Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 35 doc

4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 323
where:
Y
t
= the net cash flow at the end of period t.
In applying NPV, the net cash flows are usually available as input data, which are
assumed to occur instantaneously at the ends of the periods t. Also usually known is
an estimate of the discounting rate, i, to be used. Under these conditions, finding the
NPV is straightforward. The result is a point estimate of a single value at a partic-
ular interest rate i. While the point estimate of NPV is informative, in that one can
determine if it is positive, negative, zer o or indeter minate, the behaviour of the cri-
terion as a function is more informative. For the case of unconstrained assumptions
concerning project acceptance, the general rule is to accept the project if the NPV is
positive. This is true when the present value of the cash inflows exceeds the present
value of the cash outflows (Bussey 1978).
The NPV decreases with increasing discount rate. This is true of any project
for which the cash flow increases on average throughout the project. Secondly, if
the cash flow is negative in the first part of the project, as is true of any project
requiring an initial capital investment, th ere exists some discount rate for which
the NPV becomes zero. This is known as the internal rate of return (IRR).The
IRR constitutes the most useful single characterisation of the financial viability of
a project. It represents the break-even discount rate that will just allow repaym ent
of the initial investment. If the actual discount rate (i.e. interest rate plus any other
related financial charges) is less than the IRR, a profit will result. However, if the
discount rate is higher than the IRR,theNPV will be negative, and the project will
result in a loss, prompting the need for redesign o f critical systems of the proposed
engineered installation, or outright rejection o f an engineering project’s particular
technology, or even of the project itself.
In the alternative approach of using future value, rather than present value, the
estimated life-cycle costs over the project lifetime are reflected for each significant
period in the project’s life-cycle stages, calculated from the required cap ital and the

interest rate for that period. Subtracting these estimated life-cycle cost of capital
from each period’s expected net cash flows yields the future net value. As expected,
it also goes to zero as the discount rate reaches the IRR, which is independent of the
method of calculation. Net profit, or future net value, results from subtracting the
cost of capital from the net cash flow.
The internal rate of return criterion The net present value, described in the pre-
vious sub-section, depends upon the knowledge of an external interest rate for its
application (i.e. external to the project, such as the cost of capital). The internal
rate of return (IRR) method is closely related to NPV in that it also is a discounted
cash flow method, but it seeks to avoid the arbitrary choice of an interest rate. In-
stead, it attempts to find some interest rate, initially unknown, which is internal to
the project.
The procedure is to find an interest rate that will make the present value of the
cash flow of a project zero—that is, some interest rate that will cause the present
value of cash inflows to equal the present value of cash outflows. IRR is defined as
the interest rate i that will cause the net present value P to become zero. Thus, IRR
324 4 Availability and Maintainability in Engineering Design
is the value i such that
P(i)=
N
∑
t=0
Y
t
(1+ i)
−t
= 0 . (4.14)
The IRR must be found by trial and error or by a computer search algorithm tech-
nique, since it is an unknown root (or roots) of a polynomial in i. Thus, if we start
with known values of each cash flow, we can possibly find one or more values that

will make the above equation tru e. These values, if they exist as real numbers, are
known as the project’s internal rate of return,ortheeconomic yield of the project
(in contrast to the economic loss consid ered previously). The selection criterion is
to accept the design project if the IRR is greater than the ma rginal investment rate;
otherwise, the p roject is rejected or, as in the case of a negative NPV, the result is
the redesign of critical systems or the rejection of the project’s specific technology,
rather than of the pro ject itself.
Internal rate of return (IRR) has long been advocated as a project acceptance cri-
terion because, in this criterion, the interest rate is the unknown value that relates
project returns to capital investment outlays. In the sense that it is the functional
value to be established by the expected cash outlays and inflows of the project itself,
it has been called the internal rate of return. However, in many cases, the economic
meaning of IRR as a selection criterion of a design project or proposed engineered
installation is not fully understood.For example, the IRR is not only the interest rate
that causes the net present value of the cash flow of a project to be zero, but it is also
the interest rate that causes exact recovery of investment over the life of the project,
plus a return on the un-recovered investment balances during the life of the project.
A common misinterpretation of IRR is that it is an interest rate expressing a rate o f
return on the initial investment. This is not so. If the IRR is applied periodically to
the initial investment only, then the cash flows fail to recover the initial investment
plus interest at the end of the project life. The fundamental economic meaning o f
IRR is the rate of interest earned on the time-varying, un-recovered balances of in-
vestment, such that the final investment balance is zero at the end of the project’s
life. Since the IRR does not measure the return on initial investment, it has meaning
only when the level of investment is considered along with all the other cash flows
of the project, relative to the project’s total life-cycle costs. These are estimated total
costs incurred in the design, development, production, operation, maintenance, sup-
port and final disposition of the proposed engineered installation over its anticipated
useful life (Aslaksen et al. 1992).
Internal rate of return as a figure-of-merit Under the assumptions of certainty,

it is sometimes possible to use internal rate of return as a figure-of-merit for de-
termining whether a particular design project should be undertaken. It could thus
be viewed as an economic trade-off measure to assess the conditions under which
the IRR may be used as a selection criterion, and when it may not. One of the main
problems encountered in using IRR as such a criterion is the concept of multiple
and indeterminate rates of return. When attempting to obtain the internal rate of
return with certain forms of cash flow, it is possible to find either that a unique so-
lution does not exist for the IRR, and more than one interest rate will satisfy the
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 325
formula, or that no solution can be found at all. When more than one solution exists
mathematically, the cash flow is said to yield multiple rates of return and, when no
solution exists, it is said to have an indeterminate rate of return.
e) Trade-Off Measurement for Life-Cycle Costs
LCC needs to be calculated early in the engineering design stage, to influence final
design outcomes of the proposed engineered installation. Making major changes
in LCC after engineering design projects reach the production stage is often not
possible. LCC helps d etermine optimal maintenance and repair shutdown cycles of
inadequately assessed engineering installations subject to frequent repair at great
expense. Sufficient financing is seldom available to design the project correctly but,
somehow, there is always money available to make major modifications to poorly
configured engineering design installations (Barringer 1998). Consequently, trade-
off measurement methods for LCC early in the life cycle become essential. The cost
effectiveness (CE) equation is one method for LCC trade-off calculations involv-
ing operational and failure probabilities. It offers a figur e-of-merit, and measures
the chances of achieving the intended final design results against predefined life-
cycle costs. The effectiveness equation has been described in several different f or-
mats (Aslaksen et al. 1992; Kececioglu 1995; Pecht 1995; Blanchard et al. 1995).
Each element is a probability. The issue, however, is finding a system effective-
ness value that gives lowest long-term cost of ownership with trade-off considera-
tions.

Cost effectiveness and life-cycle costs Cost effectiveness (CE), as viewed from
a systems engineeringperspective,can be defined as the ratio of system effectiveness
(SE) to its life-cycle cost (LCC; Aslaksen et al. 1992), which is expressed in the
following relationship
CE =
SE
LCC
. (4.15)
In this context, SE is expressed in dollars; so, CE will be a dimensionless parameter.
It is apparent that the evaluation of CE cou ld be separated into the evaluation of SE
and the evaluation of LCC. The definition therefore leads to a conceptually simple,
universal criterion governing all engineering decisions—the decision is good if it
results in an increase in cost effectiveness. This criterion is appropriate for engi-
neering decisions—however, it may not always be entirely suitable for investment
decisions, and there is a significant d ifference between cost effectiveness and IRR
as a figure-of-merit.
System effectiveness System effectiveness (SE) can be defined as a measure of how
well a system will perform the functions that it was designed for, or how well it will
meet the requirements of the system specification. It is often expressed as the prob-
ability that the system can successfully meet an operational d emand within a g iven
operating time under specified conditions. This definition implies a number of im-
portant aspects:
326 4 Availability and Maintainability in Engineering Design
• Operating time may be critical, and SE is often a function of time.
• Maintenance is not excluded; and the specified conditions will in most cases
include both scheduled and unscheduled shutdowns.
• Operational demand implies that there aretwo separate classes ofsystem failures:
– The system can be in an inoperable condition when needed.
– The system can fail to perform sufficiently during the required operating pe-
riod.

• The inclusion of both operational demand and specified conditions shows that
possible failure (i.e. failure to meet operationaldemand)and the conditions under
which the system is intended to be utilised (i.e. operationa l stresses) are related.
It thus follows that, while SE is obviously influenced by system design, it is equally
influenced by the way the system will be used and maintained b y the logistic system
that supports its operation. The definition expressed in terms of a probability is par-
ticularly useful for systems that are required to operate for a prescribed, relatively
short period (i.e. systems fulfilling an intermittent task, as is the case for periodic
operational requirements). For most other systems, however, the period of opera-
tion is the lifetime of the system, and this is usually very long, compared with the
timescales for other events affecting the system, such as shutdowns, etc.
As a result, the system settles into a steady state that is characterised by an aver-
age performance or, more specifically, by an average deviation from design specifi-
cation performance. However, as the performance of a system is usually a complex
multi-dimensional variable, measuring it in terms of a probability is not very appro-
priate. The proper approach is to determine the decrease in the value of the system
as a function of the decrease in performance. The definition of SE can thus be for-
mulated as th e value of the system over its design lifetime (Aslaksen et al. 1992).
Factors affecting the value o f a system: Every system has some value—otherwise,
its development would not even be contemplated. Furthermore, this value must in
some way depend on how well the system performs; if it did not perform at all, its
value would be zero. The problem arises in tryin g to move from a qualitative state-
ment, such as ‘improved availability’, to a quantitative statement such as ‘incr ease
in availability from 0.85 to 0.90 is worth $3.285 million’. It is then found that the
value of a system, particularly its dependence o n various performance parameters,
is often a highly subjective matter. Nevertheless, it is a problem that must be solved
because, without assigning some value to system performance, there is no basis for
taking rational engineering decisions with respect to its cost effectiveness.
Design effectivenessand life-cycle costs Design effectiveness (DE) for LCC trade-
off calculations involves probabilities of design integrity criter ia (i.e. reliability,

availability, maintainability and safety) offering a figure-of-merit that measures the
chances of achieving the intended final design results against integrity constraints
(Blanchard et al. 1995). Such an effectiveness equation is of the following format
Design effectiveness (DE) =
System effectiveness (SE)
Life-cycle costs (LCC)
. (4.16)
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 327
LCC in this case is a measure of resource usage that cannot include all possible cost
elements but must include critical cost items.
System effectiveness System effectiveness in this case is a measure of integrity
(although it rarely includes all integrity elements, as many are often too difficult to
quantify). Based on probability, it varies from 0 to 1. Thus:
System effectiveness = Design integrity×Capability .
Design integrity is reliability/availability/maintainability/safety, and capability is
product of efficiency multiplied b y utilisation.
System effectiveness quantifies important elements of design integrity and life-
cycle costs to find areas for improvement to increase overall effectiveness and to
reduce economic loss.
For example, if availability is 98% and capability is 65%, the opportunity for im-
proving capability is usually much gr eater than for improving availability. System
effectivenessin this contextis helpful for understandingbenchmarksand future pos-
sible status for LCC trade-off information. Figure 4.6 gives a graphical presentation
of effectiveness and life-cycle costs. Although the preference is to select engineer-
ing designs, or projects that have low life-cycle costs and high effectiveness, this
may often not be accomplished in reality (Barringer 1998).
Capability deals with productive output compared to inherent productive out-
put. This index measures the systems capability to pe rform the intended function
on a system basis, and can be expressed as the product of efficiency multiplied
by utilisation. Efficiency measures the expected productive work output versus the

work input. Utilisation is the ratio of expected time spent on productive effort to
the total operational time. For example, suppose efficiency is estimated at 80% and
utilisation is 82.19% because the operation is conducted 300 days per year out of
365 days: the capab ility is 0.8×0.8219= 65.75%.Capability measures how well the
Parameter
Effectiveness
LCC
New
Plant
Last
Plant
Last
Plant
Best
Plant
Last
Plant
New
Plant
Best
Plant
A
0.95
0.3
0.7
0.7
0.14
80
0.95
0.4

0.7
0.8
0.22
100
0.98
0.6
0.7
0.6
0.25
95
BC
Availability
Reliability
Maintainability
Capability
Effectiveness
LCC
Trade-off Area
Worst
Best
A
C
?
?
B
Fig. 4.6 Design effectiveness and life-cycle costs (Barringer 1998)
328 4 Availability and Maintainability in Engineering Design
production activity is performed compared to the datum (Barringer 1998). A more
comprehensive and, in fact, mathematically cor rect definitio n of process capability
is considered in Sect. 4.2.1.2.

Availability and maintainability compared to IRR as figure-of-merit for LCC
Putting aside the elements of reliability and safety in the design integrity equation
in this chapter, the sign ificance of availability and maintainability in design effec-
tiveness and life-cycle costs is specifically considered. Availability deals w ith the
duration of uptime for system s and e quipment. Availability characteristics are usu-
ally determined by the expected operational conditions, which then impact upon
operational procedures and the expected durations of productive time. Availability
measures how productive time is used. Thus, as availability increases, because the
systems and equipment are functional and operational for a longer period of time,
so also does the potential for an increase in the IRR.
Maintainability deals with the duration of downtime for maintenance outages, or
how long it takes to complete maintenance actions compared to a standard. Main-
tainability characteristics are usually de termined by engineering design, which then
impacts upon maintenance procedures and the expected durations of shutdowns.
A key maintainability figure-of-merit is the mean time to repair (MTTR) c ompared
to a limit for th e maximum repair time. Qualitatively, it refers to the ease with
which systems and eq uipment are restored to a functioning state. Quantitatively,
it is a probability measure based on the total downtime for maintenance. Maintain-
ability measures the probability of timely repairs. Thus, as maintain abilityincreases,
because systems and equipment are down for a shorter period of time, so also does
the potential for increase in the IRR.
4.2.1.2 Availability Modelling Based on System Performance
System performance, in the context of designing for availability, can be perceived
as the combination of a system’s process capability with regard to the process char-
acteristics of capacity, input, throughput, output and quality, a system’s functional
effectiveness with regard to the functional characteristics of efficiency and utilisa-
tion, as well as consideration of a system’s operational condition with regard to
operational measures such as temperatures, pressures, flows, etc. All these charac-
teristics may serve as useful indicators in designing for availability without having
to formulate the specific operational variables of each individual system,andto

consider instead a system’s capability, effectiveness and condition.
In order for designers to be confident about using novel manufacturingprocesses,
and still achieve the necessary availability constraints during the design of engi-
neered installations, a more intimate dialogue between engineering design and man-
ufacturing is necessary. Ideally, all aspects of the manufacturing process should be
accessible and understood. For example, designers should be able to run process
simulations, at either a superficial or detailed level, on partial or whole designs. D e-
sign engineers should be able to obtain ‘manufacturability’ and ‘constructability’
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 329
rules and guidelines that can be loaded directly into the relative engin eering de-
signs’ computer aided design (CAD) environments. Furthermore, design engineers
should be able to load processing constraints (e.g. materials or feature dimensions)
into their CAD systems and have these checked and enforced before submitting de-
signs to manufacturers. In this way, designers can become familiar with the design’s
specific manufacturing and construction requirements. In some cases, an overview
description of the process capabilities may suffice. In other cases, when it is es-
sential to minimise manufacturing costs, or to meet stringent demands on design
specifications or material properties, the d esigner must have detailed information
on the specific design’smanufacturing characteristics and constraints. An important
aspect of being able to submit designs with confidence that the end result will meet
design specifications is the adoption of conservative design rules that specify design
features that are manufacturable (Mead 1994).
A variety of CAD tools can be used that provide a standard mechanism by which
designers can obtain process capability models from disparate processes, and load
these into their CAD environments. Specifically, the mechanism should enable de-
signers to acquire capability models that can be used to compute a system’s process
capability, functional effectiveness, operational condition and manufacturability of
evolving designs with accuracies necessary to meet the design requirements. (In this
context, ‘manufacturability ’ includes both the ease of fabrication and the ease of
assembly/construction, as considered by Taguchi’s methodology for implementing

rob ust design; Taguchi 1993.)
Robust design (RD) is an important methodology for improving the design’s
manufacturability and for increasing process system stability. Since its introduction
to the US industry in 1980, Taguchi’s approach to quality engineering and robust
design has received much attention from designers, manufacturers, statisticians, and
quality professionals.
Essentially, the central idea in robust design is that variations in a process sys-
tem’s performance can inevitably result in poor quality and monetary losses during
the system’s life cycle. The sources of these variations can directly be classified into
the two categories of controllable and uncontrollableparameters. In a typical design
application, factors such as geometric dimensions (sizing) of equipment can easily
be controlled by designers. Uncontrollable factors, such as environmental variables,
component deterioration or manufacturing imperfections, are also sources of vari-
ations having effects that cannot be eliminated, and must especially be considered
in designing for availability. Therefore, RD’s main function is to reduce a design’s
potential variation by reducing the sensitivity of the design to the sources of vari-
ation, rather than by controlling these sources. In oth er words, RD reduces poten-
tial system response variations by designing appropriate capability model settings
for controllable parameters, in order to dampen the effects of hard-to-control vari-
ables. Taguchi’s methodology for implementing robust design is essentially a four-
step procedure that includes not only formulating the design problem but planning,
analysing and verifying the design results as well (Taguchi et al. 1989).
A communication mechanism should also allow unsolicited information, such
as updates on process capabilities, to be transmitted from manufacturing facilities
330 4 Availability and Maintainability in Engineering Design
to designers. To enable such a dialogue between designers and manufacturers, the
following issues must be addressed:
• How is process capability or func tional effectiveness represented?
• How are capability models located and acquired by the designer?
• How are capability models mapped into the design space?

• How is information contained in these models applied throughout engineering
design?
These issues require some further form of methodology for information exchange,
not only between engineering design teams but also between designers and manu-
facturers. Such a methodology should include an object-oriented architecture that
expedites the task of combining CAD environments with process manufacturing
and/or construction planning, a mechanism for knowledge representation that en-
ables the exchange of design integrity information, and a communication protocol
between designers and manufacturers.
Such a methodology addresses the possible and practical application of artificial
intelligence (AI) modelling techniques, with the inclusion of knowledge-based ex-
pert systems within a blackboard model, in the development of intelligent computer
automated methodology for determining the integrity of engineering design. The
blackboard model provides for automated continual design reviews of engineering
design, including communication protocols and an object-oriented language that al-
lows segregate design groups to remotely exchange collaborative information via
the internet (McGuire et al. 1993; Olsen et al. 1995; Pancerella et al. 1995).
On this basis, different engineering design expertise groups, and manufacturing
companies specialising in specific engineering systems can concurrently participate
in collaborative design from around the world, whereby input of design parameters
and criteria into a blackboard model provides for automated continual design re-
views of the overall engineering design. Such a blackboard model, together with its
knowledge-based expert systems, must be suitable both in programming language
efficiency and in communication protocols for internet application.
a) Process Capability
In the context of industrial processes, the definition of process is “a series of op-
erations performed to produce a result or product”, and capability is defined as
“effective action”. Process capability can thus be defined as “the effective action of
a series of operations to produce a result or product”.
A process capability model is a m athematical model that compares the behaviour

of a process characteristic to engineering specifications. A process capability index
is a numerical summary of th e model, also called a capability or performance in-
dex or ratio, where capability index is used as the generic term. A capability index
relates design specification limits to a particular process characteristic. The index
indicates that the process is capable of producing results that, in all likelihood, will
meet or exceed the design’s requirements. A capability index is convenient because
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 331
it reduces complex information about the process to a single number. Capability in-
dices have several applications, though the use of the indices is driven mostly by
monitoring requirements specified by design criteria.
Many design engineers require manufacturers to record capability indices for all
the design’s process characteristics on a heuristic basis. The indices are used to in-
dicate how well the process may perform. For stable or predictable processes, it is
assumed that these indices will also indicate expected future performance. Suppli-
ers or manufacturers may use capability indices for specific system characteristics
to establish priorities for improvements after installation. Sim ilarly, the effects of
process change can be assessed by comparing capability indices that are calculated
before and after the change. However, despite the widespread use of capability in-
dices in industry, and some good review articles (Gunter 1989a, b, c, d), there is
much confusion and misunderstanding regarding their interpretation and appropri-
ate use, particularly as a tool for comparing process characteristic to engineering
specifications in designing for availability.
Process capability in quantified terms is the ratio of the deviation of a process
characteristic from the specification limit, divided by a measure of a process char-
acteristic’s variability. Process capability can be r epresented in mathematical terms
as (Steiner et al. 1995):
Process Cap ability = min

USL−
μ

3
σ
μ
−LSL
3
σ

(4.17)
where:
USL and LSL are the upper and lower specification limits respectively,
μ
and
σ
are the mean and standard deviation respectively for measures of the
process characteristic of interest.
Calculating the process capability requires knowledge of the process characteristic’s
mean and standard deviation,
μ
and
σ
. These values are usually estimated from
trial or test data collected from a pilot process. The two most widely used capability
indices, P
pk
and C
pk
, are defined as
Capability P
pk
= min


USL− ¯a
3
σ
¯a−LSL
3
σ

(4.18a)
where:
USL and LSL are the upper and lower specification limits respectively,
¯a the overall average, is used to estimate the process m ean
μ
and
σ
,
σ
is the stand ard deviation of the process characteristic of interest.
Capability C
pk
= min

USL− ¯a
3
σ
Rd
¯a−LSL
3
σ
Rd


(4.18b)
where:
¯a the overall average, is used to estimate the process mean
μ
and
σ
,
σ
Rd
is the estimate o f the process standard deviation
σ
,
332 4 Availability and Maintainability in Engineering Design
d is an adjustment factor that is needed to estimate the process standard
deviation from the average trial or test data sample range R.
The sample standard deviation is given by the formula
σ
=

n
∑
j= 1
m
∑
i=1
(X
ij
− ¯a)
2

/(nm−1) (4.19)
where:
m is the total number of subgroups, and n is the subgroup sample size.
Since d is also used in the derivation of control limits for X and R control charts,
it is also tabulated in standard references on statistical process control, such as in
the QS-9000 SPC manual (Montgomery 1991). Large values of P
pk
and C
pk
for
several specific process characteristics should correspondto a processthat is capable
of operating within the design specification limits. The commonly used index P
p
and the related index C
p
in process design are similar to P
pk
and C
pk
.However,P
p
and C
p
ignore the current estimate of the process characteristic mean, and relate
the specification range directly to the process characteristic variation. In effect, P
p
and C
p
can be considered convenient conceptual design measures that suggest how
capable the process should be if the process characteristic’s mean is centred midway

between the specification limits.
The indices P
p
and C
p
are not recommended for process evaluation purposes dur-
ing the detail design phase, since the information they provide to supplement P
pk
and C
pk
is independent of data. Histograms of trial or test data collected from a pilot
process, usually established during the detail design phase of the engineeringdesign
process, are preferable because they also provide other useful process information.
However, various important issues relating to the calculation and interpretation of
capability indicesrequire closer attention. The designcapability of a process is even-
tually estimated from pilot trial or test data that represent a sample of the envisaged
total production.
Clearly, the capability indices P
pk
and C
pk
are greatly influenced by the way
in which the process data are collected, what is normally called the process view.
A process view is defined by the time frame and sampling method (sampling fre-
quency, sample size, etc.) u sed to obtain the pilot process data. Using an appropriate
process view is crucial, since different views can lead to very different conclusions.
For example, in one view the process may appear stable, while in another the pro-
cess could appear unstable. To define the process view, the first choice involves the
time frame over which the pilot process data will be collected. Often, the time frame
is stipulated as a typical cycle-time in terval. For example, the capab ility of each se-

lected process characteristic may be measured as a function of the operating time in
relation to the process cycle-time.
In other situations, the time frame is restricted to a shorter interval, such as the
period needed for the pilot process to produce a specific number of productionunits.