The cost of downtime for maintenance : preliminary
considerations
Citation for published version (APA):
Geraerds, W. M. J. (1984). The cost of downtime for maintenance : preliminary considerations. (EUT - BDK
report. Dept. of Industrial Engineering and Management Science; Vol. 11). Technische Hogeschool Eindhoven.
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Published: 01/01/1984
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University of Technology
the Netherlands
Department of
Industrial Engineering
& Management Science
The cost of downtime for maintenance :
preliminary considerations
by W .M .J . Geraerds Report EUT/BDK/11 ISBN 90-6757-011-7 Eindhoven, 1983C O N T E N T S
Page Summary
3 1 . Introduction 3 2 . Research Project Objective 4 3 . Failure 4 4 . Maintenance 5 5 . Failure related consequence 7 5 .1 . Damage 7 5 .2 . Production function 8 6 . Optimal maintenance cost 10 i 6 .1 . Cost of damage 10 6 .2 . Cost of downtime 11 6 .3 . Optimal maintenance cost 12 7 . Aspects in the determination of the cost of downtime 12 8 . Conclusions
18 9 . Ongoing research
18 10 . Comments and suggestions 18
SUMMARY
The subject of the paper is the problem of determining
the cost of downtime for maintenance in a diversity
of situations . The objective of the research project
concerned is to establish a systematic way for that
determination
. After defining failure and maintenance,
failure related consequences for a production unit
in the form of damage and consequences for the
pro-duction function, a global model for optimal maintenance
is presented, in which downtime is one of the cost
factors . A number of aspects is mentioned, which have
to be taken into account in the determination of the
cost of downtime, depending on the situational
circumstances . The ongoing research is mentioned,
contributions to which would be appreciated .
1 . Introduction
At the Department of Industrial Engineering and Management Science of the Eindhoven University of Technology the subject Maintenance is part of the research programme of the department. Economic considerations play a dominant role in a multitude of situations in maintenance . The rationale for maintenance, essejxtially, lies with restoration instead of renewal and in general with reduction of the consequences of
failure. Generally, the cost of loss of production is considered to be the dominant consequence, clearly outlined and easy to assess . In practice however, it appears to be difficult to determine the actual cost, needed in the trade-off against the cost of possible maintenance activities
. This problem does not originate from a lack of economic
knowledge, but from the inadequacy of the models used for the determination of the cost. In view of the importance of this cost component a study of suitable models is required. In these preliminary considerations a general framework for the relationships between maintenance related costs is given first, because of the interdependency between maintenance cost and downtime cost .
2 . Research Project Objective
The objective of the research project "Determination of the cost of downtime for maintenance" is :
to establish the model, or the set of models each for its well defined application, which furnishes the cost of downtime of a production unit .
3 . Failure
In view of the diversity of interpretation of many terms in maintenance some key words will be defined as understood in this paper .
In respect to the object showing failures and to be maintained we shall use the term production unit .
A production unit is a hardware entity which fulfils a function relevant in the production process .
A production unit could be e .g . a lathe, a blast furnace, an elevator, a computer, etc .
An assembly is a set of interrelated components, which, as a feature of the design of the production unit, can be replaced as a whole. A component is a part of a production unit, which cannot be
split up without losing its identity .
A spare part is an assembly or a component which has been taken up in the assortment of parts held in stock for maintenance purposes . A failure is the transition of a component into the physical state
that it cannot fulfil its intended function anymore .
A defect , or absolute faulure,is a failure of which the termination of the ability to operate is absolute .
A boundary failure
is a failure, of which the ability to operate is determined by the crossing of the specified, normative, threshold value of a failure relevant physical property .
An item is inoperable
if it is in the physical state that it cannot fulfil its intended function due to failure .
4 . Maintenance
Maintenance is : all activities aiming at keeping an item in, or
restoring it to, the physical state considered necessary for the ful-filment of its production function .
Replacement of a production unit by a new one is not considered to be maintenance, but an investment decision, which is outside the scope of this paper. Replacement of a component or of an assembly, however, is considered to be a maintenance activity .
Even if modification can be cost effective in view of maintenance, it is not considered to be a maintenance activity, because it essentially is partial redesign, that is design .
On the basis of the failure behaviour of a production unit, and on several more considerations not considered in this paper, the maintenance concept of the production unit is established .
The maintenance concept of a production unit is the ordered set of rules, prescribing what maintenance should be executed and by what event or
decision that maintenance will be generated .
With regard to the relation between the generating of maintenance activities and their rationale three elementary maintenance
Failure Based Maintenance ( FBM)which is maintenance which will not be carried out until the event of failure ;
Use Based Maintenance
( UBM) which is maintenance which will be carried out after a specified period of use . UBM is,
usually but not necessarily, carried out at fixed intervals of use or time .
Condition Based Maintenance (CBM) which is maintenance which primarely consists of a test in order to determine if reaching a specified
boundary value is imminent, further maintenance actions being dependent on the outcome of the test. C3M is, usually, but not necessarily,
carried out at fixed intervals of use or of time .
With regard to the purpose to be reached by the execution of maintenance the categories corrective maintenance and preventive maintenance are distinguished .
Correo tiye Maintenance
(CM) is maintenance, carried out after the
event of failure, with the objective to restore the production unit
to the physical state considered necessary for the fulfilment of its
production function .
Preventive Maintenance
(PM) is maintenance, carried out before the
event of failure, with the objective to reduce the probability of
failure in the period following .PM .
FBM belongs to the category CM
. UBM and CBM as such belong to the
category PM, but the category CM will be included as for the fraction
of failures that are not prevented, because they turn up before the
time at which UBM or CBM i s executed,
PM is justified by the trade-off of the PM maintenance effort and downtime required for PM execution against the reduction in the consequences of failure .
5 . Failure related consequences
Failure consequences become manifest on the one hand,with respect to the production unit and its environment,in the form of damage, and on the other hand,with respect to the production function,in the form of downtime .
5 .1 . Damage
As for the cause of damage three cases can be distinguished
: primary failure, secondary failure and external cause.
A primary failure
is a failure which is not caused by any other failure . A secondary failure
is a failure which is caused by another failure. An external cause or foreign cause
is any cause outside the production unit leading to damage to the production unit .
Corresponding with this distinction four cases of resulting damage can be distinguished
: primary damage, secondary damage, foreign damage and environmental damage .
Primary da _mage is damage to'the production unit as a result of primary failure .
Secondary damage is damage to
the production unit as a result of secondary failure .
Environmental damage
is damage to the environment of the production unit as a result of primary or secoridary failure .
Foreign damage is damage
to the production unit as a result of an external cause .
Reduction of primary damage requires reduction of the primary failure, which can be achieved by preventive maintenance .
Reduction of secondary damage requires reduction of the primary failure causing the secondary failure, which can be achieved by preventive maintenance directed at the primary failure.
Reduction of environmental damage requires reduction of its cause, which can be primary failure, secondary failure or an external cause . Reduction of foreign damage requires the reduction of appearance of the external cause, which is not maintenance of the production unit concerned .
5 .2 . Production function
The production function is the manufacturing of goods or the providing of services in a required volume and not later than at a required time .
The failure related consequence on the production function lies in the fact that the execution of maintenance takes time, usually necessitating the production unit to be inoperative
. This can lead to an economic loss due to loss of production
. Generally it is assumed that a production unit can be in one of two states, "operable" or "up " and "inoperable" or "down" .
U time is the sum of the times that a production unit is operable, measured over a representative period of time.
Downtime i s the sum of the times that a production unit is inoperable due to maintenance, measured
over a representative period .of time .
A property to quantify the share of the uptime of a production unit is availability .
Availability is the ratio of the uptime and the period of time over which it is measured
. This period of time is equal to the sum of uptime and downtime .
The event of a production unit becoming unoperable is known as breakdown or as shutdown .
Breakdown is the event of a production unit becoming inoperable due to absolute failure. Generally this implicates that breakdown turns up at an unexpected moment .
Shutdown
is the event of a production unit becoming unavailable for production as a result of a maintenance control decision.
A failure of a component does not necessarily lead to production unit breakdown, e .g
. because it concerns a redundant component . Also the execution of maintenance does not always necessitate a production unit to become inoperative, because some maintenance actions can be, sometimes must be, carried out without interruption of the production unit's function, known as running maintenance . Some condition based maintenance techniques have to be carried out as running maintenance . The majority of production units will not be required to operate continuously or almost continuously, utilizing all uptime disposable
. Utilization
is the total time that a production unit operates, measured over a representative period of time
. Uptime is the maximum utilization achievable .
The utilization factor
of a production unit is the ratio of the utilization and the uptime, measured
over the same period of time . Many of the objects to be maintained in an organization are needed for reasons which cannot very well be expressed in a product, goods or services, which eventually interests the outside client
. Their contribution has the nature of ensuring meeting conditions considered necessary for normal operation, in which a direct relation with the production process can be non-existant, e .g
. buildings, air-conditioning . In those cases, in which the interruption of the contribution leads to interruption of the production process, the study of the downtime of the production unit will have to include the interrelated downtime behaviour of the contributing unit
. Apart from this possible exception, they can be neglected in respect of their influence on downtime of the production unit .
Indirectly downtime can influence the production process by the impact on the image of the organization concerned in respect of the confidence of the clients in meeting promised delivery dates and in the quality of the product .
6 . Optimal maintenance cost
In respect of the cost of failure related consequences we can distinguish :
- the cost of damage, and - the cost of downtime . 6 .1 . Cost of damage
The cost of damage to the production unit, due to primary failure, secondary failure or foreign damage, consists of the cost to be made for corrective maintenance actions, in order to restore the production unit to the physical state considered necessary. The cost of the effort to reduce primary or secondary damage consists of the cost of
preventive maintenance actions . The cost of environmental damage consists of the cost of corrective maintenance actions, to be made to restore the environment to the state desired ; penalties may have to be added . The cost of the effort to reduce environmental, damage consist of the cost of preventive maintenance actions. The cost of the effort to reduce external causes are considered to be outside the scope of this paper .
If no preventive maintenance is applied, the cost of damage comes down to the cost of corrective maintenance . In the cost of maintenance execution we can distinguish the components labour (L), spare parts (P) and maintenance management (MM), expressed in :
in which :
M .C(CM) = total cost of maintenance, if only corrective maintenance (CM) is applied
L .C(CM) = the cost of labour, if only CM is applied P
.C(CM) = the cost of spare parts, if only CM is applied
MM-C(CM)
= the cost share in the cost of maintenance management,
if only CM is applied .
If preventive maintenance is applied, the cost of preventive maintenance will have to be added, and the corrective maintenance cost will change . Equation (1) then changes into :
M .C(CM + PM) = M .C(CM I PM) + M.C(PM) (2)
in which :
M
.C(CM + PM) = total cost of maintenance, if preventive maintenance
(PM) is applied
M.C(CMfPM) = the total cost of corrective maintenance, if preventive maintenance is applied
M
.C(PM) = the total cost of preventive maintenance .
Corresponding to the components distinguished in equation (1)
M .C(CM+PM) = L .C(CMIPM) + P .C(CMIPM) + MM .C(CMIPM) (3) and
1d .C(Pri) = L .C(PM) + P .C(PM) + MM .C(PM)
(4) 6 .2 . Cost of downtime
In respect of downtime we can distinguish between the event,that corrective maintenance is applied, and the event that preventive
only maintenance is applied. Some preventive maintenance actions may have been
introduced exclusively for the purpose of downtime reduction instead of for the purpose of damage reduction
. For reasons of simplicity we include both in the presented equations .
We denote as
D .C(CM) the cost of downtime, if only CM is applied and
D .C(CM+PM) the cost of downtime,
i f preventive maintenance is applied .
6 .3 . Optimal maintenance cost
Eventually the cost of damage and the cost of downtime have to be carried by -the products manufactured on the production units concerned
. The desired minimum of these
cost will be reached if they are optimal, which will be the case for :
max[{M .C(CM) + D .C(CM)} - {M .C(CM + PM) + D .C(CM + pM)}] (5)
applied to each failure individually, taking into account common set-up times .
7. Aspects in the determination of the cost of downtime (1) General remarks
Maximization of equation (5) with respect to downtime comes down to reducing failures by means of preventive maintenance requiring less downtit;;e, and/or to reduction,of the maintenance through-put time. Considerations about possible preventive actions have
to take into account what benefits can be expected from the re-duction in downtime. This is important, because a reduction in downtime does not necessarily result in a reduction of cost in all cases .
Reduction of downtime by means of reduction of maintenance throughput times can be achieved by a diversity of measures in maintenance management . Clustering of activities into packages
in order to combine maintenance actions with a common set-up time, in particular of use based and condition based maintenance, goes together with a reduction of the ultimate period of execution
allowed for each of the individual actions that are combined . The costs involved in the resulting loss of residual useful life have to be
traded off against the benefits as a result of the gain in uptime achieved . Decisions to take up a number of components or assemblies in the stock of spare parts aim at limiting the waiting time for parts, which
eventually is limiting the maintenance throughput time .
Not only in maintenance management decisions, such as the fore
mentioned examples, but also in production planning and in production control downtime is an important variable, e .g . in the application of priority rules for bottleneck capacities and in estimating expected production throughput time .
(2) Global model
In general models it is supposed that the loss of revenue due to downtime is a linear function of the downtime :
D .C=DTxdc
in which :
D .C = the loss of revenue due to downtime DT = downtime duration in units of time
dc = loss of revenue due to downtime per unit of time . (6)
As will be shown in the following aspects this model concerns a very special case and is unsuitable for general application . (3) Running maintenance
If maintenance actions can be executed without interruption of the production process, known as running maintenance, the execution of that maintenance does not lead to downtime .
(4) Postponable maintenance
If a redundant component or assembly requires maintenance, the production unit will still be operable, even if the physical state
of the production unit as it should be includes that all
components and assemblies would be operable. If that maintenance can be postponed to a moment that the production unit will be down for other maintenance actions, it does not by itself require downtime . The same goes for other postponable maintenance actions,e .g . in the event that the threshold value of a condition property or of a maintenance interval allows for some float in addition to the nominal value of the threshold property
. Many production units have more than one mode of operation
. If a production unit is inoperable in respect of one of its modes of operation which is not called upon for the time being, its maintenance may be postponed to a period of downtime for other reasons .
(5) Opportunistic maintenance
Opportunistic maintenance, which is maintenance that according to the maintenance concept will be carried out only when the upportunity arises due to the necessity to carry out other maintenance, does not lead to downtime, unless the duration of the maintenance has to be extended for the execution of the upportunistic maintenance .
(6) Delayed delivery
Instead of a total loss of production output due to downtime, the consequence of downtime may manifest itself in a delay of the delivery time promised for products, goods or services, The cost
iRvolved may vary from nil to a clearly defined penalty in the contract . (7) Alternative supply
If interruption of the production process goes together with a low stock level of ready products it may be impossible to deliver as promised. In some cases promised due dates can be met, by using,
product, on the basis of an agreement for mutual assistance . In event that downtime costs are determined by the price and benefit relations and by the incidental additional management effort for the arrangements to be effected .
the
(8) Making up for downtime
If the utilization and the time until delivery allow to make up for the loss of production during downtime by overwork, the cost of downtime is determined by the additional cost for the overwork and for the Additional managerial activities .
Making up for lost production time is also possible if the
production rate is adjustable, allowing to catch up the time lost by an increase of production output volume after maintenance execution, e .g . a ship travelling at a higher speed to catch up after a delay during the voyage . Downtime cost will be determined by the additional effort, e .g . energy cost . (9) Alternative production units
Some products can be manufactured on more than just one type of
production unit . If production, in the event of downtime of a production unit, can be rescheduled to other production units, often with low
utilization and available on a standby basis, downtime cost will be limited to the difference in the effort . A special form of the use of alternative production units is contracting out, sometimes on the basis of a "on-call" contract .
(10) Decrease of performance
Strict interpretation of the definition of failure implies that a production unit can be in only one of the two clearly distinguishable states "up" or "down" . In some cases however the changing physical state of a production unit may lead to a gradual decrease in performance, e .g . a decrease in product quality or a decrease in production volume . The decision to take a production unit out of operation for maintenance is primarily based on trade-off considerations, rather than merely on downtime .
(11) Limiting facilities
Some maintenance activities require special facilities, such as docks for ships, hangars for aircraft and special bays for motorvehicles. If their utilization is high, waiting for them becoming available for use will increase the downtime of the production unit requiring the facility
. Considerations about an increase of the number of facilities in use, usually a discrete decision problem, must be based upon the trade-off of the invest-ment to be made against the benefits of the achievable reduction of downtime .
(12) Utilization rate
If the utilization of a production unit is low, the periods of non-utilization can be used for the execution of maintenance without leading to a penalty for downtime. If the utilization rate is moderate downtime for maintenance may coincide sometimes with the periods that the production unit should be operative. Only if the utilization rate is high, downtime becomes a dominant factor .
(13) Production Profile
Some production units are expected to operate in correspondence with a specific schedule, the production profile. Execution of maintenance during the production-free periods will not include loss of production. The maintenance concept can make
maximum use of this possibility by fitting in periodical maintenance, and maintenance planning can make use of it in short time scheduling, also of non-repetitive maintenance . The planning of production may be reconciled with the planning of maintenance as an integrated process, in the air forces known as "planned flying - planned
servicing" .
(14) Maintenance float
If production requires a number of a type of production unit to be available,an additional number may be required, which is allowed to be down for maintenance without reducing the number in operation .
The cost of downtime in that case is determined by the investment for the additional production units, the maintenance float .
Determination of the size of the maintenance float is a discrete decision problem .
(15) Pointwise availability
Sometimes the primary interest from the point of view of production is the availability of a production unit when it is called upon at a specific moment of time, rather than primarily a length of time . Expressed as a probability it is known as pointwise availability . In aviation the pointwise availability in accordance with the flight schedules is known as dispatch reliability. In this type of cases downtime does not have the nature of process duration, but of the occurrence of an event .
(16) Mission completion
The majority of production units does not operate continuously, but is called upon at certain moments in order to complete a job with a certain duration. Apart from the fact that the production unit should be operable at the start it should not become
inoperable during the execution of the job or mission . If a mission is interrupted, that may cause an inconvenience, within certain time limits independent of the duration of the corrective actions . Similar to pointwise availability the event of production interruption may determine the penalty of becoming inoperative, rather than the incidental duration of the downtime .
(17) Diffused consequences
In some situacions there is no direct relationship between product and client . Even if the client may suffer by downtime, he is not in a position to execute direct influence . An example is clàsing roads for road maintenance, which will cause a
nuisance to a diffuse group of individuals out of a large
population, without any direct influence from that side on downtime . Considerations about limiting downtime and the budgettary conse-quences usually will be the responsibility of some intermediate body .
(18) Indirect consequences
Indirect consequences, mentioned in section 5 .2, may play a non-negligible role . In that case determination of the
conse-quences of downtime will have to make shift with an estimate to be provided by management as a policy decision .
8 . Conclusions
Downtime of production units is a cost factor, playing a non-negligible role in many management decisions, in particular in maintenance, but also in other decision areas .
The diversity of situations in which downtime plays a role necessitates to distinguish a number of aspects with complex interrelations .
Further research is required in order to establish the model, or the set of models each for its well defined application, which furni-shes the cost of downtime of a production unit .
9 . Ongoin g research
The ongoing research in this phase at the Eindhoven University of Technology concentrates on three parallel channels :
(1) A study of models for the determination of the cost of downtime published in scientific textbooks or other publications ;
(2) a study of publications in which real situations are described ;
downtime calculations made in (3) interviews with functionaries in industry who have been involved
in the problem .
10 . Comments and suggestions
The author welcomes comments or reactions from anybody interested in the subject to the following address :
W .M .J . Geraerds Firmamentlaan 11
5632 AA EINDHOVEN
NETHERLANDS
