Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 36 pot

There are thus three different definitions of process capacity that are applicable to availability in engineering design: • Design capacity Cd: the maximum ability of a series of operati

To obtain a reasonable measure of the process capability, the length of the time frame should be chosen such that it is long enough to reflect all the substantial sources of variation in the process Defining the sampling method or procedure is also important The pilot process output should be sampled in such a way that a ‘fair’ representation is obtained of the process over the chosen time frame For capability calculations, it is not always necessary for the samples to be collected in subgroups However, sub-grouping of the pilot process data can also be used to create control charts that may be helpful in understanding a particular process characteristic Altering the process view can substantially change the conclusions about the process capability As a result, specific guidelines regarding the time frame, and the sampling method used to collect the pilot process data necessary for calculat-ing capability, are essential Another important issue related to the process view is

the number of data points used in the estimation Ppkis an estimate of the process capability and, thus, even if the process is unchanged, taking another sample and recalculating the index is unlikely to yield precisely the same result The amount of uncertainty is based on both the properties of the process and the number of data ob-servations used to calculate the capability index Larger sample sizes provide more information and, thus, tend to lead to better estimates of the process capability

A further important aspect in considering process capability as an indicator in

designing for availability is process stability A process is considered stable if all the points on its X and R control charts fall within the design control limits, and

there are no apparent deviation patterns The stability of a process is an important property in designing for availability because, if the process design is considered stable, it is likely to also be stable in its installation and in the future, assuming that no major changes occur Thus, the total output of a stable process is, in some sense, predictable If the output of a process is considered stable, then the process’ capability is predictable, from design to manufacture through to installation and/or construction On the other hand, if the process output is not deemed to be stable,

it might still be possible that over time the process capability index can appear to

be stable, depending on the complexity of the process and/or the complex integra-tion of the relevant process systems The predictability of process capability can be obtained by considering the performance of the process in terms of its process ca-pability over time If the pilot process caca-pability values exhibit a stable pattern, then there would be some confidence predicting the installed process capability indices,

which affects the consequences of using the capability indices of Ppkand Cpk If

the process is stable, then Cpkis approximately equal to Ppk, since a stable process has little variability Thus, if the process is stable, it does not matter much which

measure is used (although Ppk is preferred) On the other hand, if the process is

unstable, there will be substantial variability between the data subgroups, and Cpk

is thus not equal to Ppk In the case of process instability, Cpkwill overestimate the

process capability, since it does not include variability The same principle applies if

the process is unstable and yet predictable As a result, in all situations, Ppkprovides

a better measure of the process capability than does Cpk

Thus, in the development of intelligent computer automated methodology for determining the integrity of engineering design, particularly through the use of

a blackboard model to provide for automated continual design reviews with respect

to designing for availability, such reviews inevitably need to include capability

mod-els of each process system Each capability model includes a combination of declar-ative design rules and constraints, design criteria documentation, and process simu-lation results The design rules represent constraints that apply to the design’s mate-rials and processes associated with each process capability model, such as process and functional characteristics, geometric symmetries, and expressions constraining the parameters of specific system features

Process simulations take as input the geometric model of a design or partial design, and return estimates on the process and functional characteristics, or pro-vide a graphical display of the characteristics and their effects For the purpose of ensuring design for manufacturability, a set of design rules that will ensure easy manufacturability is paramount Representations of process-derived geometric con-straints provide a way of assuring manufacturability while maintaining the neces-sary distinction between the representation of the design and the description of the processes used to manufacture it The neutral descriptions of these constraints also enable their use for constraint propagation in qualitative reasoning systems such as

knowledge-based expert systems.

b) Process Characteristics

Process characteristics include the following measures:

• process capacity,

• process input,

• process throughput,

• process output,

• process quality.

Process capacity: Capacity can be defined as “holding or receiving ability”.

The capacity of an engineering process normally represents a limit on the

maxi-mum holding ability of the process In this context, process capacity can be defined

as “the ability of a series of operations to receive and/or hold the result or product inherent to the process”.

Process capacity has thus to do with receiving an input, and a system’s ability

to hold or retain an operational throughput as a result of delivering an output, and

should not be confused with the specific measures of a system’s input, throughput or output Process capacity is the maximum amount of material or product in process.

Process capacity decisions are perhaps the most fundamental of all conceptual engi-neering design considerations One reason for the importance of capacity decisions relates to the impact on the ability of the process to meet future demands—capacity essentially limits the rate of possible output

A second reason for the importance of process capacity decisions is the initial cost involved Capacity is usually a major determinant of a design’s manufactur-ing and installation costs Another reason for the importance of process capacity

decisions stems from the long-term commitment of resources required in the oper-ation of the installed design, and the fact that once installed, it may be difficult to modify the process without incurring major costs

The term process capacity generally refers to an upper limit on the rate of pro-cess output Even though this seems to be simple enough, there are difficulties in

actually measuring process capacity These difficulties arise because of different

in-terpretations of the term process capacity, and problems with identifying suitable

measures Underlying these interpretations, though, is the single fact that process

capacity reflects the availability of process resources.

There are thus three different definitions of process capacity that are applicable

to availability in engineering design:

• Design capacity (Cd): the maximum ability of a series of operations to receive

and/or hold the result or product inherent to the process

• Effective capacity (Ce): the ability of a series of operations to receive and/or hold the result or product inherent to the process, given a specific product mix, production schedule, maintenance, and quality constraints

• Rated capacity (Cr): the throughput actually achieved from operational

con-straints placed upon the ability of a series of operations to receive and/or hold the

result or product inherent to the process Rated capacity is maximum throughput.

Measuring process capacity Process capacity can be expressed in terms of outputs

or inputs, though no single capacity measure is universally applicable Expressing process capacity in terms of output measures is the usual choice for line flow

pro-cesses However, product mix becomes an issue when the output is not uniform in

work content Expressing process capacity in terms of input measures is normally

used for flexible flow processes where process output varies in work content, and

a measure of total production or units produced becomes meaningless

Maximum process capacity can be measured in terms of the average output rate and the average utilisation rate expressed as a percentage

Maximum Capacity(Cmax) = Average output rate

Average utilisation/100 . (4.20) Process input (Ip): Process input is the quantity or volume of process material that

enters the system or equipment over a period of time in accordance with the system’s

operational time Production input in continuous processes is the quantity or volume

of process material that can enter the system or equipment according to its process capacity Maximum input is the maximum ability to receive and/or hold the result

or product inherent to the process, i.e design capacity.

Process throughput (Tp): Process throughput has to do with quantities of

mate-rial entering and leaving the system process over a period of processing time With

continuous processes, throughput is the quantity of material entering and leaving the process in a continuous flow The material or product in process, at rated ca-pacity, is the difference between the input and output at any specific point in time The throughput rate is equivalent to the rated capacity per unit of time Process

throughput rate is indicative of the capability of the process to achieve the de-sired result or output From Little’s law (Little 1961), the formula for the relation of

throughput, cycle time and work in progress in any production line is given as

Production throughput(Tprod) =Work in progress

In the context of discrete industrial processes, work in progress is synonymous to

the material or product in process Thus

Process throughput(TD

proc) =Material in progress

where cycle time in discrete industrial processes= processing time + added time

due to operational constraints and inspection

Process throughput of a continuous process system can be defined as “the ratio

of a system’s material in process over a period of processing time”

Process throughput(TC

proc) = Material in progress

Processing time (4.23)

= Rated capacity (Cr)

Process output (Op): Output can be defined as “the quantity produced or yielded” Process output can be defined as “the quantity of product, or yield of a production process” Process output has to do with yield quantities of product or material from the production process The relationship between process throughput and process output is given by the following

Process output(Op) = Process throughput (Tp) (4.24)

× Yield percentage (Y %) Utilising the previous formula for rated capacity as maximum throughput, the rela-tionship between output and yield in accordance with a process plant’s rated capac-ity gives the following

Process output(Op) = Rated capacity (Cr) (4.25)

× Yield percentage (Y %)

Process or product yield Yield can be defined as “the amount produced or the

output result”.

Product yield in quality terms (without reject product) is the throughput multi-plied by the percentage of successful output result (yield percentage)

Process yield(Yp) = Process throughput (Tp) × Yield percentage (Y %) (4.26)

= Process output (Op)

c) Functional Effectiveness

Functional effectiveness in engineering processes indicates the results produced It represents functional characteristics of the process, such as process efficiency, util-isation and productivity Availability in engineering design, particularly in produc-tion processes, is often looked upon as a funcproduc-tional characteristic synonymous to

productivity in that it relates process output to input.

Process effectiveness in itself is an indication of the design’s manufactured and/or

installed accomplishment against the design’s intended capability Process effective-ness is a ratio of process results (i.e actual output) to process capability (i.e design output)

Process Effectiveness(Wp) = Actual output

Design output. (4.27)

Process efficiency is the ratio of process output achieved through the process throughput (or, in certain cases, process input) In order to understand the concept

of efficiency correctly, and not confuse it with the concept of effectiveness, it is

nec-essary to consider these definitions with regard to related terminology

Inasmuch as output is defined as the quantity produced or yielded, so can effi-ciency be defined as “the capability of producing or yielding an output quantity”.

In fact, it is this capability of output quantity that forms the basis of efficiency mea-surement.

Efficiency measurement is the measurement of productive capability Efficiency

measurement of engineering processes is thus the measure of the capability of pro-ducing or yielding a product It is the measure of the capability of output quantity

Efficiency measurement of a process, as a ratio, must therefore include output quan-tity compared to some or other production parameter of the equipment in order to reflect its capability of output quantity As this productive capability logically relates directly to the amount that can be put through a process, it is conclusive that the pro-duction parameter must be process throughput Efficiency measurement of an engi-neering process is thus a comparison of the output quantity to its process throughput.

Thus

Process efficiency(Xp) = Process output

= Process throughput× Yield percentage

Process throughput

= Yield percentage (Y%)

The measure of efficiency must not be confused with the measure of productivity, which is the ratio of output compared to input Productivity is the “ratio of process output to process input”

Productivity(Z) = Process output

= Process throughput× Yield percentage

Process input

Process utilisation Process utilisation is the ratio of process output to the

con-strained ability to receive and/or hold the result or product inherent to the process (i.e rated capacity)

Process utilisation(Up) =Process output

Functional effectiveness in engineering processes represents the functional charac-teristics of a process, such as efficiency, productivity and utilisation These char-acteristics relate process output to throughput, output to input, and output to ca-pacity respectfully Availability in engineering design is thus considered from the perspective of these functional characteristics, and designing for availability, partic-ularly engineering process availability, considers measurements of process through-put, outthrough-put, input and capacity

d) Mathematical Modelling

For each process system, there is a set of performance measures that require partic-ular attention in design Mathematical models for expressing systems process char-acteristics, and functional effectiveness for both discrete and continuous process systems involve respectively summation and integration of their conjunct variables

over time These models serve as useful indicators in designing for availability, and

adequately represent performance measures of each system that can be described in

matrix form in a parameter profile matrix (Thompson et al 1998):

Discrete process throughput



TprocD 

=∑P

p=1

Continuous process throughput



TprocC 

=

T



t

(Mt /t)dt 0 < t < T (4.32)



TprocC  max= (Cr)

Process output



Op

=

T



t



Op

 max= (Cr) × (Y%)

Process effectiveness



Wp

=

T



t

(Mt /t)(Y t /Od) dt (4.34)



Wp

 max= (Op)max/Od

Process efficiency

(Xp) =

T



t

(Mt /t)Y t /TC

proc



(Xp) = (Y %)

Productivity

(Z) =

T



t (Mt /t)Y t /Ipt



(Z) =



Op



Ip



Process utilisation



Up

=

T



t (Mt /t)(Y t /Cr) dt (4.37)



Up

=



Op

(Cr)

where:

M t = material in process in time t

M t /t = process flow rate or mass-flow rate

Ip = process input

Od = design output

Cd = design capacity

Cr = rated capacity

Opt = process output in time t

(Op)max= maximum process output

In general continuous flow processes, there are certain governing equations of flow,

where the design process flow rate or the mass-flow rate M t /t (i.e throughput, which

is a pivotal parameter in the performance measures for expressing systems process characteristics) is the base measure of fundamental fluid flow The amount of fluid

(or material) flowing through a specified cross section is referred to as the volumetric flow rate.

Let W = Mt /t be the total mass-flow rate of fluid flowing through a specified

cross section Then

where:

V = volumetric flow rate

ρ = fluid density

The average linear velocity of flow is the ratio of the volumetric flow rate to the cross-sectional flow area, as given by the following relationship

ˆ

where:

ˆ

w = average flow velocity

F = cross-sectional flow area

Mass velocity can be expressed as the average velocity modified by the specific weight of the fluid, which is the fluid’s specific gravity

where:

G = fluid mass velocity

γ = fluid specific gravity

For a continuous flow process under steady-state conditions, the mass-flow rate

M t /t, or W, must be the same at any section within the process This is the prin-ciple of mass-flow balance

The mass-flow balance is a statement of continuity, which can also be written as

F1G1= F2G2= F3G3= etc (4.42) where:

F = cross-sectional flow area

G = fluid mass velocity

and:

ρ = fluid density

γ = fluid specific gravity

ρ/γ= constant

Without going into the depths of fluid mechanics and hydraulics, which is not rel-evant to the objectives of this handbook, the nature of general flow regimes needs

to be considered in order to address not only the principle of mass-flow balance in continuous flow processes but their total energy balance as well, so that these

mea-sures can be used in determining system performance characteristics that may serve

as useful indicators in designing for availability without having to formulate the specific operational variables of each individual system This is best done through simulation, which is considered more closely in the next section on analytic

devel-opment

There are fundamentally three general flow regimes in continuous flow

pro-cesses: laminar flow, transition flow and turbulent flow.

The laminar flow regime occurs at relatively low fluid velocities, providing

a smooth flow pattern with no or very little mixing of the fluid particles Transi-tion flow denotes the onset of turbulence In a turbulent flow regime, fluid velocities are higher, and an unstable pattern within the mass flow is observed in which eddy current forces move at all angles to the axis of normal flow

The dependency of a particular flow regime is denoted by the dimensionless Reynolds number whereby a critical Reynolds number indicates the transition from one flow regime to another For instance, if the Reynolds number for flow in

a straight circular pipe is less than 2,100, the flow is laminar When the Reynolds number exceeds 4,000, the flow is turbulent Flow between these two critical num-bers is transitional

The mathematical model for the Reynolds number is given by the following re-lationships

Re = W · D/ν= ˆw · D ·ρ/μ= W · D/μ (4.43) where:

Re= Reynolds number

W = mass-flow rate

D = system or tube (pipe) diameter

ν = kinematic viscosity

ˆ

w = average flow velocity

ρ = fluid density

μ = dynamic viscosity.

Specific mathematical models for volumetric flow rates, V , and average flow

veloc-ities, ˆw, for laminar flows in a variety of systems are available in determining the

Reynolds number

In considering the total energy balance, the flow energy input of a continuous flow process is the sum of the kinetic energy, Ek, the potential energy, Ep, the

vol-umetric energy, Ev, and the internal energy, Ei Any disruption in one or another

of these energies in the total energy balance is an indication of degradation in the performance or operability of the process and, thus, these are important criteria in

its engineering design

The availability of the process or system is concerned with expected system per-formance over a period of expected operational time The prediction of inherent availability of systems is based upon a prognosis of systems performance and sys-tems operability under conditions subject to various performance criteria, such as

mass-flow balance and total energy balance

Inclusive of any heat input from heat exchangers, or mechanical work derived from pumping, the total energy balance of a continuous process flow consists of the

four energies Ek, Ep, Evand Ei, whereby the total energy balance can be formulated

as follows

Ek1+ Ep 1+ Ev 1+ Ei 1= Ek 2+ Ep 2+ Ev 2+ Ei 2 (4.44)

The kinetic energy, Ek, is a function of the fluid mass and the fluid’s linear velocity:

Ek1 = ˆw2

1/2gα

Ek2 = ˆw2

2/2gα

where:

α= correction coefficient and, for turbulent flow,α= 1

The potential energy, Ep, is a function of the weight, Z, of the fluid:

Ep1 = Z1

Ep2 = Z2

The volumetric energy, Ev, under pressure P, is equivalent to the energy required to hold volume v at that pressure:

Ev1 = P1v1

Ev2 = P2v2 The internal energy, Ei, is a thermodynamic property of the flow system, with

refer-ence state energies, E1, E2, which on the input side is a function of heat input from

heat exchangers, He, and mechanical work from pumping, Me, approximated by the

enthalpies i1and i2:

Ei1 = state E1= He+ Me

Ei2 = state E2

i1= E1+ P1v1

i2= E2+ P2v2 The total energy balance can now be formulated as follows (Cheremisinoff 1984):

ˆ

w21/2gα+ Z1+ P1v1+ He+ Me= ˆw2

2/2gα+ Z2+ P2v2+ E2 (4.45) ˆ

w21/2gα+ Z1+ He+ Me= ˆw2

2/2gα+ Z2+ (i2− i1)