Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 41 ppsx

4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 383
• Equipment and/or system utilisation.
• Failure occurrence in the equipment.
• Failure mode of the failed component.
• Failure consequence and severity.
• Number of similar parts or components.
• Frequency of preventive maintenance replacement.
Although seemingly problematic from the perspective of complexity, the multiplic-
ity of similar parts in each component, with usually a large number of similar com-
ponents within each system, is in fact beneficial in characterising the demand for
different kinds of spares. It validates the application of classical limit theory con-
cerning the maintenance renewal process. This is illustrated by the following theo-
rem (Drenick 1960):
given N components, indexed by i = N, K, 1, of which the failure processes are
independent renewal processes, let F
i
(t) be the distribution for the time between
failures o f component i.Furthermore,
λ
i
is the expected number of renewals per
time unit, so that its reciprocal, 1/
λ
i
, is the expected time b etween failures of
component i.
Let G
N
(t) be the distribution of the time between failures across all components. If:
(i) lim
N→∞

λ
i
/
N
∑
i=1
λ
i
= 0
(ii) F
i
(t) ≤ At
σ
and A > 0,
σ
> 0ast →0 ∀i
then
lim
N→∞
G
N

t/
N
∑
i=1
λ
i

= 1−e

−
λ
t
for t > 0 . (4.115)
Consequently, Drenick’s theorem states that, under the above assumptions, the
pooled output will approach a Poisson process as the number of failures increase.
Condition (i) is non-restrictive. Condition (ii) is satisfied by all failure distributions
commonly used—for example, the Weibull distribution. Thus, when the demand for
a spare is the result of several component failure processes (which it normally is),
the demand tends to be approximated by a Poisson distribution—that is, the demand
rate is constant, irrespective of whether the individual components have arbitrary
failure characteristics.
There are only a few quantitative methods available when determining spares
requirements. These are identified as analytical methods based on constant demand
rates, analytical methods based on renewal theory, as well as simulation models.
Analytical methods based o n constant demand rates tend to be the most applicable
for spares requirements modelling.
Renewal theory describes component failure by the renewal process that is char-
acterised by a distribution for the time between renewals denoted F(t). If the distri-
bution F(t)=1− e
−
λ
t
, then the renewal process is a Poisson p rocess with rate
λ
.
Hence, the renewal process is usually a generalisation of the Poisson distribution.
384 4 Availability and Maintainability in Engineering Design
However, the renewal process does not include several properties o f the Poisson
distribution. Most importantly, the result of two independent renewal processes is

not a renewal process unless both processes are Poisson processes. Furthermore,
the probabilistic split of a renewal process does not yield independent renewal pro-
cesses.
As indicated p reviously, when modelling for sp ares requirements, the demand is
ultimately dependent upon several factors. Spares demand is in most circumstances
the result of the component failure characteristics. If the component failure is mod-
elled as a renewal process, the spare demand is not a renewal process. In effect,
models based on renewal theory have limited applicability in terms of spares op-
timisation. Such models are limited to a single process—that is, a single system,
single component, and single part situation, which is very rare when determining an
optimum spares requirements strategy for a real-world engineering design.
Simulation models are generally impractical for spares optimisation (or, in fact,
any kind of optimisation). Event-driven simulation can be applied to a nalyse basi-
cally any stochastic system or process. In terms of optimisation, however, it is not
applicable. The reason for this is the relatively extensive time required for a single
function evaluation. Any optimisation algorithm iteratively evaluates an objective
function and/or its derivatives numerous times in order to establish the optimal so-
lution. If each function evaluation takes time, the optimisation algorithm soon be-
comes imp ractical. Function evaluation is generally much faster, and optim isation
feasible with analytical models based on Poisson demand (constant demand rate).
An analytical method for spares requirements based on a Poisson demand, or con-
stant demand rate, which is approximated by the constant failure rate, can thus
be developed (with a sufficient degree of acceptance) as the probability of having
a spare when required. Such a probability takes into consideration the constant fail-
ure rate of an item (component or part) that is intended to h ave a spare, the number
of items in the equipment and/or system that are intended to have spares (critical
items), and the number of items in the system as a whole. The following model can
be used to determine the spares requirement quantity (Blanchard et al. 1995):
SP =
m

∑
i=0
[(−1)ln(e
−n
λ
t
)]
i
e
−n
λ
t
/i! (4.116)
where:
SP = the probability of having a spare when required
m = the number of items in the system as a whole
n = the number of items intended to have spares
t = perio d of time in which an item is likely to fail
λ
= the constant failure rate of an item intended to have a spare.
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 385
4.2.3 Theoretical Overview of Availability and Maintainability
Evaluation in Detail Design
Availability and maintainability evaluation determines the measures of time that are
subject to equipment failure, particularly known values of failure rates and repair
rates for each individual item of equipment at the lower systems levels of the sys-
tems breakdown structure. Availability and maintainability evaluation is con sidered
in the detail design phase of the engineering design process, with determination of
the rates and frequencies that component failures occur and are repaired over a spec-
ified period of time. The most applicable methodology for availability and maintain-

ability evaluation in the detail design phase includes basic concepts of mathematical
modelling such as:
i. Dependability modelling for availability and maintainability
ii. Operational availability modelling subject to logistic support
iii. Maintainability evaluation and built-in or non-destructive testing
iv. Specific application modelling of availability and maintainability.
Due to the increasing complexity of engineering processes, it is unrealistic to ex-
pect that standard specifications covering the operational evaluation of a system are
adequate for detail engineering designs. The problem in the specification of the op-
erational process is complexity. Potential deviations from the expected operational
behaviour can be caused by unexpected failures in a complex system environment,
or by the complex integration of several systems. To challenge the problems of
complexity,all possible operational sequences must be considered in an operational
specification, essential for modelling a complex system in its expected operational
state, or at least according to a predetermined level of abstraction of such an oper-
ational state. This form of modelling, which incorporates operational specifications
during the detail design phase of the engineering design process, is often termed
operational modelling. The aim of operational modelling is to determine the op-
erational view of an engineering design, and to integrate it with operational and
technical specifications to guarantee model consistency.Various operational models
are considered, including a gr aphical formalism appropriate f or modelling concur-
rent processes, and thus for describing the operational view of complex integrated
systems.
4.2.3.1 Dependability Modelling for Design Availability and Maintainability
Dependability is the measure of a system’s condition during operation, provided that
it is available for operation at the beginningof its application (i.e. operational avail-
ability, which will be considered in detail in the following section ). Dependability
can also be described as the probability that a system will accomplish its intended
application (or mission), provided that it was available for operation from the begin-
ning (Dhillon 1999b). Dependability models used for the evaluation of performance

386 4 Availability and Maintainability in Engineering Design
of an engineering design are considered from a twofold meaning of the concept of
dependability (Zakarian et al. 1997):
• System operational integrity
(reliability, availability and maintainability).
• System performance
(dependence on the performance of equipment).
A dependability model that consid ers the operational integrity of a process engi-
neering system, where the system is considered to be operational as long as its
functional requirements are satisfied, includes the measures of operational integrity
(operational reliability R
o
, operational availability A
o
, and operationalmaintainabil-
ity M
o
). A dependability model that co nsiders system performance includes mea-
sures of the process characteristics. In other words, a process system is assumed to
function properly if it is able to achieve the required level of performance where the
process capability, as given in Eq. (4.17), exceeds a given lower bound of a partic-
ular process characteristic. Careful consideration of these concepts of dependability
of a process engineering system during the engineering design stage can definitely
improve system dependability.
Dependability D
s
, considering system operational integrity, is modelled as
D
s
= M

o
(1−R
o
)+A
o
(R
o
) (4.117)
where:
R
o
= oper a tional reliability as fraction/percentage
A
o
= oper a tional availability as fraction/percentage
M
o
= oper a tional maintainability as fraction/percentage.
Expressing system dependability in performance measures for operational relia-
bility, availability and maintainability would include the measures of MTTR and
MTBF. In this case, system dependability is the sum of the ratios of system uptime
to total cycle time, and system repair time to total downtime.
It is therefore an indication of the fraction of time that a system is available in
a cycle of system operation and failure, plus the fraction of time that the system
is repairable when it is down (i.e. the ability of being used when it is up plus the
ability of being repaired w hen it is down). Thus
D
s
= A
o

+ MTTR/MDT (4.118)
In the case where the performance measure of operational availability can be ex-
pressed as
A
o
=
MTBF
MTBF+MDT
(4.119)
where:
MDT = expected mean downtime
MDT = T
pm
+ T
cm
+ T
ld
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 387
where:
T
pm
= preventive maintenance downtime
T
cm
= corrective maintenance downtime
T
ld
= logistics and administrative downtime
then
D

s
=
MTBF
MTBF+MDT
+
MTTR
MDT
. (4.120)
In the case where the expected mean downtime includes only preventive mainte-
nance downtime, the availability performance measure becomes inherent availabil-
ity,andD
s
is expressed as
D
s
=
MTBF
MTBF+MTTR
+
MTTR
T
pm
. (4.121)
4.2.3.2 Operational Availability (A
o
) Modelling with Logistic Support
Operational availability, unlike inherent availability or achieved availability, cov-
ers all segments of time that the system’s equipment is intended to be operational
(total time in Fig. 4.1). The same uptime and downtime relationship exists, except
that it has b een expanded. Uptime now includes operating time p lus non-operating

(standby) time when the equipment is assumed to be operable. Downtime has been
expanded to include preventive and corrective maintenance and the associated ad-
ministrative and logistics lead time. All are normally measured in clock time. This
relationship is intended to provide a r ealistic measure of equipment availability
when the equipment has been installed and is functioning in an operational envi-
ronment. Operational availability is used to support operational testing assessment
and life-cycle costing.
Operational availability is the most desirable form of availability to be used in
evaluating the operational potential of equipment, and is an important measure of
system effectiveness b ecause it relates the system’s equipment, logistic support and
environment characteristics into one meaningful parameter—an index depicting the
state of equipmentat the beginningof its operation in an engineered installation. Be-
cause it is an effectiveness-related index, operational availability is used as a starting
point for n early all system effectiveness and sizing analyses during the later stages
of the engineering design process.
One significant problem associated with evaluating ope rational availability is that
it becomes costly and time-consuming to define all the various parameters, espe-
cially during the detail engineering design phase when all equipment (assemblies
and components) are being identified. For instance, defining administrative and lo-
gistics downtime per equipment per specified period, and total preventive mainte-
nance under normal operational conditions is very difficult and not feasible in many
cases. Nevertheless, evaluating operational availability does provide an accepted
methodology of relating standard reliability and maintainability characteristics into
388 4 Availability and Maintainability in Engineering Design
a single effectiveness-oriented parameter. As such, it is an essential tool for deter-
mining the integrity of engineeringdesign. An important aspect to take note of when
evaluating operational availability is that it is affected by equipment u sage or util-
isation rate. The less an item is used in a given period, the higher the operational
availability will b e.
Therefore, when defining the ‘total time’ period, it is important to exclude

lengthy periods during which little or no system usage is anticipated. One other ex-
pression for operationalavailability is when standby time is assumed to be zero,typ-
ical of single stream processes with no equipment redundancy. While maintenance-
oriented, this form of oper ational availability still retains consideration of the same
basic time elements. The downtime interval includes corrective and preventive
maintenance, as well as administrative and logistics downtime. This form of op-
erational availability would generally prove more useful in support of d efining pre-
ventive maintenance requirements and logistic support analysis during the detail
design phase of the engineering design process. The general mathematical model
for operational availability is (Conlon et al. 1982):
A
o
=
OT + ST
OT+ ST+ TCM+ TPM+ALDT
(4.122)
where:
OT = operating time
ST = standby time
TCM = total corrective maintenance
TPM = total preventive maintenance
ALDT = administra tive and logistics downtime.
Inherent availability looks at availability from a design perspective, whereas op-
erational availability considers system effectiveness and the operational potential
of equipment, and is used for analysing the sizing of equipment during the later
stages of the engineering design process. Thus, more encompassing maintainabil-
ity measures of mean time between main tenance and mean downtime are used in
the operational availability equation. Operational availability is, in effect, a model
of maintainability measures in which downtime resulting from both corrective and
preventive maintenance is considered. A

o
is thus a smaller availability value than A
i
.
Operational availability can thus be mathematically expressed as
A
o
=
MTBM
(MTBM+MDT)
(4.123)
where:
MTBM = mean time between maintenance
MDT = mean downtime.
The mean time between maintenance (MTBM) includes all corrective and preven-
tive actions (compared to MTBF, which accounts for failures—in contrast to the
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 389
concept of A
o
for dependability in Eq. (4.119)). The mean downtime (MDT) in-
cludes all time associated with the system being down for corrective maintenance
including delays (compared to MTTR, which addresses only repair time), including
downtime for preventive maintenance (PM), plus administrative and logistics down-
time. Although it is preferred to design equipment for which most PM actions can
be performed while the equipment is operating (such as built-in testing, BIT), PM
in this context implies a certain downtime.
The uptime and downtime concepts for constant values of availability indicate
the relative difficulty of increasing availability at higher percentages, compared to
improving availability at lower percentages. This is illustrated by the fact that in-
creasing availability from 99 to 99.9% requires an increase in MTBM by one order

of magnitude or a decrease in MDT by one order of magnitude, whereas increasing
availability from 85 to 90% requires improving MTBM by less than 1/2orderof
magnitude or decreasing MDT by 3/4 order of magnitude.
a) General Approach for Evaluating Operational Availability
The operational and maintenance concepts associated with system utilisation must
be defined in detail using terminology compatible with all involved in the design
of engineered installations. Using these definitions, a time-line availability model is
constructed that reflects the availability parameters, as illustrated in Fig. 4.9 (Conlon
et al. 1982).
Figure 4.9 displays elements of availability,particularly standby times (ST
W
)and
(ST
C
), which are included in quantitative operational availability.
The up or down status of a system during p reventivemaintenancemust be closely
examined because, generally, a portion of the preventive maintenance period may
be considered as uptime. Standby time must also be examined closely before deter-
mining system up or down status during this period. With the aid of the time-line
model, all time elements that represent uptime and downtime are determined. For
example, a maintenance strategy may be definedso that the equipment is maintained
in a committable or up-state during the performance of preventive maintenance.
Additionally, for multi-mode systems, it will be necessary to determine uptimes
and downtimes as a function of each mode. This generally will require the use of
a separate time-linemodel for each identifiable operational mode. Separate time-line
Total time (TT)
TCM ALDT TPM
up up down down up/down up or down
Operating time
(OT)

Standby time
(ST
W
)
Standby (cold)
(ST
C
)
Fig. 4.9 Operational availability time-line model—generalised format (DoD 3235.1-H 1982)
390 4 Availability and Maintainability in Engineering Design
models are g enerally required to support the availability analyses of systems that
experience significantly different continuous, periodic, and surge utilisation rates.
Quantitative values for the individual time-line models are determined and coordi-
nated with the engineering design project management baselines. Time elements are
computed and availability evaluated, using the definitions of operational availabil-
ity appropriate for the detail design phase. Availability model status is continually
checked and updated as required. The model is updated as the operational, mainte-
nance and logistics support concepts progressivelybecome defined and quantifiable.
b) System Availability Evaluation Considerations
As ind icated previously, the quantitative evaluation of availability must be carefully
and accurately tailored to each system. However, there are certain general concepts
that will apply to different types of process engineering systems, such as recovery
time. Normally, availability measures imply that every hour has equal value from
the viewpoint of operations and maintenance/logistics activities. The operational
concept requires the system to function only for selected periods. The remaining
time is traditionally referred to as ‘off-time’ during which no activity is conducted.
An alternative to ‘off-time’ or ‘cold standby’ is the use of the term ‘recovery time’.
Recovery time represents an interval of time during which the system may be up or
down (Fig. 4.10) . Recovery time, RT, does not appear in the operational availability
calculation that is based only on the total time period TT. Significantly, corrective

maintenance time TCM is found in both TT and RT time intervals.
Corrective maintenance performed during the TT period is maintenance required
to keep the system in an operational available status. Corrective maintenance per-
formed during the RT period generally addresses malfunctions that do not result in
a downtime status.
The principal advantage of using recovery time analysis is that it can provide
a meaningful availability evaluation for systems with operational availability that
is predictable, and preventive maintenance that constitutes a significant p ortion of
maintenance time. The recovery time calculation technique concentrates availability
calculation during the operational time period, thereby focusing attention on critical
uptime and downtime elements.
Total time (Disregarding recovery) Recovery time
(RT)
TCM TCMALDT TPM
up up down down up/down up or down
Operating time
(OT)
Standby time
(ST
W
)
Recovery
Fig. 4.10 Operational availability time-line model—recovery time format (DoD 3235.1-H 1982)
4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 391
4.2.3.3 Maintainability Evaluation and Built-In or Non-destructive Testing
Maintainability has been defined as a characteristic of design and installation. It is
this inherent characteristic of a completed engineering design that determines the
type and amount of maintenance required to restore or retain it in a specified con-
dition. Where maintainability is a design consideration, maintenance is the con-
sequence of the design. It is thus apparent that the ability and need to perform

maintenance actions is the underlying consideration when evaluating maintainabil-
ity. The consideration of maintenance when designing engineering systems is not
new. There have been very successful efforts in the development of design for acces-
sibility, built-in testing, etc. What is new is the emphasis on quantitative assessment
and evaluation that results in a complete change in engineering design philosophy,
methodology and management. In the past, design for maximum or optimum reli-
ability and maintainability was emphasised. However, all this resulted in was un-
known reliability and maintainability from the design stage through to installation.
New techniquesand methods allow design integrity judgment to be quantitatively
measured, as in the case of maintainability evaluation. Maintainability evaluation is
the determination of desig n considerations and testing, intended to evaluate system
maintainability characteristics that are based on quantitative measures or indices. In
addition to evaluating these characteristics, maintainability evaluation should also
address the impact of physical design features on system maintenance and mainte-
nance action frequency.
There are various mathematical indices used to evaluate system maintainability
characteristics. These indices must be composed of measurable quantities, provide
effectiveness-orienteddata, and must be readily obtainable from applicable develop-
ment testing, such as the use of non-destructive testing (NDT) internal or integrated
diagnostic systems, also referred to as built-in-test (BIT) or built-in-test-equipment
(BITE), and applied to pilot systems as well as to the engineered installation. The
use of maintainability evaluation indices enables engineering designers to evaluate
system and/or equipment characteristics as well as logistics and maintenance prac-
tices more precisely during the detail design phase.
a) Main tainability Evaluation Indices
Mean time to repair (MTTR) As noted previously,the maintainability measure of
mean time to repair (MTTR) is the total corrective maintenance downtime accumu-
lated during a specific period, divided by the total numberof correctivemaintenance
actions completed during the same period. MTTR is commonly used as a general
equipment maintainability measure, although it can be applied to each maintenance

level individually. MTTR considers active corrective maintenance time only. Be-
cause the frequency of corrective maintenance actions and the number of man-hours
expended are not considered, this index does not provide a good measure of the
maintenance burden.
392 4 Availability and Maintainability in Engineering Design
Maximum time to repair (MaxTTR) MaxTTR is the maximum corrective main-
tenance downtime within which either 90 or 95% (as specified) of all corrective
maintenance actions can be accomplished. A MaxTTR requirement is useful in
those special cases in wh ich the re is a tolerable downtime for the system.
An absolute maximum is ideal but impractical because there will be failures that
require exceptionally lon g repair times. A 95th percentile MaxTTR specification
requires that no more than 5% of all corrective maintenance actions take longer
than MaxTTR.
Maintenance ratio (MR) MR is the cumulative number of man-hours o f main-
tenance to be expended in direct labour over a given period of time, divided by
the expected cumulative number of end-item operating hours. Both corrective and
preventive maintenance are included. Man-hours for off-system repair of replaced
components, and man-hours for daily operational checks are included for some sys-
tems. Particular care must be taken that the operating hour base be clearly defined,
such as in the case of p ower-generatingsystems, when either system operating hours
or power delivery hours can be used. MR is a useful measure to determine the rela-
tive maintenance burden associated with a system. It providesa means of comparing
systems and is useful in determining the compatibility of a system with the required
size of the maintenance organisation.
Mean time between maintenance actions (MTBMA) MTBMA is the mean of
the distribution of the time intervals between either corrective maintenance actions,
preventive maintenance actions or all maintenance actions. This index is frequently
used in availability calculations and in statistically oriented maintenan ce analyses.
Average number of maintenance man-hours required The average number of
maintenance man-hours r equired at each maintenance level provides a quantitative

means of expressing the personnel requirementsof the overallmaintenanceconcept.
This index also provides a conversion factor from active downtime to labour hours.
Maintainability cost indices Maintainability is a significant factor in the cost of
equipment. An increase in maintainability results in a r eduction of logistic support
costs of engineered installations. A more maintainable system inevitably reduces
maintenancetimes and operating costs, and a more efficient maintenanceturnaround
reduces downtime. There are many factors o f maintainability that contribute to the
investment costs of engineered installations. These include a direct effect on sys-
tem and equipment hardware costs, support equipment, built-in testing, and contract
spares.
Off-system maintainability indices The indices MTTR, MaxTTR and MR all
specifically exclude off-system maintenance actions. Off-system measures are par-
ticularly important if a system ’s maintenance strategy involves extensive use of
modular removal and replacement for workshop repair/overhaul, since this type of
concept transfers the maintenance burden to off-system maintenance. As a main-
tainability evaluation tool for engineered installations, off-system maintainability
measures are essential. Without these, it is not possible to evaluate the ability of