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Reliability, Maintainability, Availability

- Reliability Engineering (PE-4211)

Chapter-1

Introduction to Reliability

Engineering

1 - The importance of reliability

Electrical, electronic and Mechanical equipment is used in a number

of fields — in industry for the control of processes, in computers, in

medical electronics, atomic energy, in weapon systems, defence

equipments, communications, navigation at sea and in the air, and

in many other fields. It is essential that this equipment should

operate reliably under all the conditions in which it is used. In the

air navigation, military and atomic energy fields, for instance, failure

could result in a dangerous situation.

Very complicated systems, involving large numbers of separate

units, such as avionic and aerospace electronic systems are coming

into use more and more. These systems are extremely complex and

use a large number of component parts. As each individual part is

liable to failure, the overall reliability will decrease unless the

reliability of each component part can be improved.

2 - Mechanical reliability

The well-reported failures, such as the Space Shuttle Challenger, Chernobyl

nuclear accidents, and the Bhopal gas escape, emphasize vividly the necessity for

mechanical reliability.

Buildings, bridges, transit systems. railways, automotive systems, robots, offshore

structures, oil pipe lines and tanks, steam turbine plates, roller bearings, etc., all

have their particular modes of failure affecting their reliability.

There are a number of common modes of mechanical failures, which are worth

listing, e.g. with structures:

(1)Corrosion failures

(2) Fatigue failures

(3) Wear failures

(4) Fretting failures

(5) Creep failures

(6) Impact failures

These may be considered the main failure modes, but there are of course many

others, such as ductile rupture, thermal shock, galling, brinelling, spalling,

radiation damage, etc.

A ‘failure’ is any inability of a part or equipment to carry out its

specified function.

3 - Reliability Engineering

• Reliability engineering is

an e

ngineering fi

eld that deals

with

the

study,

evaluation,

and lif

e-cycle

management o

f r

eliability: the ability of a s

ystem o

r

component to perform its required functions under stated

conditions for a specified period of time

• Reliability engineering is a sub-discipline within s

ystems

engineering. Reliability is ofen measured as p

robability of

failure, frequency of failures, or in terms of a

vailability, a

probability

derived

from

reliability

and

maintainability. Ma

intainability a

nd m

aintenance a

re

ofen important parts of reliability engineering. - Well-publicized system failures such as those listed below may have

also contributed to more serious consideration of reliability in

product design

• Space Shuttle Challenger Disaster:

This debacle occurred in 1986, in which all crew members

lost their lives. The main reason for this disaster was design

defects.

• Chernobyl Nuclear Reactor Explosion:

This disaster also occurred in 1986, in the former Soviet Union,

in which 31 lives were lost. This debacle was also the result of

design defects.

• Point Pleasant Bridge Disaster:

This bridge located on the West Virginia/ Ohio border collapsed

in 1967. The disaster resulted in the loss of 46 lives and its

basic cause was the metal fatigue of a critical eye bar. - RELIABILITY SPECIALIZED AND APPLICATION

AREAS

• Mechanical reliability

This is concerned with the reliability of mechanical

items. Many textbooks and other publications have

appeared on this topic.

Example:

Critical mechanical component assessment

Shaf strength

Selection of flexible couplings and transmission brakes

Gear life assessment; screening of belt drives

Assessment of bearing life, load ratings of slider bearings and shaf

sealing devices

Bolt loading and lubrication systems - • Software reliability.

This is an important emerging area of reliability as the

use of computers is increasing at an alarming rate.

• Human reliability.

In the past, many times systems have failed not due to

technical faults but due to human error. The first book

on the topic appeared in 1986

• Reliability optimization.

This is concerned with the reliability optimization of

engineering systems

• Reliability growth.

This is basically concerned with monitoring reliability

growth of engineering systems during their design and

development - • Structural reliability.

This is concerned with the reliability of

engineering structures, in particular civil

engineering

• Power system reliability.

This is a wel -developed area and is basically

concerned with the application of reliability

principles to conventional power system

related problems. Many books on the subject

have appeared over the years including a vast

number of other publications - • Robot reliability and safety.

This is an emerging new area of the application

of basic reliability and safety principles to robot

associated problems.

• Life cycle costing.

This is an important subject that is directly related

to reliability. In particular, when estimating the

ownership cost of the product, the knowledge

regarding its failure rate is essential.

• Maintainability.

This is closely coupled to reliability and is concerned

with the maintaining aspect of the product. - RELIABILITY HISTORY

• The history of the reliability discipline goes back to the

early 1930s when probability concepts were applied to

electric power generation related problems. During World

War II, Germans applied the basic reliability concepts to

improve reliability of their V1 and V2 rockets.

• In 1947, Aeronautical Radio, Inc. and Cornell University

conducted a reliability study of over 100,000 electronic

tubes. In 1950, an ad hoc committee on reliability was

established by the United States Department of Defense

and in 1952 it was transformed to a permanent body:

Advisory Group on the Reliability of Electronic Equipment

(AGREE).

10 - RELIABILITY HISTORY

• In 1951, Weibul published a statistical function that subsequently became

known as the Weibul distribution. In 1952, exponential distribution received a

distinct edge afer the publication of a paper, presenting failure data and the

results of various goodness-of-fit tests for competing failure distribution, by

Davis.

• In 1954, a National Symposium on Reliability and Quality Control was held for

the first time in the United States and in the following year, the Institute of

Electrical and Electronic Engineers (IEEE) formed an organization cal ed the

Reliability and Quality Control Society. During the following two years, three

important documents concerning reliability appeared: 1956: a book entitled

Reliability Factors for Ground Electronic Equipment, 1957: AGREE report, 1957:

first military reliability specification: MIL-R-25717 (USAF): Reliability Assurance

Program for Electronic Equipment.

• In 1962, the Air Force Institute of Technology of the United States Air Force

(USAF), Dayton, Ohio, started the first master’s degree program in system

reliability engineering. Nonetheless, ever since the inception of the reliability

field many individuals have contributed to it and hundreds of publications on

the topic have appeared.

11 - TERMS AND DEFINITIONS

• Reliability: This is the probability that an item will

carry out its assigned mission satisfactorily for the

stated time period when used under the specified

conditions.

• Failure: This is the inability of an item to function

within the initially defined guidelines.

• Downtime: This is the time period during which the

item is not in a condition to carry out its stated mission.

• Maintainability: This is the probability that a failed

item will be repaired to its satisfactory working state.

• Redundancy :This is the existence of more than one

means for accomplishing a defined function.

12 - Active redundancy: This is a type of redundancy when all redundant

items are operating simultaneously.

Availability: This is the probability that an item is available for

application or use when needed.

Useful life: This is the length of time an item operates within an

acceptable level of failure rate.

Mission time: This is the time during which the item is performing its

specified operating condition.

Human error: This is the failure to perform a given task (or the

performance of a forbidden action) that could lead to disruption of

scheduled operations or result in damage to property/equipment.

Human reliability: This is the probability of completing a job/task

successfully by humans at any required stage in the system operation

within a defined minimum time limit (if the time requirement is

specified).

13 - MEAN TIME BETWEEN FAILURES (MTBF): The mean exposure

time between consecutive failures of a component. This applies to

repairable items, and means that if an item fails, say 5 times over

a period of use totaling 1000hours, the MTBF would be 1000/5 or

200hours.

MEAN TIME BETWEEN MAINTENANCE (MTBM): The average

time between all maintenance events that cause downtime, both

preventative and corrective maintenance, and also includes any

associated logistics delay time.

MEAN TIME TO FAILURE (MTTF): Mean Time To Failure (MTTF): It

is the average time that elapses until a failure occurs. MTTF is

commonly found for non repairable items such as fuses or bulbs,

etc.

14 - NEED OF RELIABILITY IN PRODUCT DESIGN

• There have been many factors responsible for the consideration of

reliability in product design including product complexity, insertion of

reliability related-clauses in design specifications, competition,

awareness of cost effectiveness, public demand, and the past system

failures.

Some of these factors are described below in detail.

• Even if we consider the increase in the product complexity with

respect to parts alone, there has been a phenomenal growth of some

products. For example, today a typical Boeing 747 jumbo jet airplane

is made up of approximately 4.5 million parts, including fasteners.

Even for relatively simpler products, there has been a significant

increase in complexity with respect to parts. For example, in 1935 a

farm tractor was made up of 1200 critical parts and in 1990 the

number increased to around 2900.

15 - RELIABILITY IN THE PRODUCT DESIGN PROCESS

• Reliability of the design, to a large extent, is determined by

the reliability tasks performed during the product design.

• These reliability tasks include: establishing reliability

requirements

definition,

using

reliability

design

standards/guides/checklists, al ocating reliability, predicting

reliability,

reliability

modeling,

monitoring

subcontractor/supplier reliability activities, performing

failure modes effects and criticality analysis, monitoring

reliability growth, assessing sofware reliability, preparing

critical items list, and performing electronic parts/circuits

tolerance analysis.

• Reliability tasks such as those listed above, if performed

effectively, wil contribute tremendously to the product

design.

16 - NEED OF QUALITY IN PRODUCT DESIGN

• The importance of quality in business and

industry is increasing rapidly because of factors

such as competition, growing demand from

customers for better quality, increasing number

of quality-related lawsuits, and the global

economy. Nonetheless, the cost of quality

control accounts for around 7–10% of the total

sales revenue of manufacturers. Today,

companies are faced with reducing this amount

and at the same time improving the quality of

products and services for their survival in the

internet economy.

17 - Reliability Engineering Department Responsibilities

A reliability engineering department may have various kinds of responsibilities.

However, the major ones are as fol ows:

• Establishing reliability policy, plans and procedures

• Reliability al ocation

• Reliability prediction

• Specification and design reviews with respect to reliability

• Reliability growth monitoring

• Providing reliability related inputs to design specifications and proposals

• Reliability demonstration

• Training reliability manpower and performing reliability-related research and

development work

• Monitoring the reliability activities of subcontractors, if any

• Auditing the reliability activities

• Failure data collection and reporting

• Failure data analysis

• Consulting

18 - Definition of Reliability

• Reliability is the probability of a device

performing its purpose adequately for the

period intended under the given operating

conditions

This definition focus four important factors

the reliability of a device is expressed as a probability

the device is required to give required performance

the duration of performance

the operating conditions are prescribed.

19 - Definition of Maintainability

Maintainability is a measure of the speed with which

loss of performance is detected, diagnosed and made

good.

Maintainability is the probability that a unit or system

will be restored to specified conditions within a given

period when maintenance action is taken in accordance

with prescribed procedures and resources.

It is a characteristic of the design and installation of the

unit or system.

The ‘availability’ or time an equipment is functioning

correctly while in use depends both on reliability and on

maintainability.

20 - Definition of Availability

Availability. Availability is defined as the percentage of

time that a system is available to perform its required

function(s).

It is measured in a variety of ways, but it is principally

a function of downtime.

Availability can be used to describe a component or

system but it is most useful when describing the nature

of a system of components working together. Because it

is a fraction of time spent in the “available” state, the

value can never exceed the bounds of 0 < A < 1. Thus,

availability will most often be written as a decimal, as

in 0.99999, as a percentage, as in 99.999%,

21 - Availability

• Availability

This is the probability that an item is available for

application or use when needed.

Maintainability

together

with

reliability

determine the availability of a machinery

system. Availability is influenced by the time

demand made by preventive and corrective

maintenance measures.

Availability(A) is measured by:

A= MTBF/MTBF + MTTR - Quality and reliability

The quality of a device is the degree of performance to

applicable specification and workmanship standards.

What is the difference between Quality and Reliability?

Quality means good performance and longevity.

Quality of any manufactured product is determined by its design,

the materials from which it is made and the processes used in its

manufacture.

Quality control measures performance and its variations from

specimen to specimen by statistical methods to determine

whether production satisfies the design requirements.

Quality of a product is determined by conformity and reliability.

In Reliability it matters how long a product will maintain its

original characteristics when in operation.

23 - Reliability activity in system design

For large engineering systems, management of design and reliability becomes

an important issue.

Reliability design begins with the development of a (system) model. Reliability

and Availability models use block diagrams and

f ault trees t o provide a

graphical means of evaluating the relationships between different parts of the

system. These models may inc

orporate predictions based on failure rates

taken from historical data. While the (input data) predictions are ofen not

accurate in an absolute sense, they are valuable to assess relative differences

in design alternatives. Maintainability parameters, for example MTTR, are

other inputs for these models.

The most important fundamental initiating causes and failure mechanisms are

to be identified and analyzed with engineering tools.

A diverse set of practical guidance and practical performance and reliability

requirements should be provided to designers so they can generate low-

stressed designs and products that protect or are protected against damage

and excessive wear.

24 - A Fault Tree Diagram

One of the most important design techniques is redundancy. This means that if

one part of the system fails, there is an alternate success path, such as a backup

system. By creating redundancy, together with a high level of failure monitoring

and the avoidance of common cause failures, even a system with relative bad

single channel (part) reliability, can be made highly reliable (mission reliability)

on system level.

25 - Furthermore, by using redundancy and the use of dissimilar design and

manufacturing processes (different suppliers) for the single independent

channels, very high levels of reliability can be achieved at al moments of

the development cycles (early life times and long term).

Redundancy can also be applied in systems engineering by double

checking requirements, data, designs, calculations, sofware and tests to

overcome systematic failures.

Another design technique to prevent failures is cal ed physics of failure.

This technique relies on understanding the physical static and dynamic

failure mechanisms. It accounts for variation in load, strength and stress

leading to failure at high level of detail, possible with use of

modern Finite Element Method ( FEM) sofware programs that may

handle complex geometries and mechanisms like creep, stress relaxation,

fatigue and probabilistic design (Monte Carlo simulations / DOE). The

material or component can be re-designed to reduce the probability of

failure and to make it more robust against variation.

26 - Another common design technique is component derating: Selecting

components whose tolerance significantly exceeds the expected stress, as

using a heavier gauge wire that exceeds the normal specification for the

expected electrical current.

Another effective way to deal with unreliability issues is to perform

analysis to be able to predict degradation and being able to prevent

unscheduled down events / failures from occurring. RCM(Reliability

Centered Maintenance) programs can be used for this.

Many tasks, techniques and analyses are specific to particular industries

and applications. Commonly these include:

Built-in test (BIT) (Testability analysis)

Failure mode and effects analysis (FMEA)

Reliability Hazard analysis

Reliability Block Diagram analysis

Fault tree analysis

Root cause analysis

27 - Accelerated Testing

Reliability Growth analysis

Weibul an

alysis

Thermal analysis b

y Finite Element Analysis (FEA) and / or Measurement

Thermal induced, shock and vibration fatigue analysis by FEA and / or

Measurement

Electromagnetic analysis

Statistical interference

Predictive and preventive maintenance: Reliability Centered Maintenance

(RCM) analysis

Human error analysis

Operational Hazard analysis

Results are presented during the system design reviews and logistics reviews.

Reliability is just one requirement among many system design requirements.

28 - Probability Basics

As the basis for reliability theory is probability, this section presents basic

properties of probability. Some of these properties are as follows

• The probability of occurrence of event, say A, is

O ≤ P(A) ≤ 1

(2.11)

• Probability of the sample space S is

P(S) = 1

(2.12)

• Probability of the negation of the sample space S is

P(S¯) = 1

(2.13)

Where S is the negation of the sample space S.

• The probability of the union of n independent events is

n

P( A A A ...A ) 1

1

(

P(A ))

1

2

3

n

i

i 1

(2.14)

Where Ai is the I th event; for i = 1, 2, …, n.

P (Ai) is the probability of occurrence of event Ai ; for i = 1, 2, …, n.

For n = 2, Equation (2.14) reduces to

29 - P( A A ) P( A ) P( A ) P( A )P( A )

1

2

1

2

1

2

(2.15)

• The probability of the union of n mutually exclusive events is

n

P( A

...

)

(

)

1 A2 A3

A

P A

n

i

i 1

(2.16)

• The probability of an intersection of n independent events is

P( A A A ) P( A )P( A ) P( A )

1

2

n

1

2

n

(2.17)

• The probability of occurrence and nonoccurrence of an event, say A, is

__

P( )

A P( )

A 1

where

(2.18)

P (A) is the probability of occurrence of A.

P (A) is the probability of nonoccurrence of A.

30 - DEFINITION OF PROBABILITY

This is expressed as

P( )

A lim(N / n)

n

Where

P(A) is the probability of occurrence of event A.

N is the number of times that A occurs in the n repeated experiments.

Bayes' theorem :

Mathematically, Bayes' theorem gives the relationship between the probabilities

o

f A and B, P(A)

and P(B),

and

the conditional probabilities

o

f A given B an

d B g

iven A, P(A|B) and P(B|A).

In its most common form, it is:

31 - Distribution functions

A more useful diagram, for continuous data, is the probability density function.

The y axis is the percentage measured in a range(shown on the x-axis) rather

than the frequency as in a histogram. If you reduce the ranges(or intervals) then

the histogram becomes a curve which describes the distribution of the

measurements or values.

This distribution is the probability density function or PDF. Figure 4, below,

shows an example of a PDF. The area under the curve of the distribution is

equal to 1, i.e.

The probability of a value falling between any two values x1and x2 is the

area bounded by this interval, i.e.

32 - Cumulative Distribution Function

In reliability since we are usually discussing time we will change x to t, i.e. f(t).

The cumulative distribution function or CDF, F(t), gives the probability that a

measured value will fall between -∞ and t, i.e.

33 - Figure 5, below, shows the CDF as x tends to ∞ F(t) tends to 1.

34 - In reliability engineering we are concerned with the probability that an item

will survive for a stated interval of time (or cycles or distance etc.) i.e. there is

no failure in the interval (0 to t). This is known as the survival function or

Reliability function and is given by R(t). From the definition:

35 - KEY POINTS

• Reliability is a measure of uncertainty and therefore

estimating reliability means using statistics and

probability theory

• Reliability is quality over time

• Reliability must be designed into a product or service

• Most important aspect of reliability is to identify cause

of failure and eliminate in design if possible otherwise

identify ways of accommodation

• Reliability is defined as the ability of an item to

perform a required function without failure under stated

conditions for a stated period of time

• The costs of unreliability can be damaging to a

company

36