Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 45 pps

4.3.1.2 System Performance Analysis and Simulation Modelling Section 3.3.1.2 considered system performance within the context of designing for availability, which can be perceived as the

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 period 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 pressure 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 by 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 performance within the context of designing for availability, which can be perceived as the combination of:

• a system’s process capability (with regard to the process characteristics of ca-pacity, input, throughput, output and quality);

• a system’s functional effectiveness (with regard to the functional characteristics

of efficiency and utilisation);

• a system’s operational condition (with regard to operational measures such as temperatures, pressures, flows, etc.).

All these characteristics may serve as useful indicators in designing for

availabil-ity whereby system performance simulation modelling is generally considered the

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 has 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 performance analysis

techniques can be applied in determining the performance characteristics of pro-posed designs, and to identify those areas of the design where performance prob-lems may be experienced It is focused on determining how systems behave 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 design 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 are 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 that these interactions are usually numerous 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 occur, 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 performance are This would then lead to pos-sible modifications of the system’s design to improve the performance measure of concern

Development of 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

design, and designed out of the system prior to firming up design configurations and system specifications in the preliminary or schematic design phase Without this approach, there is a real danger that the actual bottlenecks 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 project should not be underesti-mated, the potential savings that can be made from avoiding redesign and/or rework when a system fails to meet its performance objectives will more than justify the cost

Thus, from an engineering design perspective, it becomes essential not only to understand the dynamic behaviour 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 of 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 characteristics has extended the range of engineering design problems that may be solved (Law et al 1991)

For design problems that can be solved using these techniques, analytic

mod-els are ideal However, the integration of analytic modmod-els 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 performance 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 number of factors affect the behaviour of a complex integration of systems In

such cases, system performance simulation modelling is most appropriate (Emshoff

et al 1970)

b) System Simulation Modelling

There are two main types of 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 concentrations will vary smoothly with time (at a fine enough timescale) and, at each instant of time, the reaction 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 pipe The volume may increase or 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 from one time step to the next (Dia-mond 1997)

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 performance simulation modelling is at the conceptual engi-neering design phase, with further modelling refinements as the design progresses 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 therefore essential 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 being 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 gleaned as to where potential bottle-necks might exist The critical areas can then be refined to gain further 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 usefulness 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 balance 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 depth in a given time; conversely, if the same effort is put into a narrow scope, then a greater depth of available modelling detail can be added The 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

4.3.1.3 Uncertainty in System Performance Simulation Modelling

In considering the various uncertainties involved in system performance simulation

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 model 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 ables) It is also termed ‘input parameter uncertainty’ Examples include the

vari-ability associated with process characteristics of capacity, input, throughput and quality, functional characteristics of efficiency and utilisation, operational

condi-tions, material properties, and physical dimensions of constituent parts

• Internal uncertainty:

This type of uncertainty has two sources One is due to the limited information

in estimating the characteristics of model parameters for a given, fixed model structure, which is called ‘model parameter 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 that comprises

a complex integration of systems is that the effect of the uncertainties of one sys-tem’s performance characteristics may propagate to another through linking model variables, resulting in the overall systems 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 design 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 design 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).

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 condition approach 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 Furthermore, 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 engineering designs Relatively recent 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 of

per-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 propagating and managing the effect of uncer-tainties is proposed Two approaches, namely the extreme condition approach and the statistical approach, are simultaneously developed to propagate the effect of 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) Propagation 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)

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 x1with uncertainty (external uncertain-ties describe by a rangeΔx1, or certain distributions)

Due to the external uncertainty and the internal uncertainty, which is modelled

asε1(x1) in simulation model I, the output vector of model I, which is given by the

expression

y = F1(x1) +ε1(x1)

will have deviationsΔy or described by distributions.

For simulation model II, the inputs are the linking variable vector y and the design variable vector x2 Because of the deviations existing in x2and y, and the internal uncertaintyε2(x2y), associated with simulation II, the final output vector, given by

the expression

z = F2(x2y) +ε2(x2y)

will also have deviationsΔz or described by distributions.

For simulation model I, the output expression for y consists of the simulation model F1(x1) and the corresponding error model of the internal uncertainty,ε1(x1)

For simulation model II, the inputs are the linking variable y and the design vari-able x2 The output expression for z consists of the simulation model F2(x2y) and the

corresponding error model of the internal uncertainty,ε2(x2y ) 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 x2and y, and the

in-ternal uncertaintyε2(x2y ), 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 Approach for 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

“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 uncertainties are characterised by the intervals

[x1−Δ x1,x1+Δx1] and [x2−Δx2,x2+Δx2] Optimisations are used to find the

max-imum and minmax-imum (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, zmin, zmaxare given as (Du et al 1999c): i) Given a set of nominal values x1and rangeΔx1for simulation model I,

min-imise (maxmin-imise) F1(x1) andε1(x1) by selecting values from [x1−Δx1,x1+

Δx1] to obtain the values F1 min(x1), F1 max(x1), andε1 min(x1),ε1 max(x1)

ii) The optimisation model is:

Given: the nominal value of x1and the rangeΔx1

Subject to: x1−Δ x1≤ x1≤ x1+Δx1

Optimise: minimise F1(x1) to obtain F1 min(x1)

maximise F1(x1) to obtain F1 max(x1)

iii) Obtain the extreme values of internal uncertaintyε1 min(x1) andε1 max(x1)

over the range[x1−Δx1,x1+Δx1]

iv) Obtain the interval[ymin,ymax] using:

ymin= F1 min(x1) +ε1 min(x1)

ymax= F1 max(x1) +ε1 max(x1)

v) Given a set of nominal values x2and rangeΔx2, for simulation model II,

min-imise (maxmin-imise) F2(x2) andε2(x2) by selecting values from [x2−Δx2,x2+

Δx2] to obtain the values F2 min(x2), F2 max(x2), andε2 min(x2),ε2 max(x2)

vi) The optimisation model is:

Given: the nominal value of x2and the rangeΔx2

Fig 4.15 Flowchart for the

extreme condition approach

for uncertainty analysis (Du

et al 1999c)

Given Range [x 1min , x 1max ] and [x2min, x2max]

Minimize y over [x1min, x1max]

to obtain ymin

Maximize y over [x1min, x1max]

to obtain ymax

Minimize z over [x 2min , x 2max ] and [y min , y max ]

to obtain zmin

Maximize z over [x 2min , x 2max ] and [y min , y max ]

to obtain zmax [y min , y max ]

[z min , z max ]

Subject to: x2−Δx2≤ x2≤ x2+Δx2

Optimise: minimise F2(x2) to obtain F2 min(x2)

maximise F2(x2) to obtain F2 max(x2)

vii) Obtain the extreme values of internal uncertaintyε2 min(x2) andε2 max(x2)

over the range[x2−Δx2,x2+Δx2]

viii) Obtain the interval[ymin,ymax] using:

zmin= F2 min(x2) +ε2 min(x2)

zmax= F2 max(x2) +ε2 max(x2)

Based on the computed interval[zmin,zmax], the nominal value of z is calculated as:

˙z=[zmin+ zmax]

The deviation of z can be calculated as:

The nominal value and deviation of a system output is based on given system input

intervals

The extreme condition approach identifies the interval of a system output based

on the given intervals of the system inputs It is applicable to the situation in which

both the external uncertainties in x1and x2are expressed by ranges Illustrated in Fig 4.15 is the flowchart of the proposed procedure of using optimisations to find the maximum and minimum (extremes) of outputs from simulation model I and sim-ulation model II, for the simsim-ulation-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, zmin, zmax, as considered in steps i) to viii) above

c) The Statistical Approach for Uncertainty Analysis

The statistical approach is developed to estimate cumulative distribution functions (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 of simulation models

It is assumed that x1and x2, and the internal uncertainty,ε1(x1) andε2(x2y),

fol-low certain probabilistic distributions that may 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-uesε1(x1) andε2(x2y ) are functions of x1,x2and y, the final distributions ofε1(x1)

andε2(x2y) are the accumulated effects of both the uncertainty in the error model

and the uncertainty of the external parameters such as x1,x2and 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)