El Paper No Es Mio

Preventive Maintenance Using Continuous- Time
Semi-Markov Processes
Curtis L. Tomasevicz, Student Member IEEE, Sohrab Asgarpoor, Member IEEE
Department of Electrical Engineering
University of Nebraska - Lincoln
Lincoln, NE 68588 - 0511
Abstract - A method is presented to determine the amount of
preventive maintenance to be performed on equipment in order
to maximize availability. Themethod uses a continuous-time
semi-Markov process that assumes equipment can fail due to

both deterioration

and random

occurrences. Preventive

maintenance can be performed from working state to prevent

deterioration failure. An example is used to demonstrate the
method using MATLAB and Maple software. Additional

flexibility in equipment modeling using semi-Markov processes isdescribed.
Index - maintenance, equipment availability, power system
maintenance, semi-Markov processes.

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II

I. NOMENCLATURE
state of equipment after unexpected failure.
state of equipment after deterioration failure.
state of equipment while in normal operating mode.
state ofequipment during preventive maintenance.
the number of deterioration states.
the total number of states for equipment.
current state number of the equipment, i = 1, 2,... ,N.
overall state number of the equipment,j 1, 2,..., N.
rate of random failure.
rate of repairing an' unexpected failure.
rate of deterioration failure.
rate of repairing a deterioration failure.
rate of minimalpreventive maintenance.
rate of repair from preventive maintenance.
general rate of going from statej to state i.
the negative sum of the elements in columnj.
vector of steady state probabilities.
the steady state probability of being in statej.
transition probability of going from statej to i.
vector of sojourn times.
sojourn time of state j.
transition rate matrix.
the proportion oftransitions that take the system into
state i.
vector of proportions of transitions
=

C. L. Tomasevicz is a graduate student at the University of Nebrasaka,
Lincoln, NE 68588 where he also received his B.S. (2003) in electrical

engineering
with
emphasis
in
electric
power.
(e-mail:
tomasevicz@hotmail.com).
S. Asgarpoor is an associate professor at the University of Nebraska
Department OfElectrical Engineering, Lincoln, NE 68588 since 1989. He
received his B.S. (1978), M.S. (1981), and Ph.D (1986) from Texas A&M

1-4244-0228-X/06/$20.OO ©)2006 IEEE

University. His areas of interest include reliability evaluation and advanced
computer applications in security and optimization of electric power systems.

(e-mail: sasgarpoorl@unl.edu).

In most power
.

II. INTRODUCTIONit is necessary to evaluate the

systems,'

of time that should be spent on the repair and/or
replacement of certain equipment. The amount of time that is
spent on the maintenance of equipment has a direct relation to
the overall up-time of the system and therefore should be
minimized. During maintenance, the system may not only
function in a derated state resulting in lower profit, butthe
maintenance itself is a cost to the system as laborers and parts
are needed.
Maintenance is needed to prevent equipment from
entering a non-operable, failed state. Successful maintenance
will improve the current state of the equipment increasing the
up time and the overall availability of the system. If
maintenance is disregarded, the equipment will ultimately fail
because of naturaldeterioration.
In general, there are two types of maintenance; unplanned
maintenance and planned maintenance [1]. Unplanned
maintenance, also called corrective maintenance, is quite
expensive and should be avoided if possible. Once equipment
reaches a completely failed state and is no longer in working
condition, corrective maintenance is needed. This maintenance
is typically more...