DFR Fundamentals and Reliability Testing Techniques

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DFR – Fundamentals for Engineers

Reliability Audit Lab

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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


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1. Need for DFR


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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


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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


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2. DFR - Process


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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


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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


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


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3. DFR - Terminology


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What do we mean by
1. Reliability

2. Failure

3. Failure Rate

4. Hazard Rate

5. MTTF / MTBF


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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.


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


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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


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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


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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


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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

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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).


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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.


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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.


Product's Hazard Rate Vs. Time : RAL
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“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


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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


Useful Life Metrics: Mean Time
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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


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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.

ht = λ=constant
1
MTBF mean time between failures =
λ
−λt
f t =λe 
−λt
F t =1−e 
Rt =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


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The Exponential Distribution
0.0003

λ=.0003
0.0002

PDF: λ=.0002
f(t)
0.0001

λ=.0001
0 4 4 4 4 4
0 1 10 2 10 3 10 4 10 5 10

Time to Failure
1

λ=.0001
0.667

CDF: F(t)
λ=.0002
0.333

λ=.0003
0 4 4 4 4 4
0 1 10 2 10 3 10 4 10 5 10

Time

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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


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3. DFR – Weibull Plotting


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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”


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


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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


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β > 1: Highest failure rate later-
Weibull Hazard Function “Wear-Out”
f t  f t 
ht  = =
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
ht  =

{ [   ]}
h(t)
β
β=1.0
t
1 - 1 - exp −
η=1000
η 0.002

β
 t  β -1
ht  = β 0 500 1000 1500 2000 2500
η
Time
β < 1: Highest failure rate early-
β = 1: Constant failure rate
“Infant Mortality”


Weibull Reliability Function RAL
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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


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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.


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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


Weibull Shape Parameter (β ) and RAL
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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


RAL
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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.


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5. DFR – System Reliability


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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.

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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

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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


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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


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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


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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


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6. DFR – Reliability Testing


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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.


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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


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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)


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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


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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 Testing … Production Reliability RAL
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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


RAL
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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


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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!


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7. DFR – Accelerated Testing


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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


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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


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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


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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


DFR Fundamentals and Reliability Testing Techniques

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