This is a three parts lecture series. The parts will cover the basics and fundamentals of reliability engineering. Part 1 begins with introduction of reliability definition and other reliability characteristics and measurements. It will be followed by reliability calculation, estimation of failure rates and understanding of the implications of failure rates on system maintenance and replacements in Part 2. Then Part 3 will cover the most important and practical failure time distributions and how to obtain the parameters of the distributions and interpretations of these parameters. Hands-on computations of the failure rates and the estimation of the failure time distribution parameters will be conducted using standard Microsoft Excel. Part 1. Reliability Definitions 1.Reliability---Time dependent characteristic 2.Failure rate 3.Mean Time to Failure 4.Availability 5.Mean residual life

1. Fundamentals of Reliability
Fundamentals of Reliability
Engineering and Applications
Part 1 of 3
E. A. Elsayed
©2011 ASQ & Presentation Elsayed
Presented live on Nov 30th, 2010
http://reliabilitycalendar.org/The_Re
liability_Calendar/Short_Courses/Sh
liability Calendar/Short Courses/Sh
ort_Courses.html

2. ASQ Reliability Division
ASQ Reliability Division
Short Course Series
Short Course Series
The ASQ Reliability Division is pleased to
present a regular series of short courses
featuring leading international practitioners,
academics, and consultants.
academics and consultants
The goal is to provide a forum for the basic and
The goal is to provide a forum for the basic and
continuing education of reliability
professionals.
http://reliabilitycalendar.org/The_Re
liability_Calendar/Short_Courses/Sh
liability Calendar/Short Courses/Sh
ort_Courses.html

3. Fundamentals of Reliability Engineering and
Applications
E. A. Elsayed
elsayed@rci.rutgers.edu
Rutgers University
Nov 30, 2010
1

4. Outline
Part 1. Reliability Definitions
1. Reliability---Time dependent characteristic
2. Failure rate
3. Mean Time to Failure
4. Availability
5. Mean residual life
2

5. Outline
Part 2. Reliability Calculations
1. Use of failure data
2. Density functions
3. Reliability function
4. Hazard and failure rates
3

6. Outline
Part 3. Failure Time Distributions
1. Constant failure rate distributions
2. Increasing failure rate distributions
3. Decreasing failure rate distributions
4. Weibull Analysis – Why use Weibull?
4

7. Part 1. Reliability Definitions
 Some Initial Thoughts
Personal Experience …Time
Dependent Characteristics
 More on Reliability Economics
 Reliability Definition
 Availability
 Mean residual life
 Conclusions
5

8. Outline
Part 1
 Some Initial Thoughts
Personal Experience
 More on Reliability Economics
 Reliability Definition
 Reliability Estimation
 System Reliability Calculations
 Role of New Technologies
 Conclusions
6

9. 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
(Pinto, Concord)
 Medical devices and organs (reliability of artificial
organs)
7

10. Failure: Types and Prediction
 Two types of failures:
1. Sudden failure (no indicators): Stress exceeds
strength ….
2. Degradation (gradual wear out): degradation indicator
such as crack growth, change of resistance, corrosion,
… This is ideal for Condition-Based Maintenance
 Failure prediction:
1. Analysis of field data at normal conditions
2. Accelerated life testing
3. Accelerated degradation testing
other testing
8

11. Examples: Component Wear out
Nov 23 2009, Consumer Product Safety
Commission recalls 2.1 million Stork Craft drop-
down-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.
9

12. Reliability Economics
Auto 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.
10

13. Prediction of Failure: Auto Recall
Feb 13 2010
Toyota 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. 11

14. Personal Experience: 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
12

15. Global Impact: Oceanic Airspace
Data Link Communication Reliability
Engine
Monitoring
AOC or Aircraft
Position Operational
Monitoring Communication
Ground
Earth
Stations
ARINC SITA
Uplink
Oakland ARTCC
13

16. Reliability Economics
Oil 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 is runs
through a pipe to gauge corrosion (utilizes ultrasound to
detect corrosion). Lack of proper inspection.
Lucent 14

17. Reliability Economics
Oil 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 Horizon’s
blowout preventer failed. Two switches — one manual and
an automatic backup — failed to start it (System Design).
15

18. Reliability Engineering
Air 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)
16

19. Reliability Definitions “Measurements”
► 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?
► Reliability of cold standby units …New tires and old
tires… 17

20. Some Initial Thoughts
Repairable and Non-Repairable
Another measure of reliability is availability (probability
that the system provides its functions when needed).
Maximum Reliability level
With R
epairs
Reliability
No Rep
airs
Time
18

21. Some Initial Thoughts
Warranty
• Will you buy additional warranty?
• Burn in and removal of early failures.
(Lemon Law).
Early Failures
Increasing
Constant Failure
Failure Rate Rate
Failure Rate
19 Time

22. Reliability Definitions
Reliability is a time dependent characteristic.
 It can only be determined after an elapsed time but
can be predicted at any time.
 It is the probability that a product or service will
operate properly for a specified period of time (design
life) under the design operating conditions without
failure.
20

23. Other Measures of Reliability
Availability is used for repairable systems
 It is the probability that the system is operational
at any random time t.
 It can also be specified as a proportion of time
that the system is available for use in a given
interval (0,T).
21

24. Other Measures of Reliability
Mean Time To Failure (MTTF): It is the average
time that elapses until a failure occurs.
It does not provide information about the distribution
of the TTF, hence we need to estimate the variance
of the TTF.
Mean Time Between Failure (MTBF): It is the
average time between successive failures.
It is used for repairable systems.
22

25. Mean Time to Failure: MTTF
∞ ∞
MTTF = ∫ tf (t )dt = ∫ R(t )dt
0 0
1 n
MTTF = ∑ ti
n i =1
1
2 is better than 1?
2
R(t)
1
Time t
0
23

26. Mean Time Between Failure: MTBF
24

27. Other Measures of Reliability
Mean Residual Life (MRL): It is the expected remaining
life, T-t, given that the product, component, or a system
has survived to time t.
1 ∞
L(t ) = E[T − t | T ≥ t ] = ∫ τ f (τ )dτ − t
R(t ) t
Failure Rate (FITs failures in 109 hours): The failure rate in
a time interval [ t1 −t2 ] is the probability that a failure per
unit time occurs in the interval given that no failure has
occurred prior to the beginning of the interval.
Hazard Function: It is the limit of the failure rate as the
length of the interval approaches zero.
25

28. Strength
mean =20 kg/mm2, Sigma=5 kg/mm2
26

29. Stress
mean =10 kg/mm2, Sigma=5 kg/mm2
27

30. Stress-Strength
28

31. Safety Factors and Reliability
Let S denote the strength random variable and s
the stress random variable. The random variable y
= (S – s) is then related to the reliability of the
component by
R = P( y ≥ 0)
(1)
When strength and stress random variables have
normal density functions, y is normally distributed
and the reliability R is given by
29

32. Safety Factors and Reliability
− z2
1 ∞
(2)
R=
2π ∫ ( µ −µ )
− S s
2 2
e 2 dz
σ S +σ s
µS − µs
z0 =
Where σ S + σ s2
2
This integral can be estimated using numerical
integration or
http://www.fourmilab.ch/rpkp/experiments/analysis/zCalc.html
30

33. Calculations of Factor of Safety
Using the mean values of the stress and strength we
obtain factor of safety = 20/10=2
The probability of failure is calculated as
µS − µs
z0 = =1.4142
σ +σ
2
S
2
s
The corresponding probability of failure =0.078652 or
About 1 in 13. The reliability is 0.921348
31

34. Example
32

35. Calculations of Factor of Safety
where z is the standard normal random variable, µS is
the mean value of the strength, µ s is the mean value of
the stress, and σ S and σ s are the standard
deviations of strength and stress, respectively. The
reliability clearly depends on the lower limit of the
integral in Equation 2. A higher value of reliability can
be obtained by lowering the lower limit.
Table 1 gives the reader an idea about the variability
in reliability related to different magnitudes of
variability in strength and stress random variables.
The factor of safety is given by µ S / µ s .
33

36. Solution using Matlab
%Load excel sheet file
[A,B]=xlsread('P1A1S2009.xls');
>> S1=A(:,1);
>> S2=A(:,2);
>> mu1=mean(S1)
mu1 = 9.8616
>> mu2=mean(S2)
mu2 =19.7842
>> sigma1=std(S1)
sigma1 = 0.9476
>> sigma2=std(S2)
sigma2 =1.9592
% Calculate z
>> z=(mu2-mu1)/(sqrt(sigma1^2+sigma2^2))
z = 4.5593
Probability corresponding to z is 0.0003 34