Chapter 3
 Preventive
Maintenance :
Concepts, Modeling and
Analysis
Chapter Objectives
1.
2.
Enable students to understand the
Basic Tools for developing Pm
Programs.
Enable students to diagnose if a plant
needs improvement in its PM program
Chapter3 Objectives
3. Enable students to develop planned
maintenance programs.
4. Enable students to formulate
models to determine PM intervals
5. Enable students to formulate and
solve inspection models.
Preventive Maintenance
Preventive maintenance is a series of
preplanned tasks performed to counteract
known causes of potential failures of those
functions.
Preventive Maintenance
Preventive maintenance is the preferred
approach to asset management:

It can prevent premature failure and
reduce its frequency
 It can reduce the severity of failure
and mitigate its consequences
 It can provide warning of an
impending
or incipient failure to
allow planned repair
 It can reduce the overall cost of asset
management
Preventive
maintenance
Conditio
n
based
Off line
Statistically and
reliability based
On line
Time
based
Use
based
Why PM is Preferred
1.
The frequency of premature failures can
be reduced through proper
lubrication, adjustments and cleaning.
2. If failure can not be prevented periodic
inspections can help reduce its severity.
Why PM is Preferred
3. Warning of impeding failure can be
detected by monitoring gradual
degradation of function or parameter.
4. The cost of planned maintenance is
always cheaper than emergency
maintenance
Critical Issues Regarding PM
1. What PM tasks should be performed to
prevent failure?
. Time based tasks
. Condition based tasks
Discuss situation where each one is
applicable.
Diagnostic Technologies
The most commonly applied conditionbased maintenance techniques are
vibration
analysis,
oil
analysis,
thermography, ultrasonics, electrical
effects and penetrants.
Vibration analysis
Vibration can be defined as the
movement of a mass from its point
of rest through all positions back to
the point of rest, where it is ready to
repeat the cycle. The time it takes
to do this is its period, and the
number of repetitions of this cycle in
a given time is its frequency
Vibration analysis
The severity of vibration is determined
by the amplitude - or maximum
movement - its peak velocity and peak
acceleration.
Vibration analysis in
condition monitoring, is accomplished
by comparing vibration characteristics of
current operation to a baseline,
measured when the machinery was
known to be operating normally. The
selection of the specific parameters to
be measured depends primarily on the
frequency of the vibration.
Vibration analysis
Vibration analysis techniques can
be used to monitor the performance
of mechanical equipment that
rotates, reciprocates or has other
dynamic actions. Examples include
gearboxes, roller bearings, motors,
pumps, fans, turbines, belt or chain
drives, compressors, generators,
conveyors, reciprocating engines
and indexing machines
Oil analysis
Ferrography and magnetic chip
detection examine the ironbased
wear
particles
in
lubrication oils to determine the
type and extent of wear, and can
help determine the specific
component that is wearing.
Oil Analysis
Spectrometric
oil
analysis
measures the presence and
amounts of contaminants in
the
oil
through
atomic
emission
or
absorption
spectrometry.
Oil analysis
It is useful for determining not only
iron, but also other metallic and
not metallic elements, which can
be related to the composition of
the various machine components,
like bearings, bushings, piston
rings, etc. It is useful when wear
particles
are
initially
being
generated in the early stages of
failure, as they are small.
Oil analysis
Chromatography measures the
changes in lubricant properties,
including viscosity, flash point,
pH,
water
content
and
insoluble, through selective
absorption and analysis.
Thermography
The
most
common
uses
for
thermography, which measures the
surface
temperature
through
the
measurement of infra-red radiation, are
for
determining
poor
electrical
connections and hot spots, furnace and
kiln refractory wear and critical boiler
and turbine component overheating. An
infra-red
camera
shows
surface
temperature variations, calibrated to
provide the absolute temperature or
temperature gradients through black and
Ultrasonic
There are several techniques for
ultrasonic testing, but they all are used
to determine faults or anomalies in
welds,
coatings,
piping,
tubes,
structures, shafts, etc. Cracks, gaps,
buildups,
erosion,
corrosion
and
inclusions are discovered by transmitting
ultrasonic pulses or waves through the
material and assessing the resultant
signature to determine the location and
severity of the discontinuity. This
technique is also used to measure flow
Electrical Effects Monitoring
There are several tests for corrosion
using a simple electric circuit
monitored by varying degrees of
sophisticated instrumentation. The
Corrator uses the electro-chemical
polarization method in a vessel with
corrosive liquid. The Corrometer
uses the electrical resistance across
a probe inserted in the active
environment eg. refinery process
equipment.
Electrical Effects Monitoring
The most common for monitoring or
testing motors or generators are voltage
generators, including mergers. These
measure the resistance of insulation,
and apply a test voltage from 250 volts
to 10,000 volts.
Penetrants
Electrostatic and liquid dye
penetrants are used to detect
cracks and discontinuities on
surfaces, caused in manufacturing,
by wear, fatigue, maintenance and
overhaul procedures, corrosion or
general weathering. The penetrant
is applied and allowed to penetrate
into the anomalies. The surface is
cleaned and the penetrant revealed
through direct visual, fluorescent or
electrostatic techniques.
PLANNED MAINTENANCE
Maintenance work carried out with
forethought control and record. It can be
applied to any of maintenance provided that
(a) The maintenance policy has been
considered carefully.
(b) The maintenance policy is planned in
advance.
PLANNED MAINTENANCE
(c) The work is controlled and directed to
conform to the prearranged plan.
(d) Historical and statistical record are
complied and maintained to assess the
results and provide guide for future
policy.
BENEFITS OF
PLANNED MAINTENANCE
1. Greater Plant Availability
2. Less Costly
3. High Level of Output
4. Greater Utilization
5. Servicing and Adjustment is not
overlooked
BENEFITS OF
PLANNED MAINTENANCE
6. Improved Budget Control
7. Improved Stocks and Spares Control
8. Provision of Information for Realistic
Forecasts
9. Focusing Attn. on Frequently Recurring
Jobs.
ELEMENTS OF PLANNED
MAINTENANCE (PM)
1. Leader
2. List of all Facilities and their
Importance (What)
3. Identification (Coding)
4. Facility Register
ELEMENTS OF PLANNED
MAINTENANCE (PM)
5. Maintenance Schedule
6. Job Specification
7. Control
8. History Record
Facility Inventory
The facility inventory is a list of all
facilities including all parts of a site and
content. It is made for purpose of
identification. An inventory sheet of all
equipment should be developed showing
equipment identification, description of
facility, location, type and priority
(importance).
Identification (Coding)
It is essential to develop a system by
which each equipment is identified
uniquely. A coding system that help in
this identification process should be
established. The code should indicate
location, machine type and machine
number. This coding system differ
from plant to plant and its design
should reflect the nature of the facility.
Facility Registor
The facility register is a file (electronic
or hard copy) including technical detail
about items that are included in the
maintenance plan. These items are the
first to be fed to the maintenance
information system.
Equipment Record
The equipment (item) record should
include, identification number, location,
type of equipment, manufacturer, date
of manufacturing, serial number,
specification, size, capacity, speed,
weight, power service requirement,
connection details, foundation detail,
overall dimension, clearance, reference
drawing number, reference number for
service manuals, interchangeability
with other units, etc.
Maintenance Schedule
A maintenance schedule must be
developed for each equipment in the
program.
The schedule is a
comprehensive list of maintenance
tasks to be carried on the equipment.
Maintenance Schedule
The schedule include the name and
identification number of the equipment,
location, reference number of the
schedule, detailed list of tasks to be
carried out (inspections, preventive
maintenance,
replacements),
the
frequency of each task, the crafts
needed to carry out the task, time for
each task, special tools needed, material
needed and details of any contract
maintenance.
Job Specification
The job specification is a document
describing the procedure for each task.. The
job specification should indicate: the
identification number of the item
(equipment), the location of the item, the
maintenance schedule reference, the job
specification reference number, the
frequency of the job, crafts required for the
job, the details of the task, components to be
replaced, special tools and equipment
needed, reference drawings, manuals and
safety procedures to be followed.
Maintenance Program
The maintenance program is a list
allocating maintenance tasks to specific
time period. When developing the
maintenance program a great deal of
coordination must be done in order to
balance the work load and meet
production requirements. This is the
stage when the planned maintenance is
scheduled for execution.
Program Control
The maintenance program developed
must be executed as planned. Close
monitoring is needed in order to
observe any deviation from the
schedule. If deviations are observed a
control action is needed
A SYSTEMATIC SIX STEP METHOD
(TOP-TO-BOTTOM)
1.Determine Critical Plant Units and
Operation Windows.
2.Classify the Plant into Constituent Items.
3. Determine and Rank Effective Procedure.
A SYSTEMATIC SIX STEP METHOD
(TOP-TO-BOTTOM)
4.Establish Plan for Identified Work.
5. Establish a schedule for On-Line
Maintenance
6.Establish Corrective Maintenance Guidance
Mathematical Models for
Optimum PM Polices
Two well known polices which are:
1. Age based policy (Type 1 policy)
2. Constant interval replacement polices
(type II policy)
Age Based Policy

Policy I (age preventive replacement) is
defined as follows: perform preventive
replacement after tp hours of continuing
operation without failure; tp could be finite
or infinite. In case of an infinite tp no
preventive maintenance (replacement) is
scheduled. If the system fails prior to tp
hours having elapsed, perform maintenance
(replacement) at the time of failure and
reschedule the preventive maintenance after
tp operation hours.
Notation





Cp = cost of preventive maintenance
Cf = cost of breakdown (failure)
maintenance
f(t) = time to failure probability density
function (p.d.f.).
F(t) = equipment or system failure
distribution, it is the integral of f(t)
r(t)= failure rate function
Notations







N(tp) = number of failures in the interval
(0,tp); N(tp) is a random variable.
H(tp) = expected number of failures in the
interval (0,tp).
R(t) = reliability or survival function.
M(tp)= expected value of the truncated
distribution with p.d.f. f(t) truncated at tp.

M(tp) =  tf (t )dt /1  R(t p )

C(tp) = expected cost per cycle
UC(tp) = expected cost per unit time.
Age Based Policy
Failure
Failure replacement
replacement
Failure
replacement
Failure replacement
Preventive
replacement
0
Preventive
replacement
tp
tp
Time
Model Development
Total expected cost per cycle
UC(t p ) 
Expected cycle length
C (t p )  C p  R(t p )  C f [1  R(t p )]
Expected Cycle Length = tp R(tp)+M(tp)(1-R(tp))
Expected Cycle Length = tp R(tp)+M(tp)(1-R(tp))

M (t p ) 
 tf (t )dt /[1  R(t

p
)]
Golden Section Method

1. Choose an allowable final tolerance
level, , and assume the initial interval
where the minimum lies is [a1,b1,] =
[a,b] and let 1 = a1+(1-)(b1-a1), 1 =
a1+(b1-a1),  = 0.618. Evaluate g(1)
and g(1), let k=1 and go to step 2.

2. If bk-ak <, stop as the optimal solution
is . Otherwise, if g( k)>g( k) go to step
3, and if go to step 4
Golden Section Continued

3. Let ak+1=k and bk+1=bk, furthermore, let
k+1=k and let k+1=ak+1+(bk+1-ak+1).
Evaluate g(k+1,), and go to step 5.

4. Let ak+1=ak and bk+1= k, furthermore let
k+1=k and let k+1= ak+1+(1-)(bk+1- ak+1),
evaluate g( k+1), and go to step 5.

5. Replace k by k+1 and go to step 1.

For more on the properties and the convergence of
the above algorithm see Bazarra et al. [4].
Example on Policy 1

An equipment has a time to failure density
function f(t) that follows a uniform
distribution between [0,10] weeks. The cost
of preventive replacement is $5 and the cost
of failure replacement is $50. Determine tp,
the optimal time of preventive replacement.
Cost Function
UC (t p ) 
C p R(t p )  C f [1  R(t p )]
t p R(t p )  M (t p )[1  R (t p )]
1
5(1 - 1/10t p ) + 50 t p
10
=
t 1
t p [1 - 1/10t p ] +
tp
2 10
5 + 4.5t p
=
1 2
tp t p
20
Applying Golden Section

[a1 , b1 , ]  [0,10],  = 0.618, 1 -  = 0.382
1 = 0 + 0.382 *10 = 3.82 1 = 0 + 0.618 *10 = 6.18
UC(1 ) = UC(3.82) =
UC(1 )  UC (  1 )
22.19
32.81
7.18, UC( 1 )  UC(6.18) 
 7.68
3.09038
4.27038
the next interval is
UC(  )  UC (  )
Inspection Models
Inspection is the process of
gathering information about the
state of an equipment in order to
catch and correct failure before it
happens.
- Why Do Inspection?
Inspection Models
f(t) =
the density function of the time to
failure of the equipment.
Ci =
cost of inspection
Cu =
the cost per unit associated with
undetected equipment failure
Tr =
repair time
EC(x1,x2,...,xn) = total expected cost per
cycle
ET(x1,x2,...,xn) = expected cycle length
UEC(x1,x2,...,xn) = total expected cost per
unit time
Model Development
The inspection policy is to conduct an
inspection at times x1,x2,x3,...,xn until
failure is detected, when failure is
detected the equipment is brought to a
new condition through maintenance
and the production cycle beings. The
horizon we have is infinite
Model Development
The objective is to determine x1,x2,...,xn
that minimizes UE(x1,x2,x3,...,xn). If
failure happened between xi-1, xi, at
time ti, the cost of the cycle would be

KCi + Cu(xi – ti) +Cr
Model Development
The expected cost is:

xi
xi 1
[iC i  C u ( xu  t )  C r )] f (t ) dt
Model Development
 x
ET ( x1 , x2 , x3 ,..., xn )    Tr   x k 1 ( xk 1  t ) f (t )dt
k 0 k
The expected cost per unit time is obtained as
 x
Cr   x k 1 k  1Ci  Cu ( xk 1  t ) f (t )dt
k
'
k

0
C ( x1 , x2 , x3 ,..., xn ) 
 x
  Tr   x k 1 ( xk 1  t ) f (t )dt
k 0 k 1
Profit Maximizing Model
The model is formulated for a machine that
is used in a production process. The
machine has a general failure distribution.
Inspections will reveal the condition of the
machine and may result in reducing the
severity of failure. Repairing a machine
failed a cost of replacing Cr is incurred.
The cost of inspection is Ci The question
how often this machine should be inspected
to maximize profit.
Profit Maximizing Model
The expected profit per cycle P(T)
consists of a profit P1(t) from a cycle
without failure multiplied by the
probability that failure does not
happens in the cycle, plus a profit
P2(T) of a cycle with a failure
multiplied by the probability of failure
in the cycle.
Model Development
For a cycle without failure P1(t) is given
as
P1 (T )  pT  C i
For a cycle with failure, assume failure occurred
at t, t < T. Then
T
P2 (T )  E[ pt | t  T ]  Ci  Cr
pt ( f (t )dt

 0
C C
F (T )
i
r
Model Development
T
P(T )  ( pT  Ci ) R(T )   ptf (t )dt  (Ci  C r ) F (T )
0
Substituting , F (T )  1  R(T )we set
T
P(T )  p R(t )dt  Cr R(T )  Ci  Cr
0
Model Development
T
P(T )  p R(t )dt  Cr R(T )  Ci  Cr
0
T

UP(T )   p  R(t )dt  Cr R(T )  Ci  Cr  / T
 0

Inspection Problem
Consider the the last inspection model also
given in section 3.72 . Derive the optimal
inspection schedule for a machine with an
exponential time to failure density function
with parameter ß in terms of p, Cr, Ci, and
 . Find the schedule if
 = 0.01, p = 500, Cr = 4000 and Ci = 50
Imperfect Maintenance
What is imperfect maintenance?
The classical assumption that
maintenance will bring the equipment
to as good as new is not realistic.
Imperfect maintenance introduced by
Nakagawa that maintenance will
improve the equipment condition and
its status will be between new and
condition before maintenance.
Factors Affecting Condition After
Maintenance
1. Spare parts
2. PM procedures
3. Workmanship
Approaches for Modeling
Imperfect Maintenance

1. An equipment after PM has the same
failure rate as before PM or is good as
new with certain probabilities.


(2) The equipment age reduces by x unit of
time by each PM.


(3) The age and the failure rate of an
equipment are reduced to the original
ones at the beginning of all PM in
proportion to the PM cost.
Delay Time Modeling

The delay time concept in its simplest
form defines a two stage failure
process. In the first stage a defect
becomes detectable and in the second
stage this detectable defect gives rise
eventually to failure of the equipment.
The period h between the time when
the defect is first detectable and the
time of failure is called delay time.
Delay Time Modeling
It has been possible to obtain
subjective estimate of the probability
density function f(h) of the delay time
h. The knowledge about f(h) enables
the construction of models of the
relationship between the inspection
period T and other variables such as
the expected downtime or the expected
operating cost per unit time.

Delay Time Basic Inspection
Model
Model assumptions:
• Defects arise either fixed as breakdown
repairs or inspection repairs.
• An inspection is performed every T units
of time at cost Ci and requires d units of
time d<<<T
• Inspection is perfect
• Defects that are identified at inspection
are fixed within inspection period.
Delay Time Inspection Model

Model assumptions:
Time of origin of fault is assumed
uniform. Faults arise k per unit
time
• The probability density function
of delay time f(h) is known.
•
Model Development
Suppose that a fault arising within the
period (0,T) has a delay time in the interval
(h,h+dh), the probability of this event being
f(h) dh. This fault will be repaired as a
breakdown repair if the fault arises in period
(0,T-h) see figure 9.4, otherwise as an
inspection repair. The probability of the
fault arising before (T-h), given that a fault
will arise, is (T-h/T) (assumption 4). The
probability that a fault is repaired as a
breakdown and has delay time in (h,h+dh)
is given by:
Delay Time Process
Delay time process. If a defect occurs before
T-h it will be repaired as breakdown repair.
h
0
T-h
T
Model Development
(T  h) / Tf ( h)dh
T h
P(T )   
f (h)dh.

h 0
 T 
T
Downtime Delay Model
1
kTdb P(T )  d 
D(T ) 
(T  d )
Expected Cost Model
 1 
 kT C f P(T )  C p 1  P(T ) CI
C (T )  
 (T  d ) 

