1

Reliability Engineering (PE-4211)Chapter-1

Introduction to Reliability Engineering

2

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.

3

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.

Reliability Engineering

• Reliability engineering is an engineering field that deals with the study, evaluation, and life-cycle management of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time

• Reliability engineering is a sub-discipline within systems engineering. Reliability is often measured as probability of failure, frequency of failures, or in terms of availability, a probability derived from reliability and maintainability. Maintainability and maintenance are often 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 mechanicalitems. Many textbooks and other publications have

appeared on this topic.Example: Critical mechanical component assessment Shaft 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 shaft

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 well-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 applicationof 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.

10

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).

11

RELIABILITY HISTORY

• In 1951, Weibull published a statistical function that subsequently became known as the Weibull distribution. In 1952, exponential distribution received a distinct edge after 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 called 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.

12

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.

13

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).

14

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.

15

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.

16

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, allocating reliability, predicting reliability, reliability modeling, monitoring subcontractor/supplier reliability activities, performing failure modes effects and criticality analysis, monitoring reliability growth, assessing software reliability, preparing critical items list, and performing electronic parts/circuits tolerance analysis.

• Reliability tasks such as those listed above, if performed effectively, will contribute tremendously to the product design.

17

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.

18

Reliability Engineering Department Responsibilities

A reliability engineering department may have various kinds of responsibilities. However, the major ones are as follows:

• Establishing reliability policy, plans and procedures• Reliability allocation• 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

19

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.

20

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.

21

Definition of AvailabilityAvailability. 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%,

Availability• AvailabilityThis 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

23

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.

24

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 fault trees to provide a graphical means of evaluating the relationships between different parts of the system. These models may incorporate predictions based on failure rates taken from historical data. While the (input data) predictions are often 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.

25

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.

26

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 all 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, software and tests to overcome systematic failures.Another design technique to prevent failures is called 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) software 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.

27

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

28

Accelerated Testing

Reliability Growth analysis

Weibull analysis

Thermal analysis by 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.

29

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

(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

))(1(1)...(1

321 i

n

in APAAAAP

30

)()()()()( 212121 APAPAPAPAAP

(2.15)

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

n

iin APAAAAP

1321 )()...(

(2.16)• The probability of an intersection of n independent events is

)()()()( 2121 nn APAPAPAAAP

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

1)()(__

APAP

(2.18)whereP (A) is the probability of occurrence of A.P (A) is the probability of nonoccurrence of A.

31

DEFINITION OF PROBABILITYThis is expressed as

WhereP(A) is the probability of occurrence of event A.N is the number of times that A occurs in the n repeated experiments.

)/(lim)( nNAPn

Bayes' theorem :Mathematically, Bayes' theorem gives the relationship between the probabilities of A and B, P(A) and P(B), and the conditional probabilities of A given B and B given A, P(A|B) and P(B|A). In its most common form, it is:

32

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.

33

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.

Cumulative Distribution Function

34

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

35

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:

36

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