4.3 Analytic Development of Availability and Maintainability in Engineering Design 423 Q10. Are sharp bends, causing forceful impingement, present? Q11. Are stagnant zones present that may hold the process fluid after flushing? Q12. How complex is the equipment? Q13. Are alignment/adjustment procedures needed on installation/replacement? Q14. Is any special equipment required to make the adjustments? Q15. Do components have many state changes (e.g. opening/closing of valves)? Q16. Is the equipment novel in design or application? Q17. Do components have arduous sealing duties? Q18. Are special materials used? Maintainability checklist Q1. Will catastrophic failure be evident in the control room? Q2. Will degraded failure be evident from the control room? Q3. Time p eriod of degraded failure detection? Q4. Does maintenance require protective clothing due to hazardous substances or hot equipment, or does the equipment need time to cool down? Q5. How easy is it to isolate equipment? Q6. What method of isolation is required? Q7. What area of plant needs to be isolated? Q8. Is p ressure release and drainage (including purging and venting) provided? Q9. Is electrical isolation of equipment required? Q10. Is scaffolding required for maintenance? Q11. Can scaffolding be erected by maintenance personnel or b y contractors? Q12. Is there adequate space to build scaffolding? Q13. Is there adequate space to manoeuvre while maintenance is taking place? Q14. How is the equipment lifted? Q15. Whatever lifting equipment is used, are there any problems foreseen? Q16. Does other equipment need to be removed before access can be gained? Q17. Is visual access to the fault good enough to carry out maintenance? Q18. Is the physical access good enough to carry out maintenance? 4.3.1.2 System Performance Analysis and Simulation Modelling Section 3.3.1.2 considered system p erformance within the context of designing for availability, which can be perceived as the combination of: • asystem’sprocess capability (with regard to the process characteristics of ca- pacity, input, throughput, output and quality); • asystem’sfunctional effectiveness (with regard to the functional characteristics of efficiency and utilisation); • asystem’soperational condition (with regard to operational measures such as temperatures, pressur es, flows,etc.). All these characteristics may serve as useful indicators in designing for availabil- ity whereby system performance simulation modelling is genera lly considered the 424 4 Availability and Maintainability in Engineering Design most appropriate methodology for predicting their integrated–interactive values. In this case, simulation modelling has been found to be an effective tool for analysing a large quantity of interrelated and compound variables in predicting a complex sys- tem design’s process capability, functional effectiveness and operational condition. Simulation modelling h as been applied in determining the performance of complex integrated systems design in Sect. 4.4. System performance analysis is concerned with the study of the behaviour of a system in terms of its measurable characteristics. System p erformance analysis techniques can be applied in determining the p erformance characteristics of pro- posed designs, and to identify those areas of the d esign where performance prob- lems may be experienced. It is focused on determining how systems b ehave under certain conditions, and can be used to compare different system designs to evalu- ate their relative merits in terms of achieving the required design criteria. However, questions relating to assurance of the integrity of a proposed design are not always included in the scope of system performance analysis. A design that is acceptable from a performance-related viewpoint may be unacceptable from an integrity point of view; similarly, a design that meets integrity requirements such as reliability and safety may not be acceptable from a system performance standpoint. System per- formance analysis is a multidisciplinary field, covering many areas. Among these are parameter performance matrices, evolutionary operation, experimental design, queuing theory, modelling techniques and dynamic simulation. System performance analysis in engineering d esign is concerned with some of these modelling techniques, in particular simulation modelling and its application to the study of the performance of systems based on process characteristics that af- fect system availability. In most engineering systems, there ar e a significant number of performance characteristics and technical constraints involved in their design. When the interactions between all of the characteristics and constraints are consid- ered, it becomes clear thatthese interactions are usuallynumerous and complex. The behaviour of the whole system cannot easily be predicted by the application of rel- atively simple algorithms, as might be expected for less complex systems based on a few process characteristics. In complex process engineering designs, it is often not totally obvious where the bottlenecks may o ccur, and what the determining factors behind system performance might be. Thus, the principle underlying the develop- ment of system performance models is that by capturing the essential real-world behaviour of a system in a mathematical or simulation model, valuable insight can be gained into its critical behaviour. Once a model of a system has been developed, verified and validated, it is possible to experiment with the model and to determine what the limiting factors in system perfo rmance are. This would then lead to pos- sible modifications of the system’s design to improve the performance measure of concern. Developmentof a model would allow performance characteristics such as sizing, capacity, mass and energy balances, and functional response issues to be addressed at an early stage of an engineering process system’s life cycle. In this way, potential performance problems are already identified at the conceptual phase of engineering 4.3 Analytic Development of Availability and Maintainability in Engineering Design 425 design, and designed out of the system prior to firming up design configurations and system specifications in the p reliminary or schematic design phase. Without this approach, there is a real danger that the actual bottlen ecks of the installed system will not be identified. In the absence of the evidence that a system performance model may provide, it is quite likely that significant amounts of resources could be spent later in ‘improving’ inherent items of the installed system that have been found to constrain its performance. System performance modelling provides a relatively inexpensive way of explor- ing the performance implications of different system design configurations. Al- though the effort involved in a major modelling p roject should not be underesti- mated, the potential savings that can be made from avoiding redesign and/or rework when a sy stem fails to meet its perfor mance objectives will mo re than justify the cost. Thus, from an engineering design perspective, it becomes essential not only to understand the dynamic b ehaviour of complex or integrated systems, in addition to formulating their expected performance characteristics, but also to ensure that the design meets both the performance objectives as well as the necessary integrity constraints. a) Types o f System Performance Models System performance models can be broadly classified as either analytic models or simulation models. Analytic models rely on formulae to represent the behaviour of system components. If such formulae exist, then their solution is likely to be fairly concise. However, in many cases formulae do not exist or are valid only under restrictive conditions. Historically, analytic models have yielded only average be- haviour patterns, and have not given insight into the likely distribution of expected values. The use of analytic techniques to find underlying distributions in the case of uncertainty in predicting essential process c haracteristics has extended the range of engineering design problems that m ay be solved (Law et al. 1991). For design p roblems that can be solved using these techniques, analytic mod- els are ideal. However, the integration of analytic models representing individual systems, each with process characteristics and performance constraints, is not triv- ial. To obtain maximum benefit, these models must link together common process characteristics and related system perfor m ance constraints, such that they provide an accurate representation of the design’s intended integration of systems. In many cases, it will not be possible to solve the analytic model to find the appropriate dis- tribution of expected values. Mean-value predictions will be limited, since a much larger numberof factors affect the behaviour of a complex integration of systems. In such cases, system performance simulation modelling is most appropriate (Emshoff et al. 1970). 426 4 Availability and Maintainability in Engineering Design b) System Simulation Modelling There are two main types o f simulation modelling, specifically: • Continuous-time simulation model • Discrete-event simulation model. In the first type of model, continuous-time simulation model, time-related activity is perceived to be continuous. This type of simulation is appropriate for continuous engineering process situations such as modelling the concentrations of chemicals in a reactor vessel. These concentrationswill vary smoothly with time (at a fine enough timescale) and, at each instant of time, the r eaction will be proceeding at a certain rate. In the second type of model, discrete-event simulation model, time-related events can be distinguished as fundamental entities and, from a modelling perspective, no points in time other than those at which events happen need to be considered. This type of model is well suited to modelling production systems or industrial processes where not only the events are discrete entities but they can take on discrete probability distributions (Shannon 1975; Bulgren 1982). Simulation models attempt to derive the overall behaviour of a system either by representing the behaviour of each component of the system separately, and speci- fying how the components interact with each other, or by representing the behaviour of the system as a whole and specifying how the process characteristics interact with each other. Thus, variables of a simulation model may change in any of four ways (Emshoff et al. 1970): • In a discrete manner at any point in time. • In a continuous manner at any point in time. • In a discrete manner only at certain points in time. • In a continuous manner only at discrete points in time. In engineering design, it is common albeit not correct to use the term ‘discrete’ to describe a system with constant periodic time steps, where the term refers to the time interval and not to discrete events during the time interval. For discrete system simulations, input is introduced into the model as a set of discrete items arriving either randomly or at specified intervals. The individual components then react ac- cordingly, and the overall behaviour of the model can be measured (Bulgren 1982). Conversely, for continuous system simulations (or process modelling), a smooth flow of homogenous values is described, analogous to a constant stream of fluid passing through a p ipe. The volume may increase o r decrease but the flow is con- tinuous. Changes in process characteristic values (i.e. inputs, throughputs, outputs, etc.) are based directly on changes in time, and time can change in equal incre- ments. These values reflect the state of the performance of the modelled system at any particular time, which advances evenly fr om one time step to the next (Dia- mond 1997). 4.3 Analytic Development of Availability and Maintainability in Engineering Design 427 Although simulation models are used to predict the behaviour of the system(s) being modelled, their behaviour must be interpreted statistically. This necessitates either many different runs or extended run periods of the model of a given system, depending on the type of simulation modelling applied, to obtain a valid sample of the behaviour that the system is likely to exhibit. Compared to the use of ana- lytic models, developing and interpreting system performance simulation models is a slow process but, nevertheless, definitely much cheaper than experimenting with real-world systems after they have been designed and installed (Law et al. 1991). As stated previously, in producing a simulation model of a system design, the intent is to determine how that system will behave under various conditions. The structure of the simulation model must therefore monitor, and be sensitive to, the behaviour of the system arising from the interaction of a potentially large number of system items (i.e. sub-systems and assemblies), and/or the interaction of a wide range of variable performance characteristics (i.e. inputs, throughputs and outputs— or, in modelling terms, exogenous, status and endogenous variables respectively). It is thus best to adopt a holistic approach, considering all of the components and processes involved at a high systems hierarchy level. This means that the preferred application of system perfo rmance simulation m odelling is a t the conceptual engi- neering design phase, with further modelling refinements as the design progr esses into the schematic or preliminary design phase. However, under a given set of con- ditions, a system will most likely be constrained by one particular item or a single performance characteristic—although this may vary depending on the set condi- tions. It is therefor e essen tial to represent within the model as many of the items and/or performance characteristics in the system as possible, so that potential bot- tleneck effects can be determined. System items that are not close to b eing a bottle- neck can be represented simply, since the fine detail of their behaviour is not likely to change much. At the conceptual design phase, all system items are represented simply so that some information can already be glean ed as to where potential bottle- necks might exist. The c ritical areas can then be refined to gain fur ther insight into these bottlenecks. Clearly, if a system item or performance characteristic is not rep- resented in the model, it can never be construed to be a constraint on the behaviour of the system. This somewhat undermines the benefit of developing a simulation model at the conceptual design phase, and also reduces its perceived u sefulness. If the system’s item or characteristic is represented, however, the model can be used to investigate how changes in the assumptions made about the item or characteristic affect the overall behaviour of the model, and the system. The b alance between detail and scope of system performance simulation mod- elling is evident—if the model has wide scope, then it can be extended only to a shal- low dep th in a given time; conversely, if the same effort is put into a narrow scop e, then a greater depth of available mod e lling detail can be added. Th e aim of a system performance simulation modelling study should therefore be to initially identify un- certainties surrounding broad characteristics of the system’s performance, and then to find those items that could place constraints on system behaviour. 428 4 Availability and Maintainability in Engineering Design 4.3.1.3 Uncertainty in System Performance Simulat ion Modelling In considering the various uncertain ties involved in system performance sim ulation modelling for engineering design, the robust design technique is a preferred appli- cation in decision-making for design integrity. It is generally recognised that there will always be uncertainties in the design of any engineering system. This is due to variations in the performance characteristics not only of the individual system but in the complex integration of multiple systems as well. Besides possible algo- rithmic errors related to computer simulation mode l implementation, two general sources contribute to uncertainty in simulation model predictions of performance characteristics in engineering system designs (Du et al. 1999b): • External uncertainty: External uncertainty comes from the variability in model prediction arising from alternative model variables (including both design parameters and design vari- ables). It is also termed ‘input parameter uncertainty’. Examples include the vari- ability associated with process ch aracteristics of capacity, input, throughput and quality, functional characteristics of efficiency and utilisation, operational condi- tions, material properties, and physical dimensions of constituent p arts. • Internal uncertainty: This type of uncertainty has two sources. One is due to the limited information in estim ating the characteristics of mod el parameters for a given, fixed model structure, which is called ‘model param eter uncertainty’, and another type is in the model structure itself, including uncertainty in the validity of the assumptions underlying the model, referred to as ‘model structure uncertainty’. A critical issue in simulation modelling of an engineering design th at comprises a complex integration of systems is that the effect of th e u ncertainties of one sys- tem’s performance characteristics may propagate to another through linking model variables, resulting in the overallsystems output having an accumulated effect of the individual uncertainties. A practical problem in large-scale systems design is that multidisciplinary groups often use predictive tools of varying accuracy to determine if the design options meet the d esign requirements, especially when performing im- pact analyses of proposed changes from other groups (Du et al. 1999b). The inevitable use of multidisciplinary groups in large-scale systems design ne- cessitates the application of collaborative engineering d esign as well as a careful study of the effect of various uncertainties as a part of design requirements tracking and design coordination. Two primary issues concerning uncertainty in simulation modelling of an engineering design that comprises a complex integration of systems, and thus an integration of multidisciplinary design teams, are: • How should the effect of uncertainties be propagated across the systems? • How should the effect of uncertainties be mitigated to make sound decisions? Techniques for uncertainty analysis include the statistical approach and the worst- case analysis or extreme condition approach (Du et al. 1999c). 4.3 Analytic Development of Availability and Maintainability in Engineering Design 429 The statistical approach relies heavily on the use of data sampling to generate cumulative distribution functions (c.d.f.) of system outputs. Monte Carlo simula- tion, a commonly used random simulation-based approach, becomes expensive in simulations of complex integrations of systems (Hoover et al. 1989). Reduced sampling techniques, such as the Latin hypercube sampling technique (Box et al. 1978) and Taguchi’s orthogonal arrays technique (Phadke 1989), are used to improve computational efficiency, though they are not commonly applied in commercial simulation programs. The extreme condition approach is to derive the range of system performance characteristics, such as process input, throughput or output, in terms of a range of uncertainties, by either sub-optimisations, first-order Taylor expansion or interval analysis (Chen et al. 1995). Use of the statistical approach as well as of the extreme con dition appr oach has been restricted to propagating the effect of external uncertainty only, prompting the need to accommodate more generic representations of both external and internal uncertainties. Furthe rmore, there are few examples associated with how to mitigate the effect of both the external and internal uncertainties in system performance sim- ulation modelling of complex eng ineering d esigns. Relatively recen t developments in design techniques have generated methods that can reduce the impact of potential variations by manipulating controllable design variables. Taguchi’s robust design is one such approach that emphasises reduction o f p er- formance variation through reducing sensitivity to the sources of variation (Phadke 1989). Robust design has also been used at the system level to reduce the perfor- mance variation caused by process characteristic deviations. The concept of robust design has been used to mitigate performance variations due to various sources of uncertainties in simulation-based design (Suri et al. 1999). An integrated methodology for p ropagating and managing the effect of uncer- tainties is proposed. Two approaches, namely the extreme condition approach and the statistical approach,are simultaneouslydevelopedto propagatethe effectof both external uncertainty and internal uncertainty across a design system comprising in- terrelated sub-system analyses. An uncertainty mitigation strategy based on the prin- ciples of robust design is proposed. A simplistic simulation model is used to explain the proposed methodology. The principles of the proposed methods can be easily extended to more complicated, multidisciplinary design problems. a) Propa gation of the Effect of Uncertainties A simulation-based design model is used to explain the proposed methodology. The principles of the methodology are generic and valid for other categories of rela- tionships between the system models. The design model consists of a chain of two simulation programs (assuming they are from two different disciplines) that are con- nected to each other through linking variables, as illustrated in Fig. 4.14 (Du et al. 1999c). 430 4 Availability and Maintainability in Engineering Design Fig. 4.14 Simulation-based design model from two different disciplines (Du et al. 1999c) The linking variables are represented by the vector y. The input to the simulation model I is the vector of the design variable x 1 with uncertainty (external uncertain- ties describe by a range Δx 1 , or certain d istributions). Due to the external uncertainty and the internal uncertainty, which is modelled as ε 1 (x 1 ) in simulation model I, the output vector of model I, which is given by the expression y = F 1 (x 1 )+ ε 1 (x 1 ) will have deviations Δy or described by distributions. For simulation model II,the inputsare the linkingvariable vector y and the design variable vector x 2 . Because of the deviations existing in x 2 and y,andtheinternal uncertainty ε 2 (x 2 y), associated with simulation II, the final output vector, given by the expression z = F 2 (x 2 y)+ ε 2 (x 2 y) will also have deviations Δz or described by distributions. For simulation model I, the output expression for y consists of the simulation model F 1 (x 1 ) and the corresponding error model of the internal uncertainty, ε 1 (x 1 ). For simulation model II, the inputs are the linking variable y and the design vari- able x 2 . The output expressionfor z consists of the simulation model F 2 (x 2 y) and the corresponding error model of the internal uncertainty, ε 2 (x 2 y). The output vector z often represents system performance parameters that are used to model the design objectives and constraints. Because of the deviations existing in x 2 and y, and the in- ternal uncertainty ε 2 (x 2 y), the final output z will also have deviations. The question is how to propagate the effect of various types of uncertainties across a simulation chain with interrelated simulation programs. Two approaches are proposed, first the extreme condition approach and, second, the statistical approach (Du et al. 1999c). b) Extreme Condition Appr oach fo r Uncertainty Analysis The extreme condition approach is developed to obtain the interval of extremes of the final output from a chain of simulation models. The term extreme is defined as 4.3 Analytic Development of Availability and Maintainability in Engineering Design 431 “the minimum or the maximum value of the end performance (final output) corre- sponding to the given ranges of internal and external uncertainties”. With this approach, the external uncerta inties are characterised by the intervals [x 1 −Δx 1 ,x 1 + Δx 1 ] and [x 2 −Δx 2 ,x 2 + Δx 2 ]. Optimisations are used to find the max- imum and minimum (extremes) of the outputs from simulation model I, and simu- lation model II. The flowchart of the proposed procedure is illustrated in Fig. 4.15. The steps to obtain the output z, z min , z max are given as (Du et al. 1999c): i) Given a set of nominal values x 1 and range Δx 1 for simulation model I, min- imise (maximise) F 1 (x 1 ) and ε 1 (x 1 ) by selecting values from [x 1 −Δx 1 ,x 1 + Δx 1 ] to obtain the values F 1min (x 1 ), F 1max (x 1 ),and ε 1min (x 1 ), ε 1max (x 1 ). ii) The optimisation model is: Given: the nominal value of x 1 and the range Δx 1 Subject to: x 1 −Δx 1 ≤ x 1 ≤ x 1 + Δx 1 Optimise: minimise F 1 (x 1 ) to obtain F 1min (x 1 ) maximise F 1 (x 1 ) to obtain F 1max (x 1 ). iii) Obtain the extreme values of internal uncertainty ε 1min (x 1 ) and ε 1max (x 1 ) over the range [x 1 −Δx 1 ,x 1 + Δx 1 ]. iv) Obtain the interval [y min ,y max ] using: y min = F 1min (x 1 )+ ε 1min (x 1 ) y max = F 1max (x 1 )+ ε 1max (x 1 ). v) Given a set of nominalvalues x 2 and range Δx 2 , for simulation modelII, min- imise (maximise) F 2 (x 2 ) and ε 2 (x 2 ) by selecting values from [x 2 −Δx 2 ,x 2 + Δx 2 ] to obtain the values F 2min (x 2 ), F 2max (x 2 ),and ε 2min (x 2 ), ε 2max (x 2 ). vi) The optimisation model is: Given: the nominal value of x 2 and the range Δx 2 Fig. 4.15 Flowchart for the extreme condition approach for uncertainty analysis (Du et al. 1999c) Given Range [x 1min , x 1max ] and [x 2min , x 2max ] Minimize y over [x 1min , x 1max ] to obtain y min Maximize y over [x 1min , x 1max ] to obtain y max Minimize z over [x 2min , x 2max ] and [y min , y max ] to obtain z min Maximize z over [x 2min , x 2max ] and [y min , y max ] to obtain z max [y min , y max ] [z min , z max ] 432 4 Availability and Maintainability in Engineering Design Subject to: x 2 −Δx 2 ≤ x 2 ≤ x 2 + Δx 2 Optimise: minimise F 2 (x 2 ) to obtain F 2min (x 2 ) maximise F 2 (x 2 ) to obtain F 2max (x 2 ). vii) Obtain the extreme values of internal uncertainty ε 2min (x 2 ) and ε 2max (x 2 ) over the range [x 2 −Δx 2 ,x 2 + Δx 2 ]. viii) Obtain the interval [y min ,y max ] using: z min = F 2min (x 2 )+ ε 2min (x 2 ) z max = F 2max (x 2 )+ ε 2max (x 2 ). Based on the computed interval [z min ,z max ],thenominal value of z is calculated a s: ˙z = [z min + z max ] 2 (4.153) The deviation of z can be calculated as: Δz =[z min −z max ] (4.154) The nominal value and deviation of a system output is based on given system input intervals. The extreme condition a pproach identifies the interval of a system output based on the given intervals o f the system inputs. It is applicable to the situation in which both the external uncertainties in x 1 and x 2 are expressed by ranges. Illustrated in Fig. 4.15 is the flowchart of the proposed procedure of using optimisations to find the maximumand minimum(extremes) ofoutputs from simulation model I and sim- ulation model II, for the simulation-based design model from two different design disciplines given in Fig. 4.14. It depicts the procedure used to obtain the range of outputs z, z min , z max , as considered in steps i) to viii) above. c) The Statistical Approach for Uncertain ty Analysis The statistical approach is developed to estim ate cumulative distr ibution fu nctions (c.d.f.) and probability density functions (p.d.f.), or population parameters (for ex- ample mean and variance) of the final outputs from a chain o f simulation models. It is assumed that x 1 and x 2 , and the internal uncertainty, ε 1 (x 1 ) and ε 2 (x 2 y),fol- low certain probab ilistic distributions that m ay be obtained by field or experimental data, or information of similar existing processes, or by judgements by engineering experience. Since the distribution parameters (i.e. mean and variance) of the uncertainty val- ues ε 1 (x 1 ) and ε 2 (x 2 y) are functions of x 1 ,x 2 and y, the final distributions of ε 1 (x 1 ) and ε 2 (x 2 y) are the accumulated effects of both the uncertainty in the error m odel and the uncertainty of the external parameters such as x 1 ,x 2 and y. Monte Carlo simulation methods are used to propagate the effect of uncertainties through the simulation chain. A flowchart of the Monte Carlo simulation procedure is given in Fig. 4.16 (Law et al. 1991). . point in time. • In a continuous manner at any point in time. • In a discrete manner only at certain points in time. • In a continuous manner only at discrete points in time. In engineering design, . uncertainties as a part of design requirements tracking and design coordination. Two primary issues concerning uncertainty in simulation modelling of an engineering design that comprises a complex integration. Development of Availability and Maintainability in Engineering Design 431 “the minimum or the maximum value of the end performance (final output) corre- sponding to the given ranges of internal and external