Experimental Design for Composite Overwrapped Pressure Vessel Life Prediction Anne Ryan Driscoll Department of Statistics Virginia Tech Blacksburg, VA 24061-0439 USA adriscoll@vt.edu 1
Outline Overview of NESC Project Statistical Based Testing Experimental Design for NESC Project Lessons Learned Communication Assumption Checking 2
NASA Strand and Vessel Testing NASA’s Engineering Safety Center (NESC) project to assess safety of Composite Overwrapped Pressure Vessels (COPVs) COPVs Transport gasses under high pressure Metal Liner Wrapped by a Series of Carbon Strands Research Question: Reliability of COPVs at Use Conditions for the Expected Mission Life Primary Focus on Strands Secondary Focus on Relationship to Vessels Strands Less Expensive to Test 3
NASA Strand and Vessel Testing Analyses Use Classic Weibull Model 𝛾 𝑢 𝑗 𝑢 𝑠𝑓𝑔 𝑇𝑆 𝜍 − R 𝑢 𝑗 = 𝑓 Observed Life Time: 𝑢 𝑗 𝑇𝑆 : Stress Ratio, ratio of stress level to strength scale parameter Critical Parameters: 𝜍 : Sensitivity to Stress Ratio 𝛾 : Shape parameter for time to Failure 𝑢 𝑠𝑓𝑔 : Reference time to Failure 4
NASA Strand Study Previous Strand Test Relevant strand study conducted at a national lab 57 strands at high loads for 10 years Net information learned: Strands either fail very early or Last more than 10 years Limited information based on 10 years of study! Estimates of Critical Parameters for Planning 5
NASA Strand Study The Core NASA Analytics Team: Reliability Engineers: • JPL • Langley Research Center • Glenn Research Center Statisticians: • Marshall Space Flight Center • Virginia Tech Project Engineers • White Sands Testing Facility 6
What is Statistically Based Testing? Begins with Scientific Method Sequential Learning Means Sequential Experimentation Steps in Planning Experiments 7
Scientific Method The heart of sound engineering practice is the scientific method. systematic approach for problem solving constant interplay between the concrete and abstract • Concrete: Actual engineering process • Abstract: Mathematical models An iterative induction – deduction process Conduct an investigation!
Scientific Method The proper application of the scientific method requires model building data collection data analysis data interpretation. In essence, the scientific method requires experimentation to support investigation! 9
Scientific Method 10
Scientific Method and Sequential Experimentation The scientific method is a discovery process that involves sequential learning. Consequently, the experimentation supporting the scientific method is sequential! 11
Sequential versus “One - Shot” Discovery versus Confirmation Discovery: Limited initial information Must determine • Important factors • Proper experimental levels (experimental region) • Appropriate region/model to address questions Discovery Requires a Sequential Approach! Final stage: Confirmation 12
Benefits of Sequential Approach Formal Sequential Strategy Allows Great Flexibility Different Factors and/or Levels Move to New Experimental Region Ability to Fit More Complex Models over Time Running the Experiment in Blocks Can Mitigate Disasters! 13
Steps in Planning Experiments 1. Define the Problem 2. Select Response Variables 3. Identify Sources of Variation 4. Choose the Experimental Design 5. Train the Experimenters/Conduct the Experiment 6. Analyze the Data 7. Reach Conclusions 14
Experiments Do Fail! Management Did Not Build Proper Team Team Lacked Essential Skills Proper soft skills Proper project management Team Did Not Put Enough Thought Prior to Collecting Data. 15
NASA Strand Study Team’s Initial Concept Much larger study that the original 10 year study Censor very early Reduces time Allows the larger study in a practical amount of time Proceed in phases Have detailed data records to track any problems 16
NASA Strand Study Experimental Phases Phase A – During “shake - out” of tests rigs Phase B – “Gold Standard” Experiment for Strands Phase C – “Proof” Study In Parallel: Vessel Studies (Opportunistic) 17
NASA Strand Study Phase A: Conducted During Shake-Out of Equipment Small study (although bigger than the national lab study!) Statistical goal: Determine if the parameters from the national lab study are valid as the basis for planning the larger study! Note: Phase A gave the team an opportunity to re-plan the larger experiment, if necessary! 18
NASA Strand Study Phase B: “Gold Standard” Experiment Planned time required: 1 year Used 4 “blocks” of equal numbers of strands • Allowed the team to correct for time effects • Allowed the team to mitigate problems, especially early Study assumed the “classic” Weibull model Size of the experiment assured ability to assess model 19
NASA Strand Study Phase A: Surprisingly Similar to Initial Study Phase B: Serious problem occurred with the gripping in the first block Serious conversations with possibility of replacing! Other three blocks well behaved and by themselves produced better than the planned precision for the estimates Final Decision: Drop the First Block 20
NASA Strand Study: Benefits Phase A: Opportunity to Confirm Initial Study Parameter Estimates Allowed opportunity to revise the experimental protocol if the estimates were significantly different 21
NASA Strand Study: Benefits Phase B: Allowed opportunity to model changes in time over the year. Mitigated the problem with the first block! Provided simple mechanism for replacing the first block if needed! 22
Lessons Learned Communication Language Is Critical Engineers and Statisticians Speak very Different Languages Must Use the Simplest Language that Can Address the Question of Interest Checking Model Assumptions Is Critical Under-appreciated by Engineers Fundamental to Statistical Standards of Practice Engineering Language Often Inadequate 23
Details on Lessons Learned 24
First Lesson Learned Common Language Is Important Classic Engineering Weibull Model: 𝛾 𝑢 𝑗 𝑢 𝑠𝑓𝑔 𝑇𝑆 𝜍 − R 𝑢 𝑗 = 𝑓 Standard Statistical Model Re-parameterization of the Engineering Model Uses Relationship between Weibull and the Smallest Extreme Value (SEV) Distributions If 𝑢 𝑗 is Weibull, then ln (𝑢 𝑗 ) is SEV 25
First Lesson Learned Common Definition of a Weibull Model: 𝛾 − 𝑢 𝑗 𝜃 𝑗 𝑆 𝑢 𝑗 = 𝑓 𝑢 𝑠𝑓𝑔 Let 𝜃 𝑗 = 𝑇𝑆 𝜍 Note: 𝛾 𝛾 𝑢 𝑗 − 𝑢 𝑗 𝑢 𝑠𝑓𝑔 𝑇𝑆 𝜍 − 𝜃 𝑗 R 𝑢 𝑗 = 𝑓 = 𝑓 26
First Lesson Learned The smallest extreme value reliability function: 𝑆 𝑧 𝑗 = 𝑓 −𝑓 − 𝑧−𝜈 𝜏 Assume that ln(𝑢 𝑗 ) follows SEV distribution; thus, 𝑧 𝑗 = ln(𝑢 𝑗 ) 1 Let 𝜈 = ln(𝜃) and 𝜏 = 𝛾 Therefore: 𝑧 − 𝜈 = ln 𝑢 𝑗 − ln(𝜃) = 𝛾 ln 𝑢 𝑗 − ln 𝜃 𝜏 1/𝛾 27
First Lesson Learned = 𝑓 −𝑓 −𝛾 ln 𝑢𝑗 −ln 𝜃 𝑆 𝑧 𝑗 = 𝑆 ln 𝑢 𝑗 𝛾 − 𝑢 𝑗 𝜃 = 𝑓 𝛾 𝑢 𝑗 𝑢 𝑠𝑓𝑔 𝑇𝑆 𝜍 − = 𝑓 Key Point: This smallest extreme value model is a re-parameterization of the classic model! More importantly: It Generalizes. 28
First Lesson Learned Note: 𝜃 𝑗 = 𝑢 𝑠𝑓𝑔 𝑇𝑆 𝜍 𝜈 𝑗 = ln 𝜃 𝑗 = ln 𝑢 𝑠𝑓𝑔 − 𝜍ln(𝑇𝑆) = 𝛿 0 + 𝛿 1 ln(𝑇𝑆) where 𝛿 0 = ln 𝑢 𝑠𝑓𝑔 𝛿 1 = −𝜍 29
First Lesson Learned Common Vessel/Strand Model: 𝜈 𝑗 = 𝛿 0 + 𝛿 1 ln 𝑇𝑆 𝑗 + 𝛿 2 𝑨 𝑗 𝑨 𝑗 = 1 if a vessel 𝑨 𝑗 = 0 if a strand Adjusts 𝑢 𝑠𝑓𝑔 for vessels. Communication Issue: This Generalization: Very natural for the statistician Very un-natural for the engineer 30
First Lesson Learned Critical Lesson: Communicate in the Simplest Language for the Question under Study Engineering Model: Planning All Phase A analyses Initial Phase B analyses Statistical Model More complicated situations (Combined Model) 31
Second Lesson Learned Checking Assumptions Is Critical to Proper Data Analysis Engineers and Statisticians View Assumptions Differently! Basic Assumption Checking Should Be a Requirement for the Final analysis Those Who Do Check Assumptions, Often Used Ad Hoc Techniques 32
Second Lesson Learned Applied Statisticians Prefer Standardized Residuals to Assess Assumptions “Raw” Residuals 𝑓 𝑗 = 𝑧 𝑗 − 𝑧 𝑗 = 𝑝𝑐𝑡𝑓𝑠𝑤𝑓𝑒 − 𝑞𝑠𝑓𝑒𝑗𝑑𝑢𝑓𝑒 Note: The units for these residuals are the same as the units of 𝑧 33
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