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Copyright © 2009, SAS Institute Inc. All rights reserved.Copyright © 2009, SAS Institute Inc. All rights reserved.
Exploring Reliability with JMP: Degradation AnalysisDavid C. Trindade, Ph.D.March 2010
Copyright © 2009, SAS Institute Inc. All rights reserved.
Topics
Reliability Concepts and Terminology
Life Distribution Fitting
Competing Cause Analysis
Accelerated Life Testing
Recurrence Analysis
Degradation Studies
Copyright © 2009, SAS Institute Inc. All rights reserved.
Reliability Analysis Without Failures?Analysis is possible when there is a measurableproduct parameter that is degrading over timetowards a level that is defined to be a “failure” level.
In addition to the model for the life distribution and the model for the acceleration factor, we must add a third model for the measurable parameter degradation in time.
The degradation model should involve a function of the measurable parameter that is changing linearly with time (or with some function of time).
Copyright © 2009, SAS Institute Inc. All rights reserved.
Parametric Degradation Modeling
For each test unit at each readout, we can plot the degradation of the actual parameter value in time.
For a simple linear degradation model, the extrapolated time to failure for each unit i can be estimated by dividing the specified distance to failure D by the rate of degradation Ri.
Repeat this procedure for every unit in every stress cell. The derived failure times represent the estimated life distribution for each cell.
Copyright © 2009, SAS Institute Inc. All rights reserved.
Linear Degradation Model
Time
Mea
sure
men
t
Failure Limit
Tr1 Tr2 Tr3Tr0t1 t2 t3 t4 t5
Five unitsFour readouts Specified failure limitLinear degradation modelFive derived failure times tiform life distribution
( 0,1,2,3)iTr i =
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Degradation ExampleA resistor used in a power supply is known to drift linearly over time,
degrading eventually to failure. Higher temperatures produce faster degradation. At a 30% change (failure limit), the power supply can no longer operate.
It is believed that failures follow a lognormal distribution and that an Arrhenius temperature acceleration model applies.
Two stress cells, each with ten resistors, are run at 105oC and 125oC. Percent change in resistance from time zero is measured for each unit at 24, 96, and 168 hours.
Let us estimate the activation energy EA and project an average failure rate over 100,000 hours of field life at use temperature of 30oC.
Copyright © 2009, SAS Institute Inc. All rights reserved.
Data for Degradation Example
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Data Table in JMP
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JMP Graph Builder Plot
Failure Level
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Least Squares Estimation of Failure Times
To estimate the time to failure for each unit, we must first estimate the rate of degradation Ri for each unit, measured by the slope of each line.
Since the change for each unit is zero at time zero, we use the formula for the least squares slope through the origin:
where xi is the readout time and yi is the percent change. Alternatively, an approximate estimate of the rate is (168 hour parameter readout value)/168.
Then, the time to 30% change is found by dividing 30 by the degradation rate for each unit.
In JMP, this estimate is found by using JMP’s formula capabilities in new columns.
2i i
ii
x yR
x= ∑
∑
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Subset of Degradation Data Table with Derived Columns
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Degradation Analysis Using Fit Life by X Platform on Subset Table
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Degradation Analysis Using Fit Life by X Platform: Plots
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Degradation Analysis Using Fit Life by X Platform: Statistics
Common Sigma
Activation Energy EA
Arrhenius Temperature Acceleration Formula
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Degradation Analysis Using Fit Life by X Platform: Profilers
CDF Estimate at 100,000 hours
Distribution Profiler Hazard Profiler
Hazard Rate Estimate at 100,000 hours
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Lessons LearnedIf the drift mechanism is understood, and a degradation parameter
can measured over time, these analysis techniques are very useful. The methods are very powerful in that valuable information can be obtained with very small sample sizes.
Three models are involved: a parametric lifetime distribution model, an acceleration model, and a time dependent degradationmodel.
Once failure times are estimated by analysis of rates of degradations, JMP Fit Life by X can provide analysis platform.
Copyright © 2009, SAS Institute Inc. All rights reserved.
Review of AR-1 Continued
• Accelerated Testing (continued)• Activation Energy• Eyring Models• Determining Model Parameters• Matrix Reliability Studies and Example• Planning Guidelines• Degradation Modeling• Sample Sizes for Accelerated Testing
• System Models• Series System• Parallel System• Analysis of Complex Systems• Standby Redundancy
• Defective Subpopulations