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1. Introduction
 With increasing complexity of equipment, the
consequences of failure have become more expensive.
 While the repair or replacement of faulty equipment may
involve unexpected costs, its unavailability when needed
may have even more serious consequences not to talk of
the potentially catastrophic behaviour of failure. This has
led to the concept of reliability.
 Reliability is defined as the probability that an item will
perform a required function under stated conditions for a
stated period of time.
1

2.  The term ‘intended function’ used to describe equipment
performance makes it possible to identify what constitutes
non-conformance (failure) of the equipment.
 “Performance under stated conditions” refers to operational
and environmental conditions or stresses that the equipment
may experience during its useful lifetime. operational
conditions vary from one piece of equipment to another, so it
is important that these conditions be fully specified.
 The definition of reliability involves a time constraint which is
not unusual.
 No product lasts forever; therefore its reliability under fully
specified conditions of use should be defined in terms of time.
2

3.  The term ‘intended function’ used to describe equipment
performance makes it possible to identify what constitutes
non-conformance (failure) of the equipment.
 “Performance under stated conditions” refers to operational
and environmental conditions or stresses that the equipment
may experience during its useful lifetime. operational
conditions vary from one piece of equipment to another, so it
is important that these conditions be fully specified.
 The definition of reliability involves a time constraint which is
not unusual.
 No product lasts forever; therefore its reliability under fully
specified conditions of use should be defined in terms of time.
3

4. THE WHOLE LIFE EQUIPMENT FAILURE
PROFILE (THE BATHTUB CURVE)
 The whole-life of equipment (failure) be divided into
three major distinct periods:
a) Infant mortality period or early failure
b) Useful life period
c) Wear-out period
 During the infant mortality period the failure rate is
high owing to the presence of weak and substandard
components.
 As these component dropout one by one, the failure
rate keeps decreasing until a relatively low more or
less constant level is obtained at time t1.
4

5.  Time t1 is the beginning of the useful period.
 For the time interval between t1 and t2 which is
known as the useful period.
 The wear-out period beginning with time t2 is
characterized by a rapidly rising failure rate as more
and more components breakdown.
® The failure rate curve commonly known as the
bathtub curve is the sum of the three separate over
lapping failure rate distributions known as burn-in
(early failure), random failure and wear-out failure.
5

6.  The decreasing failure rate known as early failures of
infant mortality or burn in, usually related to poor
manufacturing, start up, assembly, storage, quality
control
 The constant failure rate as useful life or random
failure is stress related.
 The increasing failure rate known as wear-out is due
to damage causing wear processes.
6

7. 7
Figure 8.1: The bathtub curve

8. Reasons for burn-in failures
 Inadequate quality control
 Inadequate manufacturing methods
 Substandard materials and workmanship
 Wrong start up and installation
 Inadequate processes and human error
 Inadequate handling methods
8

9. Reasons for useful life failures
 Unexplainable causes
 Human error, abuse, natural failures
 Undetectable failures
 Low safety factors
 Higher random stress than expected
9

10. Reasons for wear-out failures
 Inadequate maintenance
 Wear due to friction
 Wear due to aging
 Wrong overhaul practices
 Corrosion failures
10

11. Failure rate (λ)
 For a stated period in the life of an item the ratio of
the total number of failures to the total cumulative
observed time is defined as the observed failure rate.
λ =
𝐾
𝑇
 λ is expressed in
• Percentage failure per 1000h
• Failures/ℎ
• Failures/106ℎ
11
8.2. FAILURE RATE AND MEAN TIME BETWEEN
FAILURES

12.  Assume a batch of N items out of which a number K
has failed at time t and the total cumulative time T
can be evaluated in one of the following ways.
i. If it is assumed that each failure is replaced as it
occurs, the cumulative time is;
𝑇 = 𝑁𝑡
i. If items are not replaced as they fail, for non-
replacement condition the cumulative time is
given by;
𝑇 = 𝑡1 + 𝑡2 … . . +𝑡𝑘 + 𝑁 − 𝐾 𝑡
Where 𝑡𝑘 = occurrence of the 𝐾𝑡ℎ failure
12

13. Mean Time between Failures (MTBF)
 For a stated period in the life of an item the mean
value of the length of time between consecutive
failures, computed as the ratio of the total cumulative
observed time to the total number of failures is
defined as the MTBF.
𝑀𝑇𝐵𝐹 = 𝜃 =
𝑇
𝐾
 Apply the above equation, it can be seen that;
𝑀𝑇𝐵𝐹 = 𝜃 =
1
λ
 MTBF is the average of the value of (t)
13

14. 14
Figure 8.2: Mean time between failures
Mean time to failures (MTTF)
 For a stated period in the life of an item the ration of
cumulative time to the total number of failures is defined as
MTTF.
𝑀𝑇𝑇𝐹 =
𝑇
𝐾

15. The difference between MTBF and MTTF is in
their usage
• MTTF is applied to items that are not repairable
• MTBF is applied to items that are repairable
• MTBF excludes downtime, therefore it is the
mean up-time between failures
15

16. 16

17. 17

18. 18

19. INTRODUCTION
Availability deals with the duration of up-time for operations
and is a measure of how often
the system is alive and well. It is often expressed as (up-
time)/(up-time + downtime) with many different variants.
Up-time and downtime refer to dichotomized (separated)
conditions. Up-time refers to a capability to perform the task
and downtime refers to not being able to perform the task.
Availability issues deal with at least three main factors (Davidson1988)
for:
1) increasing time to failure,
2) decreasing downtime due to repairs or scheduled maintenance,
3)accomplishing items 1 and 2 in a cost effective manner.
19

20.  Availability has various meanings and ways of being
computed depending upon its use.
 Availability is defined as “a percentage measure of
the degree to which machinery and equipment is in
an operable and committable state at the point in
time when it is needed.”
 This definition includes operable and committable
factors that are contributed to the equipment itself,
the process being performed, and the surrounding
facilities and operations.
20

21.  Availability is herein defined as it relates to the
manufacturing processes and equipment
reliability.
 The analyses presented in this document are
designed to identify deficiencies in equipment
support resources as well as in the equipment
itself. The data collected and its analysis will
indicate to the user whether the necessary
resources are available in a timely fashion for
equipment/process support, and whether the
equipment/process is operable.
21

22.  Availability is a performance criterion for repairable
systems that accounts for both the reliability and
maintainability properties of a component or system.
 It is defined as “a percentage measure of the degree
to which machinery and equipment is in an operable
and committable state at the point in time when it is
needed.”
22

23.  The definition of availability is some what flexible and is
largely based on what types of downtimes one chooses to
consider in the analysis. AS a result, there are a number
of different classifications of availability, such as:
i. Instantaneous (or Point) Availability.
ii. Average Up-Time Availability (or mean
Availability).
iii. Steady State Availability.
iv. Inherent Availability.
v. Achieved Availability.
vi. Operational Availability.
23

24. i. Instantaneous or Point Availability, A(t)
 Instantaneous (or point) availability is the probability
that a system (or component) will be operational (up
and running) at any random time, t.
 This is very similar to the reliability function in that
it gives a probability that a system will function at
the given time, t. Unlike reliability, the instantaneous
availability measure incorporates maintainability
information.
 At any given time, t, the system will be operational if
the following conditions are met:
24

25. The item functioned properly from 0 to t with
probability R(t) or it functioned properly since the last
repair at time u, 0 < u < t, with probability:
With m(u) being the renewal density function of the
system.
25

26. The point availability is the summation of these two
probabilities:
26

27. ii. Average Uptime Availability
The mean availability is the proportion of time during a
mission or time period that the system is available for
use. It represents the mean value of the instantaneous
availability function over the period
(0, T] and is given by:
27

28. iii. Steady State Availability
The steady state availability of the system is the limit of
the instantaneous availability function as time
approaches infinity or:
28

29. The instantaneous availability function will start approaching the
steady state availability value after a time period of
approximately four times the average time-to-failure. Figure
below illustrates this graphically.
Figure : Illustration of point availability approaching steady state.
29

30. Thus steady state availability can be considered as
a stabilizing point where the system's availability
is a constant value. However, steady state
availability cannot be used as the sole metric for
some systems
30

31. iv. Inherent Availability, AI
A.Definition: Inherent availability is the steady state
availability when considering only the corrective
downtime of the system. It is defined as the expected
level of availability for the performance of corrective
maintenance only. Inherent availability is determined
purely by the design of the equipment. It assumes that
spare parts and manpower are 100 percent available
with no delays. It excludes logistics time, waiting or
administrative downtime, and preventive maintenance
downtime.
31

32. It includes corrective maintenance downtime. Inherent
availability is generally derived from analysis of an
engineering design. Inherent availability fulfills the need to
distinguish expected performance between planned shutdowns
For a single component, this can be computed by:
For a System it is written as:
32

33. Objectives: Inherent availability fulfills the need to
distinguish expected performance between planned
shutdowns
C. Formula: Inherent Availability = {Plant operating
time(C)}/ {Plant operating time(C) + Repair time (H3)}
33

34. D. Component Definitions
34

35. E. Qualification:
1. Indicator type : Lagging
2. To be used by: maintenance, reliability engineers while buying
new machinery and evaluating criteria for similar new equipment
selection.
3. Best when used at asset or component level.
4. Gives an idea of expected performance between planned shut
downs
F. Sample Calculation:
If in a manufacturing process data is logged on as mentioned, and
is observed as follows.
The plant operating cycle time per week is 40 hours
Time taken for corrective repair is 4 hrs.
Then Inherent Availability = (40/44) *100=90.9 %
35

36. v. Achieved Availability,
A. Definition:
 The probability that an item will operate satisfactorily at
a given point in time when used under stated conditions
in an ideal support environment (i.e., that personnel,
tools, spares, etc. are instantaneously available).
 It excludes logistics time and waiting or administrative
downtime. It includes active preventive and corrective
maintenance downtime.
 Achieved availability is defined as the achieved level of
availability for the performance of corrective and
preventive maintenance.
36

37.  Achieved availability is determined by the hard
design of the equipment and the facility. Aa also
assumes that spare parts and manpower are 100
percent available with no delays. Achieved
availability is very similar to inherent availability
with the exception that preventive maintenance (PM)
downtimes are also included.
37

38. It can be computed by looking at the mean time between maintenance actions,
MTBM and the mean maintenance downtime , or: This
Where MTBM is mean time between corrective and preventive maintenance
actions and MAMT is the mean active maintenance time.
Operational availability, as seen by the user, is defined MTBM
B. Objectives: This definition fulfills the need to distinguish availability when
planned shutdowns are included. The shape and location of the achievable
availability curve is determined by the plant’s hard design.
38

39. An operation is at a given point on Aa, based on
whether scheduled or unscheduled maintenance
strategies are selected for each failure. few key words
describing availability in quantitative words are: on-line
time, stream factor time, lack of downtime, and a host
of local operating terms including a minimum value for
operational availability. Even though equipment many
not be in actual operation, the production departments
wants it available at least a specified amount of time to
complete their tasks and thus the need for a minimum
availability value.
39

40. Achieved availability is very similar to inherent
availability with the exception that preventive
maintenance (PM) downtimes are also included.
Specifically, it is the steady state availability when
considering corrective and preventive downtime of the
system.
C. Formula:
Achieved Availability = {Plant operating time(C)}/
{Plant operating time(C) + Scheduled Downtime (D) +
Repair time (H3)}
40

41. D. Component Definitions
41

42. E. Qualification:
1. Indicator type : Lagging
2. To be used by: maintenance, reliability engineers to evaluate
effectiveness of condition based maintenance.
3. Best when used at asset or component level.
4. Gives an idea of the difference in metrics, when planned
maintenance is used.
F. Sample Calculation:
If in a manufacturing process data is logged on as mentioned, and
is observed as follows.
The plant operating cycle time per week is 40 hours
Time taken for corrective repair is 2 hrs.
Time taken foe planned repairs is 3 hrs
Then Inherent Availability = (40/ (40+2+3)) *100=88.89 %
42

43. .
vi. Operational Availability,
A. Definition:
 Operational availability is a measure of the average
availability over a period of time and it includes all
experienced sources of downtime, such as administrative
downtime, logistic downtime, etc.
 It is the probability that an item will operate satisfactorily at a
given point in time when used in an actual or realistic
operating and support environment.
 It includes logistics time, ready time, and waiting or
administrative downtime, and both preventive and corrective
maintenance downtime.
 The operational availability is the availability that the
customer actually experiences.
43

44. Operational availability is the ratio of the system uptime and
total time. Mathematically, it is given by
Where the operating cycle is the overall time period of
operation being investigated and uptime is the total time the
system was functioning during the operating cycle. B.
B.Objectives: Operational availability is required to isolate
the effectiveness and efficiency of maintenance operations.
It is the actual level of availability realized in the day-to-day
operation of the facility. It reflects plant maintenance
resource levels and organizational effectiveness.
44

45. C. Formula:
Operational Availability A = {In-cycle time (K)}/ {Scheduled Operating time
(E) + Scheduled Downtime (D)}
D. Component Definitions
45

46. E. Qualification:
1. Indicator type : Lagging
2. To be used by: maintenance, reliability engineers to evaluate
effectiveness of condition based maintenance.
3. It is the actual level of availability realized in the day-to-day
operation of the facility.
4. Best when used at asset or component level.
5. Operational availability is required to isolate the effectiveness
and efficiency of maintenance operations.
6. The difference between achievable and operational availability
is the inclusion of maintenance support. Achieved availability
assumes that resources are 100 percent available and no
administrative delays occur in their application.
46

47. F. Sample Calculation:
If in a manufacturing process data is logged on as
mentioned, and is observed as follows.
The plant operating cycle time per week is 40 hours
In-cycle time is 30 hrs
Scheduled Operating Time is 35 hrs.
Time taken for planned repairs (Scheduled downtime) is
3 hrs
Then Inherent Availability = (30/ (35+3)) *100=78.94
%
47

48. It reflects plant maintenance resource levels and
organizational effectiveness. Operational availability is
required to isolate the effectiveness and efficiency of
maintenance operations. Operational availability is
the bottom line of performance. It is the performance
experienced as the plant operates at a given production
level. The difference between achievable and
operational availability is the inclusion of maintenance
support. Achieved availability assumes that resources
are 100 percent available and no administrative delays
occur in their application.
48

49. Availability (Inherent, Achieved and Operational)
is herein defined and a consistent method for its
evaluation is established. The techniques established
in this document can be used on a continuing basis,
or they can be applied on a periodic basis to
investigate/identify specific current problem areas.
49

50. Definition
Maintainability, as a characteristic of design, can be defined
on the basis of a combination of the following factors:
 Maintenance times
 Maintenance frequency
 Maintenance cost
 The above three factors are dependent on the fact
that the system is operated and maintained in
accordance with prescribed procedures and
resources.
.
8.3. Maintainability

51. Definition of maintainability
Maintainability refers to the measures taken
during the development, design, and installation of
a manufactured product that reduce required
maintenance, man hours, tools, logistic cost, skill
levels, and facilities, and ensure that the product
meets the requirements for its intended use.
Maintainability is a design parameter intended
to reduce repair time, as opposed to maintenance,
which is the act of repairing or servicing an item or
equipment.

52. Maintainability: The probability that a failed
item/equipment will be restored to acceptable
working condition.
Maintainability Terms
Maintainability engineering: An application of scientific
knowledge and skills to develop equipment/item that is
inherently able to be maintained as measured by favourable
maintenance characteristics as well as figures of-merit.
Maintainability model: A quantified representation of a
test/process to perform an analysis of results that
determine useful relationships between a group of
maintainability parameters

53.  Downtime: The total time in which the
item/equipment is not in a satisfactory operable
condition.
 Serviceability: The degree of ease/ difficulty with
which an item/equipment can be restored to its
satisfactory operable state.
Maintainability function: A plot of the probability
of repair within a time given on the y-axis, against
maintenance time on the x-axis and is useful to
predict the probability that repair will be completed
in a specified time.

54.  Availability. This is the probability that a product is
available for use when needed.
 Active repair time. This is that segment of downtime
during which repair staff work to effect a repair.
 Logistic time. This is that segment of downtime
occupied by the wait for a needed part or tool.
 Design adequacy This is the probability that the
product will complete its intended mission
successfully when it is used according to its design
specifications.

55. Introduction to Maintainability
The concept of maintainability encompasses:
 An operational measure of effectiveness
 A characteristic of design
 An engineering specialty that supports design
 A cost driver
 A planned activity in each stage of product life-
cycle

56. Introduction (cont.)
• Maintainability - is the ability of an item to be maintained; this
ability stems from the aggregate of all design features which
promote serviceability.
• Maintenance - is a series of actions of appropriate character
(content, timing, quality) to restore or retain an item in an
operational state.
• Contrast:
– Reliability is time to failure, probability of no failure
– Maintainability is time to diagnose and repair a failure or time
to prevent future failure

57. Maintainability is Inherently a
Probabilistic
Measure
• Detection, diagnosis, repair, check-out all involve
uncertainty
• Human skill and learning are involved
 Differences due to individuals
 Differences due to experience
• Consider other definitions of maintainability:
The probability that:
 Item will be restored to operational status in T hours
 Maintenance will not be required more than X times
per time period
 Maintenance cost will not exceed $Z per time period

58.  Corrective and preventive active maintenance times
 Administrative and logistic delay times
 Total maintenance downtime Corrective and preventive
active maintenance times
 Administrative and logistic delay times
 Total maintenance downtime
Maintenance Elapsed-Time Measures

59. Other Maintenance Elapsed-Time
Measures
• Logistics delay time (LDT), waiting for
– facility, equipment
– Spare part
– Tool
– Transport
• Administrative delay time (ADT)
– Organizational (people, paper, priorities,
etc)
– Non-physical

60. Maintainability in the System Life-
Cycle
• The Maintainability Plan is developed during conceptual
design, reviewed internally and by customer, and includes:
– Functions to be performed
– Standards/ Procedures/ models to be used
– Schedule
– Documents/ Reports
– Organization, responsibilities, interfaces within your
company and with customer, supplier

61. cont.
The Systems Engineering Plan has a major section devoted
to integration of the engineering specialties into the design
process. The SE is responsible for assuring adequate
participation, influence, visibility, etc. is granted to
maintainability, and others.

62. Maintainability Measures and Functions
 maintenance measure
Various measures are used in maintainability analysis:
1. Mean time to repair (MTTR)
2. Mean preventive maintenance time
3. Mean maintenance downtime
In addition to these measures, maintainability
functions are used to predict the probability that a
repair, starting at time t =0, will be completed in a
time t.

63. There are two types of measure of
maintenance. These are
1.qualityative measures and
2. quantitative measures

64. 1. Qualitative Maintainability
Measures
• Especially important early in design when limited
data exist
• Examples:
– Skill level reduction
– Ease of access
– Simplicity of task
– Identification, markings, coding
– Standardization
– Safety during maintenance
– Clearly written, easy to follow instructions
– Ease of fault isolation

65. Qualitative Maintainability
Measures(cont)
• Some ways these get incorporated into design
– Management emphasis
– Experienced maintenance “chiefs” on each
team
– Checklists (see handout)
– Degree to which quantitative measures/
models are sensitive to these

66. 2. Quantitative Measures of
Maintainability
Maintenance Elapsed-Time Factors
 Mean Corrective Maintenance Time Mct (MTTR)
 Mean Preventative Maintenance Time Mpt
 Median Corrective Maintenance Time Mct
 Median Preventative Maintenance Time Mpt
 Mean Active Maintenance Time M

67. cont.
 Maintenance Labor-Hour Factors
Together with skill levels and their day rates, these factors
determine labor cost of maintenance and number in each
skill level per maintenance facility
– MLH/OH
– MLH/cycle
– MLH/month
– MLH/MA

68. cont.
• Any of above can be expressed as average over all
subsystems
• Can apply to corrective, preventive, pr total active
• Can apply to total maintenance downtime
• Conceptually, want to select skill levels and
maintenance
difficulty to minimize maintenance costs

69. cont.
 Maintenance Frequency Factors
• Meantime Between Replacement (MTBR)
– A part, component, or a subsystem must be replaced by
a spare part from inventory. Major link between
maintenance actions and logistics support system
• Meantime Between Maintenance (MTBM)
MTBM=1/(1/mtbmu) +(1/mtbms)
MTBMu is approximately MTBF, the reliability factor,
although in general MTBF ≤ MTBMu
– Meantime between maintenance = MTBM
• Unscheduled (corrective) and Scheduled (preventive)
– Meantime between replacement = MTBR

70. 1.Mean Time to Repair (MTTR)
It measures the elapsed time required to perform a
given maintenance activity.
MTTR is expressed by:
MTTR = ( ∑ λi CMTi ) / ∑ λi
Where:
k = number of units or parts
λi = failure rate of unit/part i , for i= 1, 2, 3, k,
CMTi=corrective maintenance or repair time
required to repair unit or part i, for i= 1, 2, 3,k,
 Usually, times to repair follow
exponential,lognormal, and normal probability
distributions

71. 2.Mean Preventive Maintenance Time
The mean preventive maintenance time is defined by:
MPMT = (∑ FPMi x ETPMTi) / ∑ FPMi
Where:
MPMT = mean preventive maintenance time
M = total number of preventive maintenance
tasks
FPMi = frequency of preventive maintenance task
i, for I = 1, 2, 3, ....., m,
ETPMTi=elapsed time for preventive maintenance
task i, for i= 1, 2, 3, ....., m,

72. 3.Mean Maintenance Downtime
Mean maintenance downtime (MMD) is
described as the total time required either to
restore system to a given performance level
or to keep it at that level of performance.
Downtime:
The total time in which the item/equipment
is not in a satisfactory
operable condition
It is composed of corrective maintenance,
preventive maintenance, administrative
delay, and logistic delay times.

73. MMD = MAMT + LDT + ADT
Where:
ADT = administrative delay time
LDT = Logistic delay time
MAMT = mean active maintenance time
or mean time needed to
perform preventive and corrective
maintenance associated tasks.

74.  Maintainability Functions
1. Exponential p.d.f:
Exponential p.d.f is widely used in
maintainability work to represent repair
times. It is expressed by:
ƒr(t) = (1/MTTR) exp (-t/MTTR)
The maintainability function in this case is:
M(t) = ∫ (1/ MTTR) exp (- t/ MTTR) dt
= 1- exp (- t/ MTTR)

75. 2. Weibull p.d.f:
Weibull p.d.f can also be used to
represent times to repair. It is
defined by:
ƒr(t) = (β/θ) t exp (- (t / θ))
where:
β = shape parameter
θ = scale parameter

76. The maintainability function in this case
is:
M(t) = ∫ (β/ θ ) t exp (- (t / θ) ) d
= 1- exp (- (t / θ) )
When β= 1 and θ= MTTR , the M(t)
reduces to the M(t) in the case of
exponential distribution.

77. 3. Normal p.d.f:
Normal p.d.f can also be used to represent
times to repair. It is defined by:
ƒr(t) = 1/σ √ 2 π exp (- 1/2(t – θ/ σ)²)
where:
σ = standard deviation of the variable
maintenance time t around the
mean value θ
θ = mean of maintenance times
The maintainability function in this case
is:
M(t) = 1/σ √ 2 π ∫ exp (- 1/2(t – θ/ σ)²) dt

78. The mean of the maintenance times is:
θ = ∑ ti / k
where:
k = total number of maintenance
tasks performed
ti = ith maintenance time, for i= 1,
2, 3, ...... K
The standard deviation is :
σ = [ ∑ (ti – θ)²/ (k – 1)]½

79. MAINATANABILITY TOOLS
FAILURE MODE, EFFECTS, AND
CRITICALITY ANALYSIS
A. Failure mode and effects analysis (FMEA) is a
structured qualitative analysis of a system,
subsystem, component, or function that highlights
potential failure modes, their causes, and the
effects of a failure on system operation.
B. When FMEA also evaluates the criticality of the
failure, that is, the severity of the effect of the
failure and the probability of its occurrence