Reliability & Quality Engineering (ME-524)

Instructor:Dr. Syed Amir Iqbal.

A little about me:• B.E in Mechanical, NED UET• Masters in Mechanical Engineering (Specialization in

Manufacturing), NED UET• Doctor of Philosophy, Mechanical Engineering, The

University of Manchester, UKWorking / Tecahing Experience:• Over 17 years of (combined field and teaching)

experience.

Course ContentsME-524 Reliability & Quality Engineering

Reliability EngineeringReliability Measures: The reliability function; expected life; failure rate and hazard function; reliability and hazard function for well known distributions such as exponentional; normal, log normal, Weibull, and gamma distributions; hazard models and product life; constant hazard function, linearly increasing hazard function, piecewise linear bathtub hazard function, power function model, exponential model. Static Reliability Model: Series system, parallel system, series & parallel combinations, complex system analysis, reliability considerations in design. Reliability Engineering Design: Reliability design methodology, strength and stress distributions, safety factors and reliability, reliability bounds in probablistic design. Transformation of random variables. Sums and differences of normal random variables, error analysis, statistical tolerancing. Interference Theory and Reliability Computations: General expression for reliability; reliability computations for normally, log normally, exponentionally, Gamma and Weibully distributed stress and strength; reliability design examples. Reliability in Design and Testing: Dynamic reliability models, reliability estimation, sequential life testing, Bayesian reliability in design and testing, reliability optimisation.

Quality EngineeringControl Charts: Properties of the distribution of sample means, sample range estimation of standard deviation, chance and assignable causes, control charts for mean & range, control charts for mean & standard deviation, control charts for proportion defective & defects per assembly. Tests of significance to compute confidence limits. Acceptance Sampling: Introduction, OC curve, consumer & producer risks, AQL & LTPD, Acceptance Sampling for continuous production, Acceptance by Variables, Single, Double, & Sequential Sampling. Quality, Reliability, & Maintainability: Definitions, management of quality control, economic aspects of quality decisions, capability & variability analysis, various aspects of life testing, reliability, & maintainability, Introduction to ISO 9000, and ISO 14000.

Course ContentsME-524 Reliability & Quality Engineering

Books

• Design ReliabilityBy B. S. Dhillon

• Reliability in Engineering Designby K.C. Kapur & L.C. Lamberson

• Statistical Quality Controlby D. C. Montgomery

• Engineering Statisticsby Walpole & Meyers

• Lecture Notes & handouts

Marks Distribution & Grading Scheme• Semester Exam 60%• Sessional Work 40%• Grading Scheme

LET’S KNOW WHO’S SITTING NEXT

• YOUR NAME

• FINAL DEGREE

• ORGANIZATION

• JOB TITLE

• JOB DESCRIPTION

• EXPERTIES

Reliability Importance

• One of the most important characteristics of a product, it is a measure of its performance with time (Transatlantic and Transpacific cables)

• Products’ recalls are common (only after time elapses). In October 2006, Sony Corporation recalled up to 9.6 million of its personal computer batteries

• Products are discontinued because of fatal accidents • Medical devices and organs (reliability of artificial

organs)

Failure: Types and Prediction

• Two types of failures:– Sudden failure (no indicators): Stress exceeds strength ….– Degradation (gradual wear out): degradation indicator

such as crack growth, change of resistance, corrosion, … This is ideal for Condition-Based Maintenance

• Failure prediction:– Analysis of field data at normal conditions– Accelerated life testing– Accelerated degradation testing – other testing

Examples: Component Wear out

Nov 23 2009, Consumer Product Safety Commission recalls 2.1 million Stork Craft dropdown- side cribs because at least four infants have died in them. the drop-down sides of the cribs became detached, which resulted in dozens of babies either becoming entrapped between the side and the crib frame, or falling out of the crib altogether. Latch wear out.

Reliability EconomicsAuto Warranty Cost

In 2006, Hyundai chose to woo buyers in America by promising quality and reliability. It issued an ambitious new warranty, good for five years (ten on the engine and transmission), then challenged its engineers to back that up with flaw-proof cars. The early sign are they have delivered. Hyundai has trimmed its warranty provision from 5.7% to just 1.8% of its revenue… Sales and profits are up.

Prediction of Failure: Auto Recall

Feb 13 2010Toyota recalls 2.3 million vehicles, three major weaknesses in the company’s quality monitoring include:• Lack of thoroughness in testing new cars and car parts

under varying weather conditions, gas-pedal mechanism tended to stick more as humidity increased.

• Failures in gathering information from customer complaints, especially in the United States.

• Inability to analyze and act quickly on complaints that have been received.

Design of Reliable System

• A new fiber-optic cable to carry 40,000 simultaneous call (data, voice). The ultrathin glass fibers in the cable carry information on laser beams of light.

• The glass-fiber line is suited to video transmission. It provides a security advantage for banks. Unlike satellite transmissions, which can be intercepted, a glass-fiber line is almost impossible to tap.

• Cost $700 M and 8600 miles for transpacific• Cost $350 M and 3600 miles for transatlantic• Goal : No failures in 80 years of service

Reliability EconomicsOil Pipeline Shutdown (Hardware Failure)

BP shuts oilfield August 8, 2006• Damaged pipeline in Alaska affects 8% of U.S. oil production;

crude surges; record gas prices seen.• The price of crude jumped $2.22 a barrel on the shutdown

news to over $76.• Gasoline futures rose 3.35 cents to $2.2650 a gallon.• The threat of a stoppage also endangers Alaska's budget: Oil

taxes account for more than 90 percent of its revenues.• BP officials have acknowledged they did not test the pipes

adequately using a so-called pig device which runs through a pipe to gauge corrosion (utilizes ultrasound to detect corrosion). Lack of proper inspection.

Reliability EconomicsOil Pipeline No-Shutdown (Hardware Failure)

BP Fails to Shutdown Oil Pipeline (April 10, 2010)• A “blowout” on an oil rig occurs when some

combination of pressurized natural gas, oil, mud, and water escapes from a well, shoots up the drill pipe to the surface, expands and ignites. Wells are equipped with structures called blowout preventers that sit on the wellhead and are supposed to shut off that flow and tamp the well. Deepwater blowout preventer failed. Two switches — one manual and an automatic backup — failed to start it (System Design).

Reliability EngineeringAir Traffic Delays (Software Failure)

• Nov 19 2009: A computer glitch caused flight cancellations and delays across the U.S.

• The problem involved the FAA computer systems in Salt Lake City and Atlanta that handle automated flight plans, forcing air traffic controllers to revert to the much more time consuming approach of entering flight plans by hand.

• Software failure (7000 flights)

Requirement…

• When you a buy a product or service…– you request “high quality” and “high reliability”– How do you measure it? What is “high”?– How long? Reliability: 0.99 at year 5, 0.999 at year

4…• Time dependent quality…reliability• How do companies predict reliability and

estimate warranty?

Motivation

• Intense Global Competition• Customer Expectations• Customer Loyalty• Product Liability

Motivation

• A failure free product produced at the minimum possible cost is a prerequisite for a success on the current markets.

• Rapidly Changing, Diverse & New Technologies form new challenges.

=>• Design for reliability of electronic systems and

quality in manufacturing plays a very important role.

NEED FOR RELIABILITY ENGINEERING

• During the world War II reliability was considered to be one of the pressing needs in order to study the behaviour of various systems used by the military. Several studies carried out during this period revealed startling results.– A study uncovered the fact that for every vacuum tube in use, there was one in spare and

seven tubes in transit for which orders had already been placed.– Approximately one electronics technician was required for every 250 tubes.– An army study revealed that between two thirds and three fourths of equipments were out

of commission or under repair.– An air force study Conducted over a five year period disclosed that repair and maintenance

costs were about 10 times the original cost.– A navy study made during maneuvers which showed that the electronic equipment was

operative only 30 %of the time.– A recent study showed the composition of skilled workers for mechanical, electrical and

vehicle body repairs is in the ratio of 3: 5: 2, in a field workshop.– Twenty- four maintenance man hours per flight hour were required in Navy aircraft in 1949.

It was estimated that this rose to 80 in 1948, primarily because of an increase in electronic equipment complexity from 120 parts in 1949 to 8,900 in 1960 to an estimated 33.000 in 1965.

– A study revealed that a pre- World War II civil aero plane had about $4,000 worth of electronic control, navigation and communication apparatus. The post war commercial DC-6 required in excess of $50,000 worth of electronic apparatus while a contemporary jet bomber has over $1,000,000 worth of electronic gear, a twenty fold increase over DC-6, over 200 times that of pre- World War II aero planes.

These findings serves as an impetus for further studies and Investigations.• The size of the system the intricacy of the specified functions, the length

of useful interval of the life variable, and the degree of hostility of the system's environment all influence the reliability.

• It will be clear that the tendency towards larger systems, i.e. systems with larger numbers of components, would decrease the reliability if the development of more reliable system components and structures does not keep in step. There are many such systems with a large quantitative complexity, such as energy distribution network, telecommunication systems, digital computer networks, and space probes.

NEED FOR RELIABILITY ENGINEERING

DEFINITION• The concept of reliability has been interpreted in many ways in numerous

works. Since many of these do not agree in content, it is expedient to examine the main ones.

• The following definitions of reliability are most often met with in the literature.

1. Reliability the integral of the distribution of probabilities of failure - free operation from the instant of switch- on to the first failure.

2. The reliability of a component for a system, is the probability that the component (or a system) will not fail for a time ‘t’.

3. Reliability the probability that a device will operate without failure for a given period of time under given operating conditions.

4. Reliability is the mean operating time of a given specimen between two failures.5. The reliability of a system is called its capacity for failure free operation for a

definite period of time under given operating conditions, and for minimum time lost for repair and preventive maintenance.

6. The reliability of equipment is arbitrarily assumed to be the equipment capacity to maintain given properties under specified operating condition and for a given period of time.

• One of the definitions which has been accepted by most contemporary reliability authorities is given by the Electronics Industries Association (EIA), USA:

The reliability an item (a component, a complex system, a computer Program or a human being) is defined as the probability of Performing

its purpose adequately for the period of time intended under the operating and environmental conditions encountered

• This definition stresses rote elements:– Probability– Adequate performance– Time– Operating and environmental conditions.

DEFINITION

DEFINITION Aspects…

• What is the intended function?• What are the defined operating conditions?• How should time be defined?

We must clearly define these characteristics when defining reliability for a specific application

• The true reliability is never exactly known, but numerical estimates quite close to this value can be obtained by the use of statistical methods and probability calculations.

• How close the statistically estimated reliability comes to the true reliability depends on the amount of testing, the completeness of field service reporting all successes and failures, and other essential data.

• For the statistical evaluation of an equipment, the equipment has to be operated and its performance observed for a specified time under actual operating conditions in the field or under well simulated conditions in a Laboratory. Criteria of what la considered an adequate performance have to be exactly spelled out for each case in advance.

DEFINITION

CAUSES OF FAILURES

• The specific causes of failures of components and equipment in a system can be many Some are known and others are unknown due the complexity of the system and its environment. A few of them are below:– Poor Design, Production and Use– System Complexity– Poor Maintenance

Product Reliability• According to customers interviewed on the significance of product

attributes, reliability ranks in first place as the most significant attribute.

Car purchase criteria

• Today’s development of modern products is confronted with rising functional requirements, higher complexity, integration of hardware, software and sensor technology and with reduced product and development costs. These, along with other influential factors on the reliability, are:

Factors which influence reliability

Product Reliability

• To achieve a high customer’s satisfaction, system reliability must be examined during the complete product development cycle from the viewpoint of the customer.• To achieve this, adequate organizational and subject related measures must

be taken. Methodological reliability tools, both quantitative and qualitative, can be used for a specific situation.

Reliability methods in the product life cycle

Product Reliability

• The earlier reliability analyses are applied, the greater the profit. The well-known “Rule of Ten” shows this quite distinctly

Relation between failure costs and product life phase

Product Reliability

• A qualitative reliability analysis provides a conceptual basis for the degree of confidence placed on a particular component or system and should be capable in the incipient stages of design for alteration of these components. A quantitative reliability prognosis gives a probability assessment of the component based on well founded statistical techniques.

Options for reliability analysis

Product Reliability

Function of Reliability Engineering

• Ensure that designs meet product reliability requirements.• Verify that a product will function reliably over its mission

lifetime.• Identify design discrepancies and resolve.• Evaluate potential failure modes and their effects on mission.

Then, provide guidance on corrective actions.• Recommend design configurations for redundancy.• Establish cost effective test plan based on reliability goal to

determine sample size and test duration.• Assess product failure probability at mission lifetime.• Predict systems reliability and availability.

Difference between Reliability & Quality

• Reliability deals with behavior of failure rate over a long period of operation, while quality control deals with percent of defectives based on performance specifications at a certain point of time.

• Reliability deals with all periods of existence of a product, with prime emphasis at the design stage, while quality control deals with primarily on the manufacturing stage.

• Reliability and quality control use different statistical tools to evaluate.

Metrics in Reliability Engineering

• Reliability (R) or probability of success (Ps)

• Failure probability (Pf = 1- R), equal to the cumulative density function (cdf) of a lifetime distribution.

• Failure (or hazard) rate (λ). • Mean time to failure (MTTF). • Mean time between failures (MTBF)• System availability (A)

𝑐𝑑𝑓 =∫𝑜

𝑡

𝑓 (𝑥 )𝑑𝑥 (h𝑒𝑟𝑒 𝑓 𝑖𝑠𝑝𝑑𝑓 )

Commonly Used Probability Distributions

Distribution Variable ApplicationExponential Continuous variable. Time-to-failure. Commonly used for electronic

parts/assemblies with constant failure rates.Weibull Continuous variable.

Time-to-failure.Versatile to any application.

Lognormal Continuous variable.Time-to-failure.

Mostly used for products subject to wear-out.

Chi-square () Continuous variable. Calculating confidence bounds of a constant failure rate estimate. Also used for two samples comparison, goodness-of-fit test, etc.

Binomial Discrete variable withbinary outcomes.

Estimating probability of success fromrepeated tests. Also used for sampling plan.

F Continuous variable. Calculating confidence bounds of a probabilityof success. Also used for two samplescomparison.

Reliability: The Bathtub Curve• The bathtub curve describes a particular form of a failure (hazard) rate function which

comprises three parts: early failure, random failure and wear out failure.• Military Specification requires that for life critical or system critical applications, the infant

mortality section be burned out or removed, as it greatly reduces the possibility of the system failing early in its life.

Reliability: The Bathtub Curve

Reliability: The Bathtub CurveIntroduction…

• The Bath-tub curve is the curve of failure rate �of the equipment or a machine with respect to time. �

• Is called so because it takes the shape of a bath tub. �

• It is a function of time. Also called � Hazard Function.

BATHTUB CURVERegions…

• It represents a picture of the lifecycle of a product which comprises of three stages. These are:1) Early Failure Period2) Intrinsic Failure Period3) Wear-out Failure Period

INFANT MORTALITY STAGE• � The initial region begins at time zero Customer first begin to �

use the product is characterized by a high but rapidly decreasing failure rate. This region is also known as �EARLYFAILURE PERIOD.

BATHTUB CURVERegions…

CAUSES• Defects produced while designing a �

product �• Substandard weak specimens �• Poor manufacturing �• Poor quality control

PREVENTIVE MEASURES• Appropriate specifications � �• Adequate design tolerance �• Stress testing(evaluate

design weaknesses and uncover specific materials problems) �• Debugging techniques

STABLE LIFE PERIOD• Either constant (age independent) or slowly varying failure �

rate. Failure rate much lower than in early life �period. Most systems spend most of their lifetime operating in �this flat portion of the bathtub curve . It is also known as.� USEFUL LIFEPERIOD

BATHTUB CURVERegions…

CAUSES• Unpredictable sudden stress�

accumulations outside and inside of the components. �• Mishandling Accidents.�

PREVENTIVE MEASURES �• Should be handled with care. �• Proper maintenance

WEAR-OUT FAILURE PERIOD• Failure rate increases rapidly with age� �• Properly qualified electronic hardware do not exhibit wear out

failure during its intended service life. �• Applicable for mechanical and other systems.�• Failures are intrinsic.

BATHTUB CURVERegions…

CAUSES �• Product has reached the end of its

useful life. �• Stresses accumulated over

the life of the product. �• Due to critical parts wearing out

Reliability Function

• The probability of failure as a function of time can be defined as:

• Where t is a random variable denoting the failure time. Then F(t) is the probability that the system will fail by time t , In other words F(t) is the failure distribution function.

• If we define reliability as the probability that the system will perform its intended function at a certain time t , we can write:

R (t) = 1- F (t) = P ( t > t)Where R(t) is the reliability function.

• If time to failure random variable t has a density function f(t), then:

Reliability Function

Distribution Function or Failure Probability

• In many cases, the number of failures at a specific point in time or in a specific interval is not of interest but rather, how many components in total have failed up to a time or until a certain interval is reached. This question can be answered with a histogram of the cumulative frequency.• The observed failures, see Figure a, are added together with each progressive

interval. The result is the histogram of the cumulative frequency shown in Figure b.

collected failure times in trials;

sorted failure times

histogram of the failure frequencies with empirical density function

• The actual distribution function F(t) is determined by increasing the number of experimental values.• The distribution function always

begins with F(t) = 0 and increases monotonically, since for each time or interval a positive value is added – the observed failure frequency. The function always ends with F(t) = 1 after all components have failed.

Distribution Function or Failure Probability

Survival Probability or Reliability

Survival probability R(t) as a complement to the failure probability F(t)

For the commercial vehicle transmission, Figure, a standardised lifetime of 0.2 results in a survival probability of R(t) = 90%, which corresponds to a failure probability of F(t) = 10%, Thus, 90% of the transmissions survive a lifetime of 0.2·T.

Survival probability R(t) of a 6 gear commercial vehicle transmission

Survival Probability or Reliability

Failure Rate• To describe the failure behaviour with the failure rate λ(t), the failures at the

point in time t or in a class i are not divided by the sum of total failures, as for the relative frequency, but rather are divided by the sum of units still intact:

• Figure shows the histogram of the failure rates and the function of the empirical failure rate λ *(t) for the trial run in Figure. It can be seen, that the failure rate in the last class unavoidably approaches , since there are no longer any intact units. Thus, the denominator in above Equation approaches zero.

Histogram of the failure rate and the empirical failure rate λ *(t) for the trial

run

Failure Rate

Determination of the failure rate out of the density function and survival

probability

• The example of the 6 gear commercial vehicle transmission, Figure, shows that the bathtub curve is not typical for all technical systems.• It is more common when only individual sections of the bathtub curve

occur.• The failure behaviour for complex systems is thus not characterized alone by

the bathtub curve, but much more by differing failure distributions exemplifying various behaviours in certain individual sections

Failure rate λ(t) of a 6 gear commercial vehicle transmission

Failure Rate

Various failure behaviours with examples

• Normal distribution example• • Seven units are put on a life test and run• until failure. The failure times are• 85, 90, 95, 100, 105, 110, and 115 hours.• Assuming a normal distribution, estimate the• parameters using probability plotting.

• Data to be filled in• Median rank values can be obtained from the

tables or• calculated from the total number of samples

and the• particular sample rank.