1.
RAL
VEM DFR – Design for Reliability
DFR – Fundamentals for Engineers
Reliability Audit Lab
2.
RAL
VEM
Topics that will be covered:
1. Need for DFR
2. DFR Process
3. Terminology
4. Weibull Plotting
5. System Reliability
6. DFR Testing
7. Accelerated Testing
Reliability Audit Lab
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VEM
What Customers Care about:
1. Product Life…. i.e., useful life before wear-out.
2. Minimum Downtime…. i.e., Maximum MTBF.
3. Endurance…. i.e., # operations, robust to
environmental changes.
4.Stable Performance…. i.e., no degradation in CTQs.
5. ON time Startup…. i.e., ease of system startup
Reliability Audit Lab
6.
RAL
VEM Reliable Product Vision
Failure Mode
Failure Rate Resources/Costs
Identification
(Pre-Launch)
Release Release
Resources/costs
# Failure Modes
DFR
Failure Rate
50%
No DFR
No DFR
No DFR
DFR Goal DFR
5%
Time
Time Time
Identify & “eliminate” Start with lower “running Reduce overall costs by
inherent failure modes rate”, then aggressively employing DFR from the
beginning.
before launch. (Minimize “grow” reliability. (Reduce
Excursions!) Warranty Costs)
Take control of our product quality and aggressively drive to our goals
Reliability Audit Lab
8.
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VEM
NPI Process
• Field data analysis
• CTQ Identification
DP1 DP3
• Customer Metrics DP0 Specify Design DP2 Implement
Rel. Goal Setting Production / Field
• Assess Customer needs • Establish audit program
• Develop Reliability metrics • FRACAS system using ‘Clarify’
• Establish Reliability goals • Correlate field data & test results
System Model Verification
• Execute Reliability Test strategy
Design
• Construct functional block diagrams • Continue Growth Testing
• Define Reliability model • Accelerated Tests
• Apply robust design tools
• ID critical comps. & failure potential • Demonstration Testing
• DFSS tools
• Allocate reliability targets • Agency / Compliance Testing
• Generate life predictions
• Begin Growth Testing
Reliability Audit Lab
9.
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VEM
Legacy Product DFR Process . . .
Review Historical Data
• Review historical reliability & field failure data
1 • Review field RMA’s
• Review customer environments & applications
Analyze Field & In-house Endurance Test Data
• Develop product Fault Tree Analysis
2 • Identify and pareto observed failure modes
Develop Reliability Profile & Goals
• Develop P-Diagrams & System Block Diagram
• Generate Reliability Weibull plots for operational endurance
3 • Allocate reliability goals to key subsystems
• Identify reliability gaps between existing product & goals for each subsystem
Develop & Execute Reliability Growth Plan
• Determine root cause for all identified failures
4 • Redesign process or parts to address failure mode pareto
• Validate reliability improvement through accelerated life testing & field betas
Institute Reliability Validation Program
• Implement process firewalls & sensors to hold design robustness
5 • Develop and implement long-term reliability validation audit
Reliability Audit Lab
10.
RAL
VEM Design For Reliability Program Summary
Keys to DFR:
• Customer reliability expectations & needs must be fully understood
• Reliability must be viewed from a “systems engineering” perspective
• Product must be designed for the intended use environment
• Reliability must be statistically verified (or risk must be accepted)
• Field data collection is imperative (environment, usage, failures)
• Manufacturing & supplier reliability “X’s” must be actively managed
DFR needs to be part of the entire product development cycle
Reliability Audit Lab
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VEM
What do we mean by
1. Reliability
2. Failure
3. Failure Rate
4. Hazard Rate
5. MTTF / MTBF
Reliability Audit Lab
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VEM
1. Reliability R(t): The probability that an item will perform its intended
function without failure under stated conditions for a
specified period of time
2. Failure: The termination of the ability of the product to perform its
intended function
3. Failure Rate [F(t)]: The ratio of no. of failures within a sample to the
cumulative operating time.
4. Hazard Rate [h(t)]: The instantaneous probability of failure of an item
given that it has survived until that time, sometimes
called as instantaneous failure rate.
Reliability Audit Lab
14.
RAL
VEM Failure Rate Calculation Example
EXAMPLE: A sample of 1000 meters is tested for a week,
and two of them fail. (assume they fail at the end of the
week). What is the Failure Rate?
2
2 failures
Failure Rate = = failures /hour
1000 * 24 * 7 hours 168 , 000
= 1.19E-5 failures/hr
Reliability Audit Lab
15.
RAL
VEM
Probability Distribution Function (PDF):
The Probability Distribution Function (PDF) is the distribution f(t) of times to
failure. The value of f(t) is the probability of the product failing precisely at
time t.
f (t)
Probability Distribution Function
time
t
Reliability Audit Lab
16.
RAL
VEM
Common Distributions
Probability Density Variate,
Probability
Distribution Function, f(t) Range, t
−λt
f t =λe 0≤t∞
Exponential
t
− β
β t β−1 0≤t∞
f t = ⋅ ⋅e β
Weibull
ηη
2
− t− μ
1 2
2σ
f t = ⋅e
Normal −∞t ∞
σ 2π
ln t −μ 2
1
Log 2
2σ
0≤t∞
f t = ⋅e
Normal
σt 2π
Reliability Audit Lab
17.
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VEM
Cumulative Distribution Function (CDF) :
The Cumulative Distribution Function (CDF) represents the probability that the product
fails at some time prior to t. It is the integral of the PDF evaluated from 0 to t.
t
CDF =F t =∫ f t dt
0
f (t)
Probability Distribution Function
time
t1
Cumulative
Distribution Function
Reliability Audit Lab
18.
RAL
VEM
Reliability Function R(t)
The reliability of a product is the probability that it does not fail before time t. It is therefore
the complement of the CDF:
t
Typical characteristics:
R t =1−F t =1−∫ f t dt
• when t=0, R(t)=1
0
or
• when t→∞, R(t) →0
∞
R t =∫ f t dt
t
f (t)
Probability Density Function
R(t) = 1-F(t)
time
t
Reliability Audit Lab
19.
RAL
VEM
Hazard Function h(t)
The hazard function is defined as the limit of the failure rate as Δt
approaches zero.
In other words, the hazard function or the instantaneous failure rate is
obtained as
h(t) = lim [R(t) – R(t+Δt)] / [Δt * R(t)]
Δt -> 0
The hazard function or hazard rate h(t) is the conditional probability of failure
in the interval t to (t + Δt), given that there was no failure at t. It is expressed
as
h(t) = f(t) / R(t).
Reliability Audit Lab
20.
RAL
VEM
Hazard Functions
As shown the hazard rate is a function of time.
What type of function does hazard rate exhibit with time?
The general answer is the bathtub-shaped function.
The sample will experience a high failure rate at the beginning of the
operation time due to weak or substandard components, manufacturing
imperfections, design errors and installation defects. This period of
decreasing failure rate is referred to as the “infant mortality region”
This is an undesirable region for both the manufacturer and consumer
viewpoints as it causes an unnecessary repair cost for the manufacturer
and an interruption of product usage for the consumer.
The early failures can be minimized by improving the burn-in period of
systems or components before shipments are made, by improving the
manufacturing process and by improving the quality control of the products.
Reliability Audit Lab
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VEM
At the end of the early failure-rate region, the failure rate will eventually
reach a constant value. During this constant failure-rate region the failures
do not follow a predictable pattern but occur at random due to the changes
in the applied load.
The randomness of material flaws or manufacturing flaws will also lead to
failures during the constant failure rate region.
The third and final region of the failure-rate curve is the wear-out region.
The beginning of the wear out region is noticed when the failure rate starts
to increase significantly more than the constant failure rate value and the
failures are no longer attributed to randomness but are due to the age and
wear of the components.
To minimize the effect of the wear-out region, one must use periodic
preventive maintenance or consider replacement of the product.
Reliability Audit Lab
22.
Product's Hazard Rate Vs. Time : RAL
VEM
“The Bathtub Curve”
Random Failure
Infant Mortality Wear out
(Useful Life)
h(t) decreasing
h(t) increasing
Hazard Rate, h(t)
h(t) constant
Wear out
Manufacturing
Failures
Defects
Random
Failures
Time
Reliability Audit Lab
23.
RAL
VEM
Mean Time To Failures [MTTF] -
One of the measures of the system's reliability is the mean time to
failure (MTTF). It should not be confused with the mean time between
failure (MTBF). We refer to the expected time between two successive
failures as the MTTF when the system is non-repairable.
When the system is repairable we refer to it as the MTBF
Now let us consider n identical non-repairable systems and observe the
time to failure for them. Assume that the observed times to failure are
t1, t2, .........,tn. The estimated mean time to failure, MTTF is
MTTF = (1/n)Σ ti
Reliability Audit Lab
24.
Useful Life Metrics: Mean Time
RAL
VEM
Between Failures (MTBF)
Mean Time Between Failures [MTBF] - For a repairable
item, the ratio of the cumulative operating time to the
number of failures for that item.
(also Mean Cycles Between Failures, MCBF, etc.)
EXAMPLE: A motor is repaired and returned to service
six times during its life and provides 45,000
hours of service. Calculate MTBF.
Total operating time 45 ,000
MTBF = = = 7,500 hours
¿ of failures 6
MTBF or MTTF is a widely-used metric during the
Useful Life period, when the hazard rate is constant
Reliability Audit Lab
25.
RAL
VEM
The Exponential Distribution
If the hazard rate is constant over time, then the product follows the exponential
distribution. This is often used for electronic components.
ht = λ=constant
1
MTBF mean time between failures =
λ
−λt
f t =λe
−λt
F t =1−e
Rt =e−λt
1
−λ
At MTBF: R t =e−λt =e =e−1 =36. 8
λ
Appropriate tool if failure rate is known to be constant
Reliability Audit Lab
27.
RAL
VEM
Useful Life Metrics: Reliability
Reliability can be described by the single parameter exponential distribution when
the Hazard Rate, λ, is constant (i.e. the “Useful Life” portion of the bathtub curve),
=e
t
−
MTBF − FR t Where: t = Mission length
R=e (uptime or cycles
in question)
EXAMPLE: If MTBF for a motor is 7,500 hours, the probability
of operating for 30 days without failure is ...
= 0 .908 = 90 . 8
30 ∗ 24 hours
−
7500 hours
R=e
A mathematical model for reliability during Useful Life
Reliability Audit Lab
29.
RAL
VEM
Weibull Probability Distribution
• Originally proposed by the Swedish
engineer Waloddi Weibull in the early 1950’s
• Statistically represented fatigue failures
• Weibull probability density function (PDF,
distribution of values):
β
β -1 − t
t
β η
f t = e
β
η
Equation valid for minimum life = 0
t = Mission length (time, cycles, etc.)
β = Weibull Shape Parameter, “Slope”
Waloddi Weibull 1887-1979
η = Weibull Scale Parameter, “Characteristic Life”
Reliability Audit Lab
30.
RAL
VEM The Weibull Distribution
This powerful and versatile reliability function is capable of modeling
most real-life systems because the time dependency of the failure rate
can be adjusted.
β
h t = β t β -1
η
β
β−1 − t
βt η
t = β e
f
η
β
−t
η
R t =1−F t =e
Reliability Audit Lab
31.
RAL
VEM
Weibull PDF
β
β−1 − t
βt
Exponential when β = 1.0
• η
t = β e
f
Approximately normal when β = 3.44
• η
• Time dependent hazard rate
0 .0 0 5
β=0.5
0 .0 0 4
η=1000
β=3.44
0 .0 0 3
η=1000
β=1.0
0 .0 0 2
η=1000
0 .0 0 1
500 1000 1500 2000
Reliability Audit Lab
32.
RAL
VEM
β > 1: Highest failure rate later-
Weibull Hazard Function “Wear-Out”
f t f t
ht = =
1 - F t R t 0.006
β=3.44
β=0.5
[ ]
η=1000
β−1 β
η=1000
β t t
exp − 0.004
h η η
ht =
{ [ ]}
h(t)
β
β=1.0
t
1 - 1 - exp −
η=1000
η 0.002
β
t β -1
ht = β 0 500 1000 1500 2000 2500
η
Time
β < 1: Highest failure rate early-
β = 1: Constant failure rate
“Infant Mortality”
Reliability Audit Lab
33.
Weibull Reliability Function RAL
VEM
Reliability is the probability that the part survives to time t.
1
β
−t β=3.44
η
R t =1−F t =e η=1000
0.8
β=1.0
0.6
η=1000
R(t) β=0.5
0.4
η=1000
0.2
0
0 500 1000 1500 2000 2500
Time
Reliability Audit Lab
34.
RAL
VEM
Summary of Useful Definitions - Weibull Analysis
Beta (β): The slope of the Weibull CDF when printed on Weibull paper
B-life: A common way to express values of the cumulative density function - B10
refers to the time at which 10% of the parts are expected to have failed.
CDF: Cumulative Density Function expresses the time-dependent probability that a
failure occurs at some time before time t.
Eta (η): The characteristic life, or time at which 63.2% of the parts are expected to
have failed. Also expressed as the B63.2 life. This is the y-intercept of the
CDF function when plotted on Weibull paper.
PDF: Probability Density Function expresses the expected distribution of failures
over time.
Weibull plot: A plot where the x-axis is scaled as ln(time) and the y-axis is scaled as
ln(ln(1 / (1-CDF(t))). The Weibull CDF plotted on Weibull paper will be a
straight line of slope β and y intercept = ln(ln(1 / (1-CDF(0))) = η.
Reliability Audit Lab
35.
RAL
VEM Weibull Analysis
What is a Weibull Plot ?
Log-log plot of probability of
•
failure versus age for a product
or component Weibull Best Fit
Nominal “best-fit” line, plus
•
Observed
confidence intervals Failures
Easily generated, easily
•
interpreted graphical read-out
Confidence on Fit
Comparison: test results for a
•
redesigned product can be
plotted against original product
or against goals
Reliability Audit Lab
36.
Weibull Shape Parameter (β ) and RAL
VEM
Scale Parameter (η ) Defined
β is called the SLOPE
For the Weibull distribution, the slope describes the
steepness of the Weibull best-fit line (see following
slides for more details). β also has a relationship
with the trend of the hazard rate, as shown on the
“bathtub curves” on a subsequent slide.
η is called the CHARACTERISTIC LIFE
For the Weibull distribution, the characteristic life is
equal to the scale parameter, η. This is the time at
which 63.2% of the product will have failed.
Scale and Shape are the Key Weibull Parameters
Reliability Audit Lab
37.
RAL
VEM β and the Bathtub Curve
β<1 β=1
• Implies “infant mortality” • Implies failures are “random”, individually
unpredictable
• If this occurs:
Failed products “not to print” • An old part is as good as a new part (burn-
Manufacturing or assembly defects in not appropriate)
Burn-in can be helpful
• If this occurs:
• If a component survives infant mortality Failures due to external stress,
phase, likelihood of failure decreases with maintenance or human errors.
age. Possible mixture of failure modes
β>4
1<β<4
• Implies rapid wearout
• Implies mild wearout
• If this occurs, suspect:
• If this occurs
Material properties
Low cycle fatigue
Brittle materials like ceramics
Corrosion or Erosion
Scheduled replacement may be cost
• Not a bad thing if it happens after mission
effective
life has been exceeded.
Reliability Audit Lab
39.
RAL
VEM
System Reliability Evaluation
A system (or a product) is a collection of components arranged according
to a specific design in order to achieve desired functions with acceptable
performance and reliability measures.
Clearly, th type of components used, their qualities, and the design
configuration in which they are arranged have a direct effect on the
system performance an its reliability. For example, a designer may use a
smaller number of high-quality components and configure them in a such
a way to result in a highly reliable system, or a designer may use larger
number of lower-quality components and configure them differently in
order to achieve the same level of reliability.
Once the system is configured, its reliability must be evaluated and
compared with an acceptable reliability level. If it does not meet the
required level, the system should be redesigned and its reliability should
be re-evaluated.
Reliability Audit Lab
40.
RAL
VEM
Reliability Block Diagram (RBD) Technique
The first step in evaluating a system's reliability is to construct a reliability
block diagram which is a graphical representation of the components of the
system and how they are connected.
The purpose of RBD technique is to represent failure and success criteria
pictorially and to use the resulting diagram to evaluate System Reliability.
Benefits
The pictorial representation means that models are easily understood and
therefore readily checked.
Block diagrams are used to identify the relationship between elements in the
system. The overall system reliability can then be calculated from the
reliabilities of the blocks using the laws of probability.
Block diagrams can be used for the evaluation of system availability
provided that both the repair of blocks and failures are independent
events, i.e. provided the time taken to repair a block is dependent only on
the block concerned and is independent of repair to any other block
Reliability Audit Lab
41.
RAL
VEM
Elementary models
Before beginning the model construction, consideration should be given to
the best way of dividing the system into blocks. It is particularly
important that each block should be statistically independent of all
other blocks (i.e. no unit or component should be common to a number
of blocks).
The most elementary models are the following
Series
Active parallel
m-out-of-n
Standby models
Reliability Audit Lab
42.
RAL
VEM Typical RBD configurations and related formulae
Simple Series and Parallel System
Figure a shows the units A,B,C,….Z constituting a system. The interpretation can be stated as
‘any unit failing causes the system as a whole to fail’, and the system is referred to as active series system.
Under these conditions, the reliability R(s) of the system is given by
R(s) = Ra * Rb * Rc * ………Rz
O
A B C Z
I
a) Series System
Figure b shows the units X and Y that are operating in such a way that the system will survive as long as
At lest one of the unit survives. This type of system is referred to as an active parallel system.
R(s) = 1 – (1 – Rx)(1 – Ry)
X
O
I
Y
b) Parallel System
Reliability Audit Lab
43.
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VEM
A Series / Parallel System
When blocks such as X and Y themselves comprise sub-blocks in series, block diagrams of the
type are illustrated in figure c.
Rx = Ra1 * Rb1 * Rc1 *……..Rz1;
Ry = Ra2 * Rb2 * Rc2 *……..Rz2
Rs = 1 – (1 – Rx)(1 – Ry)
A1 B1 C1 Z1
O
I
A2 B2 C2 Z2
c) Series / ParallelSystem
Reliability Audit Lab
44.
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VEM
m-out-of-n units
The figure represents instances where system success is assured whenever at least m of
n identical units are in an operational state. Here m = 2, n = 3.
Rs = (Rx)^3 + 3*(Rx)^2*Fx, where Fx = 1 – Rx.
X
X 2/3
I O
X
d) m-out-of-n System
Reliability Audit Lab
46.
RAL
VEM Reliability Testing - Why?
Reliability Testing allows us to:
• Determine if a product’s design is capable of performing its intended
function for the desired period of time.
• Have confidence that our sample-based prediction will accurately
reflect the performance of the entire population.
• Provide a path to “grow” a product’s reliability by identifying weak
points in the design.
• Confirm the product’s performance in the field.
• Identify failures caused by severe applications that exceed the ratings,
and recognize opportunities for the product to safely perform under
more diverse applications.
Reliability Audit Lab
47.
RAL
VEM Reliability Testing - Measures
Reliability Testing answers questions like …
• What is my product’s Failure Rate?
• What is the expected life?
.
. ..
• Which distribution does my data follow?
..
• What does my hazard function look like?
• What failure modes are present?
• How “mature” is my product’s reliability?
These metrics and more can be obtained with the right reliability test
Reliability Audit Lab
48.
RAL
VEM
Four Major Categories of Reliability Testing
• Reliability Growth Tests (RGT)
- Normal Testing
- Accelerated Testing
• Reliability Demonstration Tests (RDT)
• Production Reliability Acceptance Tests (PRAT)
• Reliability Validation (RV)
Reliability Audit Lab
49.
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VEM
Reliability Testing - Growth Testing
Scope: To determine a product’s physical limitations, functional
capabilities and inherent failure mechanisms.
• Emphasis is on discovering & “eliminating” failure modes
• Failures are welcome. . . represent data sources
• Failures in development = less failures in field
• Used with a changing design to drive reliability growth
• Sample size is typically small
• Test Types: Normal or Accelerated Testing
• Can be very helpful early in process when done on competitor
products which are sufficiently similar to the new design.
Used early & throughout the design process
Reliability Audit Lab
50.
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VEM
Reliability Testing … Demonstration Testing
Scope: To demonstrate the product’s ability to fulfill reliability,
availability & design requirements under realistic conditions.
• Failures are no longer hoped for, because they jeopardize compliance (though
it’s still better to catch a problem before rather than after launch!)
• Management tool . . . provides means for verifying compliance
• Provide reliability measurement, typically performed on a static design
(subsequent design changes may invalidate the demonstrated reliability results)
• Sample size is typically larger, due to need for degree of confidence in results
and increased availability of samples.
Used at end of design stages to demonstrate compliance to specification
Reliability Audit Lab
51.
Reliability Testing … Production Reliability RAL
VEM
Acceptance Testing (PRAT)
Scope: To ensure that variation in materials, parts, &
processes related to move from prototypes to full production
does not affect product reliability
• Performed during full production, verifies that predictions based on
prototype results are valid in full production
• Provides feedback for continuous improvement in sourcing/manufacturing
• Sample size ranges from full(screen) to partial (audit)
• Test Types: Highly Accelerated Stress Screens/Audits (HASS/A),
Environmental Stress Screening (ESS), Burn in
Screens and Audits precipitate and detect hidden defects
Reliability Audit Lab
52.
RAL
VEM Reliability Testing … Validation
Scope: To ensure that the product is performing reliably in the
actual customer environment/application.
• “Testing results” based on actual field data sources
• Provides field feedback on the success of the design
• Helps to improve future design / redesign & prediction methods
• Requires effective data collection & corrective action process
• Sample size depends on the customer & product type
Reliability Validation tracks field data on Customer Dashboards
Reliability Audit Lab
53.
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VEM
Reliability Testing … The Path
NPI (New Products):
Set Reliability Goals Implement Production Establish service schedule
Develop Models Reliability Demonstration Keep updated dashboards
NPI Pilot Readiness
Initial Design Audit Programs Ensure Data Collection
Mature Design
Accelerated Testing Improve future design
Pilot Testing
Initial Design Implementation Post-Sales Service
Demonstration Testing Acceptance Testing Validation Testing
Growth Testing
Legacy Products:
Implement changes
Complaint generated Revise goals
Reproduce Failure
Create case Clarify Redefine models Reliability Demonstration
Reliability Verification
Product redesign Audit Programs
Field Data Verification Product Redesign Implementation
Acquisition Growth Testing Demonstration Testing Acceptance Testing
Validation Testing
Reliability Tests are critical at all stages!
Reliability Audit Lab
55.
RAL
VEM Accelerated Testing
Scope : Accelerated testing allows designers to make predictions about the
life of a product by developing a model that correlates reliability under
accelerated conditions to reliability under normal conditions.
Model:
BASIC CONCEPT The model is how we extrapolate back
to normal stress levels.
Time to Failure
.
.
.
. Common Models:
.
. • Arrhenius: Thermal
• Inverse Power Law: Non-Thermal
Stress
}
}
• Eyring: Combined
To predict here, we test here
(Elevated stress level)
(Normal stress level)
Results @ high stress + stress-life relationship = Results @ normal stress
Reliability Audit Lab
56.
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VEM
Accelerated Testing
Key steps in planning an accelerated test:
• Choose a stress to elevate: requires an understanding of the anticipated
failure mechanism(s) - must be relevant (temp. & vibration usually apply)
• Determine the accelerating model: requires knowledge of the nature of
the acceleration of this failure mechanism, as a function of the accelerating
stress.
• Select elevated stress levels: requires a previous study of the product’s
operating & destructive limits to ensure that the elevated stress level does
not introduce new failure modes which would not occur at normal
operating stress levels.
Applicability of technique depends on careful planning and execution
Reliability Audit Lab
57.
RAL
VEM
Parametric Reliability Models
One of the most important factors that influence the design process of a
product or a system is the reliability values of its components.
In order to estimate the reliability of the individual components or the entire
system, we may follow one or more of the following approaches.
Historical Data
➢
➢Operational Life Testing
➢Burn-In Testing
➢Accelerated Life Testing
Reliability Audit Lab
58.
RAL
VEM
Approach 1 : Historical Data
The failure data for the components can be found in data banks such as
GIDEP (Government-Industry Data Exchange Program),
➢
MIL-HDBK-217 (which includes failure data for components as well as
➢
procedures for reliability prediction),
AT&T Reliability Manual and
➢
Bell Communications Research Reliability Manual.
➢
In such data banks and manuals, the failure data are collected from
different manufacturers and presented with a set of multiplying factors
that relate to different manufacturer's quality levels and environmental
conditions
Reliability Audit Lab
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