Maritime University of Szczecin
Akademia Morska w Szczecinie
2010, 24(96) pp. 124–128 2010, 24(96) s. 124–128
Exploitation process of transport devices based on preventive
strategy approach
Strategie prewencyjnego podejścia do procesu eksploatacji
środka transportu
Janusz Szpytko
University of Science and Technology Akademia Górniczo-Hutnicza
30-059 Kraków, Al. Mickiewicza 30, e-mail: szpytko@agh.edu.pl
Key words: transport device, maintenance, operating Abstract
The paper is focusing on exploitation process of transport devices based on preventive strategy approach. The two – condition based technical state of the device under operation has been described. It has been proposed time – and cost – oriented preventive type approaches to maintenance processes of the devices, which was discussed in details.
Słowa kluczowe: środek transportu, utrzymanie ruchu, obsługiwanie Abstrakt
Przedmiotem wypowiedzi są strategie prewencyjnego podejścia do procesu eksploatacji środka transportu. Sformułowano dwustanowe ujęcie procesu eksploatacji urządzenia, dla którego zaproponowano czasowe i kosztowe podejście do przedsięwzięć obsługowych typu prewencyjnego.
Introduction
The transport device is possible to characterize with the property set including their adaptation to particular operation conditions, e.g.: operation flexibility, maintainability and diagnostic ability [1]. The device can be a subject of operation or service, or waiting for the transport task request. Each device is a result of design and manufacture processes for particular transportation activities under operation. The operation process of transport device is an sequence set of activities ordered by operators and other joint cooperating devices (available to undertake the operation task). The operation process of the device is resulting his de-gradation and losing necessary operation potential correspondence with device technical state (moving from usable to unserviceable status). The unservice-able status of the device is a subject of elimination base on the maintenance process.
Devices are possible to recognize as renewable and nonrenewable based on their acceptable techni-cal states. The renewable transport devices (which are Authors’ subject of interest) are available to exist into two technical states: operation and service (subject of repairing / restoring loosed by device operation potential). Base on above a two-state model of the device is possible to elaborate – see figure 1, where: Su – operation state, So – service
Su So
P(So, Su)
P(Su, So)
Fig. 1. Two-states model of the transport device under operation
Rys. 1. Dwustanowy model środka transportu w czasie eks-ploatacji
state. The transitions between distinguished device states is possible to express by the following probabilities:
P(Su, So) – with operation states guided to service state,
P(So, Su) – from service state to operation states. The quantitative two-states model of the tran-sport device under operation is possible to describe with use mean time between failures, renewal intensity of device indicator, as well as following indicators [2, 3, 4, 5, 6, 7, 8]:
1) deplete intensity of stock dependability (operation potential) of the device (to be non-able to undertake the ordered activities):
t t t λ t Λ 0 d (1)where: (t) – failures intensity rates function (where (t) ≥ 0 is a time t function), (t) – non- -decreasing leaded time function;
2) expected usable time E(t) of the device:
0 0 d dt t f t t t R t E (2)where: f(t) – density function of random variable t probability, R(t) – reliability function of the device,
E(t) – expected usable value of the device;
3) device failure stream:
t T E t ω u d d (3)where: E(Tu) – random variable determine device
failure number monitored during the period time from operation starting until time t = Tu, (t) –
failure stream of the device.
Under the jointly operation and service pro-cesses (so-called in some references – exploitation process) the transport device is moving into different states, which is possible to describe with technical and economical characteristics and to establish in each selected time or time range of the device exploitation. Results operation activities each device is a subject of his features degradation, which are subject of repairing results preventive maintenance strategy or stoppage of activities supported by the device [5, 6]. Always the fundamental question is: when to undertake the preventive maintenance of the device?
Time based approach to the preventive maintenance
Changes into operation potential of the device are accompanying each exploitation process. The
operation potential changes of the device is possible to present by the life duration characteristics of selected subsystems (or units) in operation time or movement trajectory path durations. The example of selected device operation parameter q change in time t has been presented in figure 2. Changes of operation parameter (q) into range qB, qC are
acceptable based on quality-based strategy of the user. In time tC we are moving from stable changes
phase to accelerated changes phases of device operation parameters: exceeding of point C make operation unsafe, reduce quality of device operation and maintenance costs are increasing. Point D is a critical point in time tD and the existing
characteristic exclude device from further operation and otherwise breakdown might occur. Point E in time tE determine such a technical state of the
transport device when withdrawal from operation is necessary (breakdown).
Fig. 2. The characteristic example of the device operation parameter q change in time t
Rys. 2. Przykład typowej zmiany parametru eksploatacji urzą-dzenia q w czasie t
The device life operation characteristic (or device subsystems) results statistical data coming from operation process events that are a subject of monitoring. The device life operation characteristic express probability p(t) of failure event of selected subsystem that take place in time tD before time tE,
when the breakdown is recording. The probability of operation potential loss of the device results particular causes is presented in figure 3.
Fig. 3. The probability of operation potential loss of the device results particular causes
Rys. 3. Prawdopodobieństwo potencjalnych strat operacyjnych na podstawie wyników urządzenia w szczególnych przypad-kach tD tE qC qD qE time t q E D C alarm tC qB p(t) t tD p(tD)
To establish that known is: mean time of the device operation till breakdown (time tE),
mainte-nance cost K1 of the device in time tE and losses
results breakdown K2(tE) (as a consequence of non
– undertaking particular necessary service type), the mean operation cost K3 of the device till breakdown
is as follow:
E E E E t t K t K t K 1 2 3 (4)If the preventive type maintenance of the device has been undertaken in time tD (for tD < tE), with
breakdown probability p(tD) = 1 – p(tE) a mean
operation cost of the device K4(tD) is described by
the equation:
D D D D D t t K t p t K t K 1 2 4 (5)The preventive type maintenance of the device is well-founded at the time duration tX < tE, and
possible failure event probability of the device p(tX)
is well accepted for a user, moreover:
3
4 K
K (6)
The operation potential of the device is reproducing in maintenance process to standards acceptable by the user needs.
With the preventive type undertaken focused on selected device subsystems, questions related to exchange importance of others jointly cooperate subsystems are coming (which degradation level is known in time t = A). The presented statement needs to establish condition based usable proba-bility of selected subsystem in time t = B (required by the accepted strategy of the operation process, including consecutive service), under condition that initial degradation is respond to probability p(A), for t = A.
Condition based probability of usable device subsystem pA(t) in time t under the condition that
initial degradation with probability p(A) is describ-ing by the formula:
A p A t p t pA (7)as transformation result of equation:
t A
p A p tp A (8)
where: p(A) – usable probability of the device subsystem without degradation in time duration from t = 0 till t = A, A – time duration A bounded with operation characteristic of device subsystem, which is out of accepted tolerance zone (Fig. 2),
p(t + A) – usable probability of the device
sub-system in time t + A, for t > 0.
In practice the degradation probability of homo-geneous transport device subsystems in operation time p(t) is possible present as graph (Fig. 4).
Fig. 4. The degradation probability of homogeneous transport device subsystems in operation time
Rys. 4. Prawdopodobieństwo rozkładu jednorodnych podsys-temów urządzeń transportu w czasie pracy
The degradation probability p(t) of homo-geneous transport device subsystems in operation time t (it is possible to use also other operation parameter, e.g. travel a distance) presented in figu- re 4 is taken under consideration various degra-dation classes ID of any subsystems (with use physical parameter, e.g.: diameter, length, angle) in the function of following parameters: operation time t and degradation probability p(t):
ID = f [p(t), t] (9)
In operation processes of transport devices the services are also possible results degradation process of device subsystems fatigue and wear types. From design staff of the modern devices is necessary to require to divide all subsystems which are subject of degradation to uniform classes base on mean usable operation time in particular opera-tion regime. Design process of device subsystems based on fatigue degradation process must accom-panying knowledge related to their without break-down operation time
Cost based approach to preventive type processes
The operation potential change of the device is possible to describe with cumulated wear (t). The cumulated wear of the transport device in time t is possible to present by the formula (Fig. 5):
t eλt (10)
where: – wear intensity of the device.
Let establish that: the investment cost of the (new) device is Ko, the wear level of the device
potential results the operation during the period of
p(t)
t
01
03
time t is represented by wear cumulative parameter (t). The degradation cost of the device is equal to
Ko(t) and cost of the device in time t is equal to
Ko(1 – (t)). The wear cumulative parameter (t) is
strongly results with the operation strategy underta-ken by the user.
The exploitation process of the transport device is a combination of operation and maintenance processes that are subject of calculated costs. The above costs is possible to present as cumulative costs W(t) in time t (Fig. 5):
tμ 1
o e
k t
W (11)
where: – total cost (value) intensity change of the device, ko – reference exploitation cost of the
device.
Analysis of cumulative costs W(t) of the device change in time t can help user to establish correct operation strategy. The selected strategy of device operation must also include the investment cost Ko.
The analysis is possible to do in practice with use mean cost S(t) of all investment cost base on equation (12) – figure 6:
t t W t K t S o1 (12)where: t – ime, exploitation (including both opera-tion and maintenance) period of the device.
Fig. 6. Characteristic example of total mean costs S(t) of transport device under exploitation process
Rys. 6. Przykład całkowitych średnich kosztów S(t) środka transportu w procesie eksploatacji
Mostly the user target is to reduce total mean costs S(t) of transport device under exploitation process. User is also interesting with critical level of mean costs S(t) of the device which must be ordered to keep operation features on acceptable level. Accepted that:
t eλt
e 1
(t) t o k W
t e k e K t S t o t o1 1 (13)and results the first derivative of cost expression
S(t) and then compare new expression to null, the
following is coming:
o o t μ t λ K k t μ e t λ e 1 1 1 1 (14) The discussed problem is possible to set respect-ing time t, under condition that , , ko, Koparame-ters are known. The graphical presentation of the problem has been shown in figure 7.
Fig. 7. Device operation type characteristics including dif-ferent strategies and investment costs
Rys. 7. Charakterystyki rodzajów eksploatacji urządzeń z włą-czeniem różnych strategii i kosztów inwestycyjnych
In case that mean costs S(t) of the device after achieving minimal value is growing, the following actions should be taken under consideration: exchange the old transport device for new one, to do the maintenance in range which increase
existing operation potential of the device, to increase maintenance process effectiveness
base on preventive type.
Final remarks
A methodology designing of strategies preven-tive types to the transportation devices, that are under operation or service processes, is a complex undertaking. The object-oriented project must in-clude analysis process of device features, requested investment costs, as well as both operation and service (maintenance) costs. Research of transport
t S(t) t t Ko / ko W(t) t t (t) 1 k tk
Fig. 5. Wear intensity and operation costs of the device characteristics
Rys. 5. Intensywność zużycia i koszty eksploatacji charakte-rystycznych właściwości urządzenia
devices based on operational potential approach completed with historical type data coming from device exploitation process, helps to formulate proper both operation and maintenance strategies.
The complex devices’ structure and internal interactions required searching proper tools keeping overlooked by user operation potential of the transport device. Requirement to use the selected tools in practice is to get representative type of data (characteristics) from the device exploitation process regarding device degradation base on operation parameters and their acceptance tolerance zones.
Device operation parameters change, which is a subject of monitoring and analysis, are crucial for proper operation strategy establish to user today and / or future needs.
The work is presenting also preventive type strategies to exploitation process of the transport device. The exploitation process of the device two- -state type has been proposed, as well as time and cost based approach to preventive type maintenance has been formulated.
Acknowledgements
The research project is financed from the Polish Science budget for the year 2008–2011.
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Recenzent: dr hab. inż. Zbigniew Matuszak, prof. AM Akademia Morska w Szczecinie
