterministic approach is still popular, because many of the variables are taken under the 'umbrella' of one simple factor. If knowledge of the critical variables in the design can be estimated within a certain confidence level, then the probabilistic approach becomes more suitable. It is essential to quantify the reliability and safety of engineering components and probabilistic analyses must be performed (Weber and Penny, 1991).

There are numerous applications for probabilistic design techniques in mechanical engineering. A number of important applications exist in design optimization and reliability engineering, specifically where it would be useful to explore the level of random failure, resulting from the interaction of the distributions of loading stress and material strength, discussed in detail in Chapter 4 of the book. The approach is shown in Figure 1.22 again for a simple hole in a plate concept. All the design parameters are shown as statistical distributions rather than unique or nominal values. The final failure prediction through an appropriate probabilistic and failure analysis model reflects the distributional nature of the design parameters.

RELIABILITY TARGET

DESIGN PROPOSAL

DESIGN PROPOSAL

InlariBrBnce = failure

PROBABILISTIC .

& FA1 LURE ANALY&& MODEL

InlariBrBnce = failure

PROBABILISTIC .

& FA1 LURE ANALY&& MODEL

Figure 1.22 Hole in a plate analogy of probabilistic design

More plausible representations of stress and strength distributions for a given situation will enable meaningful failure predictions to be produced, and will be particularly useful where test to failure is not a practical proposition, where weight minimization and/or material cost reduction is important, or where development time is crucial. Engineering experience indicates that many devices are overdesigned, that is, they feature excess weight or excess occupied space. When weight and/or space is at a premium, a more realistic design process is required that permits relatively accurate predictions of device performance. A probabilistic design process, taking into account of the uncertainties with typical design inputs, provides the required realism (Bury, 1975).

In a probabilistic approach, design decisions must reduce the probability of unwanted performance to acceptable levels. In a deterministic approach, the designer can only assure that the performance remains within an acceptable domain (Ben-Haim, 1994). As the deterministic approach provides no firm basis for dealing with variability, it is not pertinent to a reliability approach (Morrison, 1997; Shigley and Mischke, 1989). As an example of this, Haugen (1968) shows that the failure probability for a particular problem can vary from zero to unity because of the variability of the design parameters, but with the factor of safety selected remaining constant. Factors of safety can lead to either an unconservative design with unacceptable high failure rates, or a very conservative design that provides the required performance with unnecessarily high product costs (Rice, 1997).

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).

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).

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:

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.

A problem may lie in the knowledge that is required as an essential input to such approaches, being both statistical in nature and from the authors' own experiences, often difficult to obtain and interpret generally. Unfortunately, experienced designers will not use statistical methodology, although statistical methods should play an important role in the design and manufacture of reliable products (Amster and

Table 1.1 Competing issues in deterministic and probabilistic design approaches

### Deterministic design

Dominated design for 150 years Design parameters treated as unique values Underlying empirical and subjective nature Factor of safety dominates determination of reliability Ignorance about the problem being multi-variable Calculations simple and data widely available Inherent overdesign - wasteful, costly and ineffective Culture of deterministic design still exists in industry

Probabilistic design

Application for approximately 40 years Design parameters treated as random variables Small samples used to obtain statistical distributions

An understanding of statistics is required Knowledge scattered throughout engineering texts Output as a probability of failure or reliability Better understanding of the effects of variability

Hooper, 1986; Carter, 1997). A principal drawback of the probabilistic design approach is that it requires a good knowledge of probability and statistics, and not every design engineer has this knowledge (Kapur and Lamberson, 1977). Summarizing the above, the main characteristics of the deterministic and probabilistic design approaches are shown in Table 1.1.

The provision for reliability must be made during the earliest design concept stage (Dieter, 1986). The more problems prevented early on through careful design, the fewer problems that have to be corrected later through a time-consuming and often confusing process of prototype (Dertouzos et al., 1989). A principal necessity then is to design to a reliability goal without an inordinate amount of component and prototype testing (Mischke, 1989). This can only be achieved by a rigorous appraisal of the design as honestly and early as possible in the product development process.

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