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Copyr ight ยฉ 2015, SAS Ins t i tu te Inc . A l l r igh ts reserved.
RELIABILITY ANALYSIS USING JMP
ยฎ
Peng Liu
Leo Wright
Michael Crotty
Copyr ight ยฉ 2017 SAS Ins t i tu te Inc . A l l r igh ts reserved.
JMP FOR THE NON-
REPAIRABLE
โข Life Distribution
โข Survival
โข Reliability Forecast
โข Fit Life by X
โข Parametric Survival
โข Cumulative Damage
โข Degradation
โข Test Plan (DOE)
โข Demonstration Plan (DOE)
โข ALT Design (DOE)
โข Reliability Block Diagram
Life Distribution
Warranty
Time-to-failure
data and design
ALT data
and design
Degradation
data and design
System Reliability
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JMP FOR THE
REPAIRABLE
โข Recurrence Analysis
โข Reliability Growth
โข Repairable Systems Simulation
Life Distribution
Poisson Process
Reliability Block Diagram
Event Action Sub-diagram
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THIS PRESENTATION
โข Life Distribution
โข Reliability Forecast
โข Repairable Systems Simulation
โข Degradation
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LIFE DISTRIBUTION
โข Purpose of the Analysis:
โข Predict probabilities, percentiles, etc.
โข Design Goal of the Software :
โข Fit distributions
โข Compare models
โข Calculate predictions
โข Data: Regular data, Censored data, Competing cause
โข Distributions:
โข Regular: Weibull, Lognormal, Normal, Logistic, etc.
โข Exotic: Zero inflated, Threshold, Defective subpopulation, Mixture, Latent Cause
โข Method: Maximum Likelihood, Bayesian, Weibayes
โข Intervals: Wald Intervals, Likelihood Intervals
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CENSORED DATALIFE DISTRIBUTION
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FIND A GOOD FIT (FIT)LIFE DISTRIBUTION
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FIND A GOOD FIT (COMPARE & SELECT)LIFE DISTRIBUTION
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PREDICTLIFE DISTRIBUTION
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STATISTICAL DETAILSLIFE DISTRIBUTION
Methods:
โข Maximum Likelihood (default)
โข Bayesian (available for regular distributions)
โข Weibayes (when there are no failures; available in Weibull reports)
Interval Types:
โข Wald (when there are sufficient failures)
โข Likelihood (otherwise)
Note: Intervals for parameter estimates and intervals for other predictions.
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EXAMPLELIFE DISTRIBUTION
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RELIABILITY
FORECAST
โข Purpose of the Analysis:
โข Predict failure counts in the future: ๐๐ก = ฯ๐๐ก,๐
โข Make a statement about the uncertainty in the prediction: (๐๐ก, ๐๐ก)
โข Design Goal of the Software:
โข Explore raw data, by batch, group, and time.
โข Fit life distributions and compare
โข Arrange risk sets, produce forecast
โข Data:
โข Nevada format, Dates format, Time-to-Event format
โข Forecasting Types: Incremental; Cumulative
โข Forecasting Intervals: Plug-in intervals; Prediction intervals
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RELIABILITY
FORECASTING
Sold
Quanti
ty
Sold
Month 8/09 9/09 10/09 11/09 12/09 1/10 2/10
2550 7/09 11 13 25 24 33 18 55
2600 8/09 8 19 30 30 29 29
2650 9/09 14 18 25 26 27
2700 10/09 13 17 34 33
2750 11/09 12 21 29
2800 12/09 6 16
2850 1/10 17
๐๐ก =
๐๐๐ก๐โ
๐batch, ๐ก
At Risk
2371
2455
2540
2603
2688
2778
2833
3/10 4/10 โฆ
๐1,1 ๐1,2
๐2,1 ๐2,2
๐3,1 ๐3,2
๐4,1 ๐4,2
๐5,1 ๐5,2
๐6,1 ๐6,2
๐7,1 ๐7,2
? ? ? ?Incre. Total
? ?? ??? ????Cumu.Total
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UNCERTAINTIES IN
FORECASTING
Uncertainty Sources
โข Knowing outcome probability, the outcome is still random, e.g. toss a coin.
โข Probabilities might be estimated. Themselves involve uncertainties.
Solutions
โข Uncertainties can be quantified using intervals.
Option Chart
No Intervals Plugin Intervals Prediction Intervals
Incremental Counts Ignore parameter uncertainty Consider parameter uncertainty
Cumulative Counts Ignore parameter uncertainty Consider parameter uncertainty
Approximate Binomial by Poisson
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RELIABILITY
FORECASTINGEXAMPLE
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REPAIRABLE
SYSTEMS
SIMULATION
โข For studying:
โข System reliability
โข When and how to repair
โข Design Goals of the Software:
โข Expressive
โข Customizable
โข System representation: Reliability Block Diagram
โข Repair representation: Event-Action Sub-diagram
โข Simulate: Events and changes of failure probabilities
โข Collect: Events (times and consequences)
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REPAIRABLE
SYSTEMS
SIMULATION
7/2/2017 screenshot
WHAT DOES IT SIMULATE?
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REPAIRABLE
SYSTEMS
SIMULATION
EXAMPLE: COST - CHEMICAL PLANT PLANNING
Conditions: 4 identical pumps, 1 different pump
Alternative 1: Replace the old with new
Alternative 2: Add one new pump
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DEGRADATION
โข Purposes of the Analysis:
โข Find pseudo failure times
โข Study kinetics
โข Design Goals of the Software:
โข Fit built-in models automatically
โข Provide a user interface for fitting custom models
โข Method: Least squares
โข Path Types: Linear; Nonlinear
โข Built-in Models
โข Custom Models
โข Model building round trips
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DEGRADATION BUILT-IN LINEAR MODELS
โข Linear path models: ๐(๐)~๐(๐ = ๐ฝ0 + ๐ฝ1๐(๐ก), ๐)
โข ๐ and ๐ are transform functions, e.g. ๐๐, ๐๐ฅ๐, ๐ ๐๐๐ก, etc.
Intercept
๐ = Zero Common Common in
Group
Different
Slo
pe Common ๐ฝ1๐(๐ก) ๐ฝ0 + ๐ฝ1๐(๐ก) ๐ฝ0,๐ + ๐ฝ1๐(๐ก) ๐ฝ0,๐ + ๐ฝ1๐(๐ก)
Common in Group ๐ฝ1,๐๐(๐ก) ๐ฝ0 + ๐ฝ1,๐๐(๐ก) ๐ฝ0,๐ + ๐ฝ1,๐๐(๐ก) ๐ฝ0,๐ + ๐ฝ1,๐๐(๐ก)
Different ๐ฝ1,๐๐(๐ก) ๐ฝ0 + ๐ฝ1,๐๐(๐ก) ๐ฝ0,๐ + ๐ฝ1,๐๐(๐ก) ๐ฝ0,๐ + ๐ฝ1,๐๐(๐ก)Subscript ๐ denotes the group ID; ๐ denotes batch ID.
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DEGRADATION BUILT-IN NONLINEAR MODELS
โข Nonlinear path models: ๐~๐(๐ = โ ๐ก, ๐, ๐ , ๐)
โข โ is specified via a JSL parameter function.
โข Reaction Rate: ๐ = ๐ทโ(1 โ ๐โ๐ ๐ร๐ด๐น ๐๐๐๐ ร๐ก)
โข Reaction Rate Type I: ๐ = ๐ทโ๐โ๐ ๐ร๐ด๐น ๐๐๐๐ ร๐ก
โข Constant Rate: ๐ = ๐(๐ฝ0 + ๐ ๐ ร ๐ ๐ก )โข Path transformation: ๐ can be Identity, ๐๐ฅ๐, ๐๐๐โข Rate transformation: ๐ can be Arrhenius, Power, or ๐๐ฅ๐โข Time transformation ๐ can be Identity, ๐ ๐๐๐ก
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DEGRADATION EXAMPLE
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Learn more about JMPยฎ
at
jmp.com
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