Reliabilty

Quality ControlQuality Control
Chapter 11- ReliabilityChapter 11- Reliability
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BesterfieldBesterfield
Quality Control, 8eQuality Control, 8e
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Besterfield: Quality Control, 8th
ed.. © 2009 Pearson Education, Upper Saddle River, NJ 07458.
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OutlineOutline
 Fundamental Aspects
 Additional Statistical Aspects
 Life and Reliability Testing Plans
 Availability and Maintainability

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When you have completed this chapter you should
be able to:
 Know the definition of reliability and the
factors associated with it.
 Know the various techniques to obtain reliability.
 Understand the probability distributions, failure
curves, and reliability curves as a factor of time.
Learning ObjectivesLearning Objectives

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When you have completed this chapter you
should be able to:
 Calculate the failure rate under different
conditions.
 Construct the life history curve and describe its
three phases.
 Calculate the normal, exponential, and Weibull
failure rate.
Learning Objectives cont’d.Learning Objectives cont’d.

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When you have completed this chapter you
should be able to:
 Construct the OC Curve
 Determine life and reliability test curves
 Calculate the normal, exponential, and Weibull failure rate
 Understand the different types of test design
 Understand the concepts of availability and maintainability
Learning Objectives cont’d.Learning Objectives cont’d.

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 Generally defined as the ability of a product to
perform as expected over time.
 Formally defined as the probability that a
product, piece of equipment, or system will
perform its intended function for a stated period
of time under specified operating conditions.
ReliabilityReliability

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 Means quality over the long run.
 A product that “works” for a long period
of time is a reliable one.
 Since all units of a product will fail at
different times, reliability is a probability.

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There are four factors associated with Reliability:
1. Numerical Value.
The numerical value is the probability that
the product will function satisfactorily
during a particular time.

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2. Intended Function.
Product are designed for particular
applications and are expected to be able to
perform those applications.

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3. Life.
 How long the product is expected to last.
Product life is specified as a function of
usage, time, or both.

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4. Environmental Conditions
Indoors.
Outdoors.
Storage.
Transportation.

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Emphasis:
1.The Consumer Protection Act of 1972.
2.Products are more complicated.
3.Automation.
Achieving ReliabilityAchieving Reliability

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As products become more complex (have more
components), the chance that they will not
function increases.
The method of arranging the components
affects the reliability of the entire system.
Components can be arranged in series,
parallel, or a combination.
System ReliabilitySystem Reliability

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RS = R1 R2 ... Rn
1 2 n
For a series systems, the reliability is the
product of the individual components.
As components are added to the series, the
system reliability decreases.
Series SystemSeries System

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Rs = 1 - (1 - R1) (1 - R2)... (1 - Rn)
1
2
n
 When a component does not function, the product
continues to function, using another component,
until all parallel components do not function.
Parallel SystemParallel System

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 Convert to equivalent series system
AA BB
CC
CC
DD
RRAA RRBB
RRCC
RRDD
RRCC
AA BB C’C’ DD
RRAA RRBB RRDD
RRC’C’ = 1 – (1-R= 1 – (1-RCC)(1-R)(1-RCC))
Series-Parallel SystemSeries-Parallel System

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 The most important aspect of reliability is the
design.
 It should be as simple as possible.
 The fewer the number of components, the
greater the reliability.
 Another way of achieving reliability is to have a
backup or redundant component (parallel
component).
DesignDesign

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 Reliability can be achieved by overdesign.
 The use of large factors of safety can increase the
reliability of a product.
 When an unreliable product can lead to a fatality
or substantial financial loss, a fail-safe type of
device should be used.
 The maintenance of the system is an important
factor in reliability.
DesignDesign

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 The second most important aspect of
reliability is the production process.
 Emphasis should be placed on those
components which are least reliable.
 Production personnel.
ProductionProduction

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 The third most important aspect of reliability is
the transportation.
 Packaging
 Shipment
 Performance of the product by the customer is
the final evaluation.
 Good packaging techniques and shipment
evaluation are essential.
TransportationTransportation

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Distributions Applicable to Reliability:
 Exponential distribution.
 Normal distribution.
 Weibull distribution.
Reliability Curves:Reliability Curves:
 The curves as a function of time.The curves as a function of time.
Additional Statistical AspectsAdditional Statistical Aspects

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Reliability Curves:
 The reliability curves for the exponential,
normal and Weibull distributions as a function
of time are given in Figure 11-2(b) .

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Failure-Rate Curve:
 It is important in describing the life-history
curve of a product.
 See Figure 11-2.
est
number of test failures r
λ = =
sum of test times t +(n - r)T∑

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 The curve, sometimes referred to as the
“bathtub” curve, is a comparison of failure rate
with time.
 It has three distinct phases:
 The debugging phase.
 The chance failure phase.
 The wear-out phase.
Life History CurveLife History Curve

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“Infant
mortality
period”
Debugging
Phase
Chance Failure
Phase
Wear Out
Phase

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1. The debugging phase:
It is characterized by marginal and short-life
parts that cause a rapid decrease in the
failure rate.
It may be part of the testing activity prior to
shipment for some products.
The Weibull distribution ß<1 is used to
describe the occurrence of failures.

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2. The chance failure phase:
Failures occur in a random manner due to the
constant failure rate. The Exponential and the
Weibull distributions β= 1 are best suited to
describe this phase.
3. The wear-out phase:
Is depicted by a sharp raise in failure rates. The
Normal distribution and the Weibull distribution ß
>1 are used to describe this phase.

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 The Weibull distribution is usually uses.
 The Normal distribution.
R(t): Reliability at time t
P(t): Probability of failure or area of the
normal curve to the left of time t. Table A.
t
0
R(t)= 1.0 - f(t)dt
R(t)= 1.0 - P(t)
∫
Normal Failure AnalysisNormal Failure Analysis

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Exponential distribution:
RRtt == ee –t/–t/өө
Where:
t: Time or cycles.
ө: Mean life.
Exponential Failure AnalysisExponential Failure Analysis

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 Can be used for the debugging phase (ß<1)
and the chance failure phase (ß=1).
 By setting = 1, the Weibull equals the
exponential.
 By setting ß=3.4, the Weibull approximates
the Normal.
RtRt == ee –(t/–(t/өө)ß)ß
Where ß is the Weibull slope.
Weibull Failure AnalysisWeibull Failure Analysis

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Steps:
1. Assume values for the mean life ө.
2. These values are converted to the failure
rate, l =1/ ө.
3. Calculate the expected average number of
failures nTl.
4. From Table C of the Appendix using nTl and
c value, get Pa.
OC Curve ConstructionOC Curve Construction

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Type of Tests:
 Failure-Terminated: These life-test sample
plans are terminated when a preassigned
number of failures occurs to the sample.
 Time-Terminated: This life-test sampling
plan is terminated when the sample obtains
a predetermined test time.
Life and Reliability TestingLife and Reliability Testing
PlansPlans

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Type of Tests cont’d.:
 Sequential: A third type of life-testing
plan is a sequential life-test sampling
plan whereby neither the number of
failures nor the time required to reach
a decision are fixed in advance.
PlansPlans

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Tests are based on one or more of the
following characteristics:
 Mean life: the average life of the product.
 Failure rate: the percentage of failures per
unit time or number of cycles.
PlansPlans

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Test are based on one or more of the following
characteristics cont’d.:
 Hazard rate: the instantaneous failure rate at
a specified time.
 Reliable life: the life beyond which some
specified portion of the items in the lot will
survive.
PlansPlans

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 Quality Control Reliability Handbook H108
gives sampling procedures and tables for life
and reliability testing.
 Sampling plans in the handbook are based on
the exponential distribution.
 Provides for the three different types of test:
failure-terminated, time-terminated, and
sequential.
Handbook H108Handbook H108

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 The handbook is over 70 pages long.
 The time-terminated plan:
1. Stipulated producer’s risk, consumer’s
risk, and sample size.
2. Stipulated producer’s risk, rejection
number, and sample size.
3. Stipulated producer’s risk, consumer’s
risk, and test time.
Handbook H108Handbook H108

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 Define customer performance requirements.
 Determine important economic factors and
relationship with reliability requirements.
 Define the environment and conditions of
product use.
Reliability ManagementReliability Management

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 Select components, designs, and
vendors that meet reliability and cost
criteria.
 Determine reliability requirements for
machines and equipments.
 Analyze field reliability for
improvement.
Reliability ManagementReliability Management

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For long-lasting products and services such as
refrigerators, electric power lines, and front-line
services, the time-related factors of availability,
reliability, and maintainability are interrelated.
Availability and MaintainabilityAvailability and Maintainability

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 It is a time-related factor that measures the
ability of a product or service to perform its
designated function.
 The product or service is available when it
is in the operational state, which includes
active and standby use.
AvailabilityAvailability

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Maintainability is the probability that a system or
product can be retained in, or one that has
failed can be restored to, operating condition in
a specified amount of time.
MaintainabilityMaintainability

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 Maintainability is the totality of design
factors that allows maintenance to be
accomplished easily.
 Preventive maintenance reduces the risk
of failure.
 Corrective maintenance is the response to
failures.
MaintainabilityMaintainability

Reliabilty

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