Design deterministic

Design variables Initial design Deterministic model Uncertain model... 

CAD /CAM techniques have provided the framework for using the computer as a tool in the drawing and analysis of chemical stmctures and, more recently, in the use of chemical stmctures to design reaction pathways and new products. The essential elements in these appHcations of CAD/CAM are that the possible stmctures are relatively deterministic and that allowable changes in stmcture through reaction are governed by thermodynamic, stoichiometric, and steric constraints. 

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. 

The movement from the deterministic design criteria as described by equation 4.1 to the probability based one described by equation 4.2 has far reaching effects on design (Haugen, 1980). The particular change which marks the development of modern engineering reliability is the insight that probability, a mathematical theory, can be utilized to quantify the qualitative concept of reliability (Ben-Haim, 1994). 

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

For example, the deterministic value for the yield strength, Sy, for SAE 1018 cold drawn steel for the size range tested is approximately 395 MPa (Green, 1992). Table 4.6 gives the mean and standard deviation as A(540,41) MPa. The lower bound value as used in deterministic design becomes ... 

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. 

CCF means different things to different people. Smith and Watson (1980) define CCF as the inability of multiple components to perform when needed to cause the loss of one or moi e systems. Virolainen (1984) criticizes some CCF analyses for including design errors and poor quality as CCF and points out that the phenomenological methods do not address physical and statistical dependencies. Here, CCF is classed as known deterministic coupling (KDC), known stochastic coupling (KSC), and unknown stochastic coupling (USC). 

The analyses of system failures which could challenge the containment or lead to the release of radioactivity form the licensing process. The design basis analyses are deterministic, and degraded core accidents are not considered. PSA determines the probabilities of the numerous sequences that could lead to core degradation and how the core behaves. 

We go next to the analysis and failure analysis block in Figure 7-11. That is, we consider the initial configuration with a particular material or materials. Then, for the prescribed loads, we perform a set of structural analyses to get the various structural response parameters like stresses, displacements, buckling loads, natural frequencies, etc. Those analyses are all deterministic processes. That is, within the limits of accuracy of the available analysis techniques, we are able to predict a specific set of responses for a particular structural configuration. We must know how a particular structural configuration behaves so we can compare the actual behavior with the desired behavior, i.e., with the design requirements. 

Thus, for both extensional loading and pure bending of isotropic metal plates, the required thickness to support a specific loading can be determined directly by an inverse of the analysis equations, i.e., the design process is deterministic. 

Chapter 8 combined transport with kinetics in the purest and most fundamental way. The flow fields were deterministic, time-invariant, and calculable. The reactor design equations were applied to simple geometries, such as circular tubes, and were based on intrinsic properties of the fluid, such as molecular dif-fusivity and viscosity. Such reactors do exist, particularly in polymerizations as discussed in Chapter 13, but they are less typical of industrial practice than the more complex reactors considered in this chapter. 

Uncertainties in amounts of products to be manufactured Qi, processing times %, and size factors Sij will influence the production time tp, whose uncertainty reflects the individual uncertainties that can be presented as probability distributions. The distributions for shortterm uncertainties (processing times and size factors) can be evaluated based on knowledge of probability distributions for the uncertain parameters, i.e. kinetic parameters and other variables used for the design of equipment units. The probability of not being able to meet the total demand is the probability that the production time is larger than the available production time H. Hence, the objective function used for deterministic design takes the form ... 

In general, there is no frequent need to design new batch plants. For all the above listed factors deterministic models for plant design will be of limited significance. Plant retrofitting (replacement of equipment, installation of new equipment, and elimination of old equipment) is more often encountered in the field of batch plants. The uncertainty then is much lower than for the design of new plants. 

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