Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 43 pptx

The equivalent mean time to outage EM Equivalent mean time to outage can be defined as “the comparison of the equipment’s operational time, to the number of full and partial outages over

Equiv Availability (EA)=Operational Time

Time Period ×Process Output

MDC

=∑[(To) · n(MDC)]

T · MDC

=[480 × (1)] + [120 × (0.5)]

720× (1)

= 0.75 or 75%

where:

Total time period = 720 h

Operational time = (480 + 120) = 600 h

MDC = maximum dependable capacity

MDC = 1 × (constant representing capacity, C)

Process output = [0.75/(600/720)][(1) ×C]

Process output = 0.9C

Process output = 90% of MDC

b) Equivalent Maintainability Measures of Downtime and Outage

It is necessary to consider mean downtime (MDT) compared to the mean time to repair (MTTR) There is frequently confusion between the two and it is important

to understand the difference

Downtime, or outage, is the period during which equipment is in the failed state Downtime may commence before repair, as indicated in Fig 4.11 (Smith 1981).

This may be due to a significant time lapse from the onset of the downtime period

up till when the actual repair, or corrective action, commences

Repair time may often involve checks or alignments that may extend beyond the downtime period From the diagram, it can be seen that the combination of down-time plus repair down-time includes aspects such as realisation down-time, access down-time,

diag-nosis time, spare parts procurement, replacement time, check time and alignment

time MDT is thus the mean of all the time periods that include realisation, access, diagnosis, spares acquisition and replacement or repair.

A comparison of downtime and repair time is given in Fig 4.11.

According to the American Military Standard (MIL-STD-721B), a failure is de-fined as “the inability of an item to function within its specified limits of perfor-mance” Furthermore, the definition of function was given as “the work that an item

is designed to perform”, and functional failure was defined as “the inability of an item to carry-out the work that it is designed to perform within specified limits of performance”.

From these definitions, it is evident that there are two degrees of severity of func-tional failure:

• A complete loss of function, where the item cannot carry out any of the work that

it was designed to perform

Fig 4.11 A comparison of downtime and repair time (Smith 1981)

• A partial loss of function, where the item is unable to function within specified

limits of performance

In addition, equipment condition was defined as “the state of an item on which its function depends” and, as described before, the state of an item on which its function depends can be both an operational as well as a physical condition.

An important principle in determining the integrity of engineering design can

thus be discerned relating to the expected condition and the required condition

as-sessment (such as BIT) of the designed item:

An item’s operational condition is related to the state of its operational function or working performance, and its physical condition is related to the state of its physical function or design properties.

Equipment in a failed state is thus equipment that has an operational or physical condition that is in such a state that it is unable to carry out the work that it is

designed to perform within specified limits of performance Thus, two levels of

severity of a failed state are implied:

• Where the item cannot carry out any of the work that it was designed to perform, i.e a total loss of function.

• Where the item is unable to function within specified limits of performance, i.e.

a partial loss of function.

Downtime, or outage, which has been described as the period during which

equip-ment is in the failed state, has by implication two levels of severity, whereby the term downtime is indicative of the period during which equipment cannot carry out any of the work that it was designed to perform, and the term outage is indicative of

the period during which equipment is unable either to carry out any of the work that

it was designed to perform or to function within specified limits of performance

Downtime can be defined as “the period during which an equipment’s opera-tional or physical condition is in such a state that it is unable to carry-out the work that it is designed to perform”.

Outage can be defined as “the period during which an equipment’s operational

or physical condition is in such a state that it is unable to carry-out the work that it

is designed to perform within specified limits of performance”.

It is clear that the term outage encompasses both a total loss of function and

a partial loss of function, whereas the term downtime constitutes a total loss of function Thus, the concept of full outage is indicative of a total loss of function, and the concept of partial outage is indicative of a partial loss of function, whereas downtime is indicative of a total loss of function only The concepts of full outage and partial outage are significant in determining the equivalent mean time to outage and the equivalent mean time to restore.

The equivalent mean time to outage (EM) Equivalent mean time to outage can

be defined as “the comparison of the equipment’s operational time, to the number

of full and partial outages over a specific period”

Equivalent Mean Time to Outage (EM)= Operational Time

Full and Partial Outages. (4.133)

The measure of equivalent mean time to outage can be illustrated using the

previ-ous example As indicated, the power generator is estimated to be in operation for

480 h at maximum dependable capacity, MDC Thereafter, its output is estimated to derate, with a production efficiency reduction of 50% for 120 h, after which it will

be in full outage for 120 h What is the expected equivalent mean time to outage of

the generator over a 30-day cycle?

Full power

at 100% Xp

Half power

at 50% Xp

MDC

MDC/2

120 hours 120 hours

480 hours

Time period = 720 hours

Measure of equivalent mean time to outage of a power generator

Full outage

EM=∑(To)

N =480+ 120

The significance of the concepts of full outage and partial outage, being

indica-tive of a total and a partial loss of function of individual systems, is that it enables

the determination of the equivalent mean time to outage of complex integrations

of systems, and of the effect that this complexity would have on the availability of

engineered installations as a whole

The equivalent mean time to restore (ER) It has previously been shown that the

restoration of a failed item to an operational effective condition is normally when

repair action, or corrective action in maintenance is performed in accordance with

prescribed standard procedures The item’s operational effective condition in this

context is also considered to be the item’s repairable condition.

Mean time to repair (MTTR) in relation to equivalent mean time to restore

(ER) The repairable condition of equipment is determined by the mean time to

repair (MTTR), which is a measure of its maintainability

= ∑(λR)

∑(λ) where:

λ= failure rate of components

R= repair time of components (h)

In contrast to the mean time to repair (MTTR), which includes the rate of failure

at component level, the concept of equivalent mean time to restore (ER) takes into consideration the equivalent lost time in outages at system level, measured against the number of full and partial outages This is best understood by defining equivalent lost time.

Equivalent operational time was previously defined as “that operational time during which a system achieves process output which is equivalent to its maximum dependable capacity”.

In contrast, equivalent lost time is defined as “that outage time during which

a system loses process output, compared to the process output which is equivalent

to the maximum dependable capacity that could have been attained if no outages had occurred”.

Furthermore, it was previously shown that the maximum dependable capacity (MDC) is reached when the system is operating at maximum efficiency or, expressed

as a percentage, when the system is operating at 100% utilisation for a given oper-ational time, i.e process output at 100% utilisation is equivalent to the system’s maximum dependable capacity

Equivalent Lost Time= Lost Output× Operational Time

Production Output at MDC (4.136) ELT= ∑[n(MDC) · To]

MDC

n= fraction of process output

Equivalent mean time to restore (ER) can be defined as “the ratio of equivalent lost time in outages, to the number of full and partial outages over a specific period”.

If the definition of equivalent lost time is included, then equivalent mean time

to restore can further be defined as “the ratio of that outage time during which

a system loses process output compared to the process output which is equivalent to the maximum dependable capacity that could have been attained if no outages had occurred, to the number of full and partial outages over a specific period” Thus Equivalent Mean Time to Restore= Equivalent Lost Time

No of Full and Partial Outages

ER= ELT

ER= ∑[n(MDC) · To]

where:

n = fraction of process output

N = number of full and partial outages

To= outage time equal to lost operational time

The measure of equivalent mean time to restore can be illustrated using the previous

example As indicated, the power generator is estimated to be in operation for 480 h

at maximum dependable capacity Thereafter, its output is estimated to diminish (derate), with a production efficiency reduction of 50% for 120 h, after which the

plant will be in full outage for 120 h What is the expected equivalent mean time to restore of the generating plant over the 30-day cycle?

Full power

at 100% Xp

Half power

at 50% Xp

MDC

MDC/2

120 hours 120 hours

480 hours

Time period = 720 hours

Measure of equivalent mean time to restore of a power generator

Full outage

ER= ∑[n(MDC) · To]

MDC· N

= [0.5(MDC) × 120] + [1(MDC) × 120]

MDC× 2

= 90 h

c) Outage Measurement with the Ratio of ER Over EM

Outage measurement includes the concepts of full outage and partial outage in

de-termining the ratio of the equivalent mean time to restore (ER) and the equivalent mean time to outage (EM) The significance of the ratio of equivalent mean time

to outage (EM) over the equivalent mean time to restore (ER) is that it gives the

measure of system unavailability, U

In considering unavailability (U ), the ratio of ER over EM is evaluated at system

level where

ER=∑[n(MDC) · To]

EM=∑(To)

N

ER

EM =∑[n(MDC) · To]

MDC· N ·

N

∑(To) ER

EM =∑[n(MDC) · To]

MDC·∑(To) .

Expected availability (A), or the general measure of availability of a system as a ra-tio, was formulated as a comparison of the system’s usable time or operational time,

to a total given period or cycle time

A=(∑To)

If the ratio of ER over EM is multiplied by the availability of a particular system

(A system) over a period T , the result is the sum of full and partial outages over the period T , or system unavailability, U

(A)system · ER

EM = ∑[n(MDC) · To]

MDC·∑(To) ·

(∑To)

= ∑[n(MDC) · To] MDC· T

= Unavailability (U) system.

Thus, equivalent availability (EA) is equal to the ratio of the equivalent mean time

to restore (ER) and the equivalent mean time to outage (EM), multiplied by the

expected availability (A) over the period T

Thus, the formula for equivalent availability (EA) can be given as:

EA= ∑[n(MDC) · To]

MDC· T

ER

EM· A = ∑[n(MDC) · To]

MDC·∑(To) ·

(∑To)

T

ER

EM· A = ∑[n(MDC) · To]

MDC· T

= EA

So far, the equivalent mean time to outage (EM) and the equivalent mean time to restore (ER) have been considered from the point of view of outages at system

level However, the concepts of full outage being indicative of a total loss of system function, and partial outage being indicative of a partial loss of system function, and

their significance in determining EM and ER make it possible to consider outages

of individual systems within a complex integration of many systems, as well as the effect that an outage of an individual system would have on the availability

of the systems as a whole In other words, the effect of reducing EM and ER in

a single system within a complex integration of systems can be determined from an

evaluation of the changes in the equivalent availability of the systems (engineered

installation) as a whole

The effect of single system improvement on installation equivalent availability

The extent of the complexity of integration of individual systems in an engineered installation relative to the installation’s hierarchical levels can be determined from

the relationship of equivalent availability (EA) and unavailability (U ) for the

indi-vidual systems, and installation as a whole

EA system= ER

EM· A system = ER

EM·(∑To)

T = U system (4.142a)

EA install.= ER

EM· A install = ER

EM·(∑To)

T = U install. (4.142b)

In this case, the ratio ER/EM would be the ratio of the equivalent mean time to

restore (ER) over the equivalent mean time to outage (EM) of the individual systems

that are included in the installation If the installation (or process plant) had only one inherent system in its hierarchical structure, then the relationship given above would

be adequate Thus, the effect of improvement in this system’s ER/EM ratio on the

equivalent availability of the installation that consisted of only the one inherent

system in its hierarchical structure can be evaluated Based on outage data of the

system over a period T , the baseline ER/EM ratio of the system can be determined Similarly, improvement in the system’s outage would give a new or future value for

the system’s ER/EM ratio, represented as:

ER

EM baselineand

ER

EM future.

The change in the equivalent availability (A) of the engineered installation, which

consists of only the one inherent system in its hierarchical structure, can be formu-lated as

ΔEA install.=

 ER

EM baseline

−ER

EM future

· Toinstall

If the engineered installation consists of several integrated systems, then the ratio ER/EM would need to be modified to the following

ΔEA install.= ∑q

j=1

ERj

EMj · A install.

(4.144)

ΔEA install.=

q

∑

j=1

ERj

EMj · Toinstall

T

where:

q = number of systems in the installation

ERj = equivalent mean time to restore of system j

EMj = equivalent mean time to outage of system j

To = operational time of the installation

T = evaluation period

The effect of multiple system improvement on installation equivalent

avail-ability The change in the equivalent availavail-ability (A) of the engineered installation,

which consists of multiple systems in its hierarchical structure, can now be formu-lated as

ΔEA install.=

q

∑

j=1

ERj

EMjbaseline−∑r

k=1

ERk

EMkfuture

· Toinstall

where:

q = number of systems in the engineered installation

ERjbaseline = equivalent mean time to restore of system j

EMjbaseline= equivalent mean time to outage of system j

r = number of improved systems in the installation

ERkfuture = equivalent mean time to restore of system k

EMkfuture = equivalent mean time to outage of system k

To = operational time of the engineered installation

T = evaluation period

This change in the equivalent availability (A) of the engineered installation, as a

re-sult of an improvement in the performance of multiple systems in the installation’s hierarchical structure, offers an analytic approach in determining which systems are critical in complex integrations of process systems This is done by

determin-ing the optimal change in the equivalent availability of the engineered installation

through an iterative process of marginally improving the performance of each

sys-tem, through improvements in the equivalent mean time to restore of system k, and the equivalent mean time to outage of system k The method is, however, compu-tationally cumbersome without the use of algorithmic techniques such as genetic algorithms and/or neural networks.

Another, perhaps simpler approach to determining the effects of change in the

equivalent availability of the engineered installation, and determining which sys-tems are critical in complex integrations of process syssys-tems, is through the

method-ology of systems engineering analysis This approach is considered in detail in

Sect 4.3.3

As an example, consider a simple power-generating plant that is a multiple inte-grated system consisting of three major systems, namely #1 turbine, #2 turbine and

a boiler, as illustrated in Fig 4.12 below

Statistical probabilities can easily be calculated to determine whether the plant would be up (producing power) or down (outage) In reality, the plant could operate

at intermediate levels of rated capacity, or output, depending on the nature of the

Fig 4.12 Example of a simple power-generating plant

Table 4.1 Double turbine/boiler generating plant state matrix

State Boiler #1 #2 Capacity

outages of each of the three systems This notion of plant state is indicated in Ta-ble 4.1, in which the outages are regarded as full outages, and no partial outages are

considered

Referring back to Eq (4.20), maximum process capacity was 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 (4.146)

Average Output Rate= (Cmax) · Average Utilisation

A system’s maximum dependable capacity (MDC) was defined in Eq (4.129) as being equivalent to process output at 100% utilisation Thus

MDC= Output (100% utilisation) (4.147) The plant’s average output rate can now be determined where individual system

outages are regarded to be full outages, and no partial outages are taken into

con-sideration The plant is in state 1 if all the sub-systems are operating and output is based on 100% utilisation (i.e MDC) Seven other states are defined in Table 4.1,

which is called a state matrix.

However, to calculate the expected or average process output rate of the plant

(expressed as a percentage of maximum output at maximum design capacity), the

percentage capacity for each state (at 100% utilisation) is multiplied by the avail-abilities of each integrated system.

Thus:

Average plant output rate with full outages only = Σ(capacity of plant state at 100% utilisation of systems that are operational × availability of each integrated system).

As an example: what would be the expected or average output of the plant if the estimated boiler availability is 0.95 and the estimated turbine generator availabilities are 0.9 each?

method-ology of systems engineering analysis... structure, offers an analytic approach in determining which systems are critical in complex integrations of process systems This is done by

determin-ing the optimal change in the equivalent...

This change in the equivalent availability (A) of the engineered installation, as a

re-sult of an improvement in the performance of multiple systems in the installation’s hierarchical