Manufacturing Environment
Today’s manufacturers face:
Reliability: The Other Dimension of Quality
William Q. Meeker
Iowa State University
• Intense global competition
• Pressure for shorter product-cycle times
Fall Technical Conference
Youden Memorial Address
• Stringent cost constraints
October 17, 2002
• Higher customer expectations for quality and reliability
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Engineering Functions that Affect Reliability
Reliability
• Define product requirements
• Condra (1993): “Reliability is quality over time”
Good quality is necessary but not sufficient!
• Product design
• Difficulty: Reliability assessed directly only after a product has been in the field for some time; reliability prediction is difficult.
• Reliability is an engineering discipline. Statistical methods are important tools for reliability engineering.
• Verify product design
• Design for product robustness
Similar, parallel steps for manufacturing process design
• Maintain quality in production
• Most statistical effort has been on methods for assessing
reliability. Much engineering effort is (correctly) focused
on reliability improvement.
Robustness: Ability (for a product or a process) to perform its intended function under a variety of operating and
environmental conditions
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Overview
Three-Sigma Quality
• Quality, variability, and reliability
• Failure modes (anticipated and unanticipated)
• Contrast between traditional reliability demonstration
and today’s need for reliability assurance
• The role of statisticians on the reliability team
• Reliability data and statistical methods
• Warranty and reliability
• A current example
• Future trends in reliability
• Comments on industrial/academic cooperation
LSL
Nominal
USL
• Concluding remarks
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Drifting Three-Sigma Quality
(Effect on Reliability)
Good and Bad Quality
<---- Good Quality
<---- Poor Quality
LSL
LSL
Nominal
Nominal
USL
USL
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Six-Sigma Quality
(Target: 3.4 Defects per Million Opportunities)
Sources of Variability (Noise)
Affecting Product Reliability
• Manufacturing (including raw materials)
• Environmental conditions
• Customer use rates
• Wear/degradation
LSL
Nominal
USL
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Unanticipated Failure Modes
Anticipated Failure Modes
Goal: To discover and eliminate failure modes as early as
possible
• Information on component reliability
• FMEA analysis in up-front design
Handbook values
Previous experience
Physical models (e.g. FEM) with some empirical model
verification.
• Robust design ideas (make product robust to external
noises)
• HALT testing
Test data and accelerated test data
• Early feedback from the field
• System reliability model
Downstream discoveries are more expensive!
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Reliability Assurance
Based on Reliability Modeling and Combining Information
Reliability Demonstration versus Reliability Assurance
Inputs:
• Example: Using minimal assumptions, to demonstrate
that reliability at time t0 hours is .99, with 95% confidence, requires testing at least 230 units for t0 hours with
zero failures. To have a 80% chance of passing the test,
requires that the true reliability be approximately .999
• Engineering knowledge
• For complicated, expensive systems, traditional reliability
demonstration is usually not practicable
• Physical experimentation
• Physical models
• Previous experience (e.g., field data)
• Factors of safety
• Reliability assurance is the alternative
Challenge: Quantify uncertainty
Approach: Responsible use of Bayesian methods (e.g. LANL
PREDICT)
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The Role of Statisticians on the Reliability Team
Structured Programs for Design for Reliability
Design for Reliability implies the use of product and process
design to eliminate problems before they occur
• Design for Six Sigma (DFSS developed at GE) has the
DMADV steps: Define, Measure, Analyze, Design, Verify
• Other company-specific reliability improvement programs.
Contrast with the traditional Build,Test,Fix,Test,Fix,... approach that uses “reliability growth modeling.”
• Contribute to the understanding and modeling of variation
• Help fill in the gaps in engineering knowledge by designing
experiments and interpreting results
• Use appropriate statistical method to make the most effective use of field and warranty data
• Develop appropriate methods for combining information
• Develop methods for quantifying uncertainty (statistical
and model)
• Develop methods (especially graphical methods) for the
effective presentation of results.
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Failure Pattern in the Bearing Cage Data
Distinguishing Features of Reliability Data
• Data are typically censored (bounds on observations).
Count
• Models for positive random variables (e.g., exponential,
lognormal, Weibull, gamma). Normal distribution not
common.
• Model parameters not of primary interest (instead, failure
rates, quantiles, probabilities).
• Extrapolation often required (e.g., have one year of data,
but want proportion failing after three years).
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288
148
124
111
106
99
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123
93
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41
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0
500
1000
1500
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Hours of Operation
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Weibull Probability Plot for Bearing Cage Data
Lognormal Probability Plot for Bearing Cage Data
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.6
Lognormal Distribution ML Fit
Weibull Distribution ML Fit
Lognormal Distribution 95% Pointwise Confidence Intervals
.5
.1
.4
.3
.05
Proportion Failing
Proportion Failing
.2
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.03
.02
.01
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.005
.003
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100
.01
.002
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.001
.0005
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.0003
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.02
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.005
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.001
.0005
.1
.05
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.0001
.00005
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Hours
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Hours
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Device-B Power Drop
Accelerated Degradation Test Results
at 150◦C, 195◦C, and 237◦C
(Use conditions 80◦C)
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Power drop in dB
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-0.8
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-1.0
-1.2
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Percent Increase in Operating Current
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Percent Increase in Operating Current
for GaAs Lasers Tested at 80◦C
(Use conditions 10◦C)
-1.4
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195 Degrees C
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Maintenance Events for a
Fleet of Earth-Moving Machines
Adhesive Bond Accelerated Degradation Test
AdhesiveBondB data
Destructive Degradation Regression Analyses
Resp:Log,Time:Square root,x:Arrhenius, Dist:Smallest Extreme Value
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Machine Number
Pounds
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50DegreesC
60DegreesC
70DegreesC
25 DegreesC
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Hours of Operation
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Warranty and Reliability
Mean Cumulative Number of Labor Hours
Mean Cumulative Cost for a Fleet of Earth-Moving
Machines
• Warranties are more related to marketing than reliability!
• In many industries, warranty costs are substantial.
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• Warranty data are messy
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• Useful information in warranty data for:
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Financial reporting
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Feedback for the next product generation
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Early warning of unanticipated problems
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Connection with laboratory testing and environmental
characterization.
Age in Hours of Operation
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NIST Cooperative Research and Development
Agreement (CRADA)
Current Example
Service Life of Organic Paints and Coatings
• Goal: Develop useful accelerated testing methods to allow the rapid screening and assessment of service life of
potential new products.
• Previous efforts in this industry have not been satisfactory
• Useful discussions at two international conferences on the
subject
• Multi-year project at National Institute of Standards and
Technology, Materials and Construction Research Division, Building and Fire Research Laboratory (Jon Martin,
Project Leader)
• Approach: Use careful experimentation and physical/chemical
theory to understand degradation mechanisms and to
build (and verify) the necessary predictive models.
• Focus on an important industrial problem.
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Scientific Plan
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Trends in the Use of Statistics in Reliability
• Careful laboratory experiments controlling UV radiation
intensity and spectrum, temperature, and humidity.
• Experimental setup based on the NIST SPHERE (Simulated Photodegradation by High Energy Radiant Exposure)
• More use of degradation data and models
• Increased use of statistical methods for producing robust
product and process designs
• More use of computer models to reduce reliance on expensive physical experimentation
• Outdoor experimental sites in four different climates, with
monitoring of UV radiation intensity and spectrum, temperature, and humidity.
• Better understanding of the product environment (e.g.
through the use of “smart chips”).
• Environmental realization, when used to drive the physical/chemical model, should produce results similar to outdoor exposure.
• More efforts to combine data from different sources and
other information (through the use of “Responsible Bayes”
methods).
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Accelerated Test Results Using Standard Censored
Data Regression
Accelerated Test Results Using Standard Censored
Data Regression
Assuming That Arrhenius Activation Energy is Known
.95
.95
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.9
.8
.8
.7
.6
.5
.4
.3
Proportion Failing
Proportion Failing
.7
.2
.1
.05
.02
.6
.5
.4
.3
.2
.1
.05
.02
.01
.005
.01
.005
.002
.002
.0005
.0005
300 Deg C
.0001
250
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175
150
100
300 Deg C
.0001
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Hours
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Academic Involvement in
Manufacturing Reliability Problems
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Facilitating Academic Involvement in
Manufacturing Reliability Problems
• Manufacturing industries have interesting, challenging,
technical problems in reliability.
• Student internships with opportunities for faculty visits
(LANL model).
• There should be more academic involvement in these
projects
• NSF GOALI (Grant Opportunities for Academic Liaison
with Industry) program
• Benefits:
• Work for free
The quality of academic research will improve with
access to real problems
High probability of impact
Cost-effective for industry
• Needs:
Academics willing to get their hands dirty (and learn
the language and science used in real problems)
Industrial sponsors willing to invest the time needed
to lead and conduct the project.
Better industry/academic relationships
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Concluding Remarks
• SPC and designed experiments have been useful for improving quality and reliability
• Statisticians have an important supporting role to play in
the reliability area
• Further improvements in reliability possible by focusing
on causes of failure
• Upstream reliability testing/analysis has important advantages
• Use downstream information (e.g. Warranty data) on
current and previous product to make upstream improvements in future product
• Problem: Importantly large savings may be difficult to
quantify to management.
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