Exploring Reliability with JMP: Degradation Analysis...time to failure for each unit . i. can be...

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


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).


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.


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 =


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.


Data for Degradation Example


Data Table in JMP


JMP Graph Builder Plot

Failure Level


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= ∑

∑


Subset of Degradation Data Table with Derived Columns


Degradation Analysis Using Fit Life by X Platform on Subset Table


Degradation Analysis Using Fit Life by X Platform: Plots


Degradation Analysis Using Fit Life by X Platform: Statistics

Common Sigma

Activation Energy EA

Arrhenius Temperature Acceleration Formula


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


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.


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

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