Probabilistic design approach

In this approach, an expression is first developed to relate total number (or density) of pathogens (N) at time t with the characteristics of the pathogenic suspension and operational parameters such as the UV exposure time (f). One typical expression is as follows  

Equation (23) is then calibrated with experimental data obtained from pilot-scale field tests. A secondary effluent has a = 10 , (3 = 1.947, y = 0.3233, X = 0, and k = p = -2.484 (19). Owing to the variability in the experimental data as well as the influent characteristics and operational parameters, statistical analysis such as Monte Carlo technique can subsequently be combined with the calibrated model for the design of the UV disinfection unit. This approach was developed by Loge and co-workers interested readers may refer to their original manuscripts for more detailed information (19,22,27,28). 

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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. 

The conceptual system selected in step 3 is designed. Reliability and maintainability of this design are assessed. Various methodologies, such as design review, failure mode and effect analysis, fault tree analysis, and probabilistic design approach, can be applied at this step. Reliability is a design parameter and must be incorporated in the system at the design step. 

The indispensable reliability level for strongly reinforced columns may be obtained only using probabilistic design approaches (Holicky, Markova 2007). 

Table I lists the dimensions of the various components making up the initial design for the TE device. Table II contains the tliermomechanical properties for the three materials involved in the module. To keep the demonstration of the proposed design methodology simple, these properties are assumed to be temperature independent. However, taking into account temperature dependent material properties can be easily incorporated into the FEA simulation and the 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... 

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

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 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. 

It should be noted that, for the selected example, the design stress determined by probabilistic means corresponds - in a deterministic design approach - to a safety factor of about 844 MPa/348 M Pa = 2.4. The advantage in the probabilistic approach is that a realistic reliability can be determined, and that total safety - which does not exist in reality - is not implied. 

A probabilistic design of the frames is carried out by FORM considering the lifetime of 50 years and reliability index 0 = 3.8. Both approaches are compared by the value of the design variable—the nominal plastic moment The results show... 

Probabilistic design allows designing closer to the properties of the material. That means a material can be used even at a high localized stress. In this approach, peak stresses and stress distributions cannot be adequately defined. Also, the true strength-flaw size distribution cannot be defined adequately. This is because local heat transfer conditions, the effects of geometry, precise loads, load application angles, and so on, are not accurately defined for the calculation of mechanical stresses. 

Abstract The processing quality control of adhesively bonded joints in actual production lines is discussed in this chapter. To improve the yield ratio of products, a scientific approach based on both probabilistic design and statistical treatment are indispensable. In addition, control of environmental conditions and materials is also very important. For the purpose, a realistic trial-and-error approach should be done to meet any demands or to solve problems occurring in the production. Investigation of reasons decreasing joint strength is another key point that should be done. The strength decrease occurs often due to mechanical or chemical mismatch of adherends and adhesives. The surface treatment of adherends is important too. Inspection, which can be carried out easily, is desirable in actual production lines. 

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

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... 

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. 

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... 

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