Chapter 3

Preventive Maintenance : Concepts, Modeling and Analysis

Chapter Objectives

1. Enable students to understand the Basic Tools for developing Pm

Programs.

2. 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

Condition

based

Statistically and reliability based

Off line On line Time based

Use based

Preventive maintenance

Condition

based

Statistically and reliability based

Off line 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 condition-based 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 analysisVibration 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 iron-based 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 analysisIt 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 white or color variations.

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 rates.

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 RecordThe 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 ScheduleThe 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) =

C(tp) = expected cost per cycle

UC(tp) = expected cost per unit time.

)(1/)( ptRdtttf

Failurereplacement

Preventivereplacement

Failurereplacement

Preventivereplacement

Time

0

Failure replacement

tp

Failure replacement

tp

Age Based Policy

Model Development

length cycle Expected

cycleper cost expected Total)( ptUC

)](1[)()( pfppp tRCtRCtC

Expected Cycle Length = tp R(tp)+M(tp)(1-R(tp))

Expected Cycle Length = tp R(tp)+M(tp)(1-R(tp))

)](1/[)()( pp tRdtttftM

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

pt

t

t

tRtMtRt

tRCtRCtUC

p

p

pppp

pfppp

2p

p

pp

p

20

1-t

4.5t+5 =

10

1

2

t+]1/10t-[1t

10

150+)1/10t-5(1

=

)](1)[()(

)](1[)()(

Applying Golden Section

68.7

27038.4

81.32)18.6()( ,18.7

3.09038

22.19=UC(3.82)=)UC(

6.18=10*0.618+0= 3.82=10*0.382+0=

0.382=-1 0.618,= ],10,0[],,[

11

11

11

UCUC

ba

)()( 11 UCUC the next interval is )()( UCUC

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 Modelsf(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:

i

i

x

x ruui dttfCtxCiC1

)()])([

Model Development

0)()(

0)()(1

),...,,,('

as obtained is unit timeper cost expected The

)()0

(),...,,,(ET

11 1

11

321

11321

kdttftx

x xT

k

xx dttftxCCkC

xxxxC

dttftk

xx xTxxxx

kk kr

kk kuir

n

kk krn

Profit Maximizing ModelThe 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

 

For a cycle with failure, assume failure occurred at t, t < T. Then 

iCpTTP )(1

P T E pt t T C Cpt f t dt

F TC Ci r

T

i r20( ) [ | ]

( ( )

( )

Model Development

 

Substituting , we set 

T

rii TFCCdttptfTRCpTTP0

)()()()()()(

F T R T( ) ( ) 1

P T p R t dt C R T C Cr

T

i r( ) ( ) ( ) 0

Model Development

ri

T

r CCTRCdttRpTP )()()(0

TCCTRCdttRpTUPT

rir /)()()(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 DevelopmentSuppose 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.

0 T-h T

h

Model Development

dhhTfhT )(/)(

.)()(0

dhhfT

hTTP

T

h

Downtime Delay Model

dTPkTddT

TD b

)()(

1)(

Expected Cost Model

Ipf CTPCTPCkTdT

TC

)(1)()(

1)(