Demystifying Weibull - Minitab

1 Demystifying WeibullA Practical Means to Locate Performance in the Bathtub CurveJoe Sipper9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsCopyright 2014 Raytheon Company. All rights Success is Our Mission is a registered trademark of Raytheon of Presentation Intent is foundational, discuss a focused facet of Weibull This is about plotting data and identifying phases in the bathtub curve, it s not about further Reliability analysis Why all these details if Minitab does all the work? Key discussion points distribution censoring and test of repair to the proper data structure for interpretations and the bathtub for Weibull Weibull plots to gain performance insightMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 21.

2 Weibull Distribution Plottinga)The big picture of today s presentationb)Scopec)Overview: analytical flowMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 31a1. The Big Picture: Today s Presentation There are lots of great Weibull applications to predict system life, reliability, success rates, preventive maintenance intervals, warranty structures, repair strategies, etc The same source data can be used for everything we ll discuss however the format needs to be in a format appropriate for each assessment Today s outputs can feed into some Weibull applications but that s for another day Today is about structuring failure data, analyzing it in Minitab , and making first-tier conclusions about where in the bathtub a performance fallsMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 41a2.

3 The Big Picture: Characterize Performances Understandingthe problem is often the hardest part of the problem; getting and arranging good data is a much easier for a problem that is well understood than for one that is not Determine what distribution best models performance For the most part, the analytical process is similar or identical across many scenarios but the data arrangement differs Data drives a model, and is then replaced by its model The Weibull model, which is highly flexible and often applicable, gives insight into performance phases of the bathtub curveMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 51a3. The Big Picture: Use Weibull for Systems? A lot depends on the question, , the needs of the assessment Some believe that Weibull can be used only for an individual failure mode, and multiple failure modes offset performance characteristics and muddy the analysis Others believe a system is simply a series of components System fails when one (random) component fails System time-to-failure = smallest of the component failure times This is equivalent to Weibull distribution Underlying premise to, but not explored in, today s presentation Ideally run a unique Weibull assessment for each failure mode, however the method given here addresses needs of the assessmentMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 61b1.

4 Distribution Plotting for this PresentationUltimately make a set of usable, value-added data with appropriate (System or Element)Repairable (System or Element) analyze patternsb/w failuresRepairable (Fleet)Typical characterizationSingle failure mode based on sample dataIndividualsystem based on field dataIndividualsystem based on field dataFleet basedon field dataRepair stateNewLike ?YesYesNoNoData analyzedElementfails vs. element usageSystem failures vs. system usageSystemfailures vs. system usageFleet failures vs. fleet usageData timelineOrdered usage from T=0 Ordered usage from T= = statistically independent and identically distributed Scope focuses on expectations of performance when the system or element is repaired, and the corresponding data structuresMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 71b2.

5 Repair Type and Data StructuresReplace Like New Repair Minimal Repair Brand new hardware restarts the clock Expectationis that the next failure is random (independent) because the history is reset, , the repair returned a system that was as good as new Next failure dependson current usage, , the system s age prior to the repair System Reliability is the same after the repair as it was before the repairXIT0= 0 T1T2T3T4 Tnt1t2t3t4 tnXXXX..Note the differences in cumulative timelines:XIXXXXIt1 XIt2It3 XIt4 XXIXXXItnXT0= 0 XIt1 XIt2It3 XIt4 XXIXXXItnXT0= 0 XIT0= 0 T1T2T3T4 Tnt1t2t3t4 tnXXXX..Timelines shown on this slide are in terms of each system studiedData structure: ordered usage from T0= 0 Data structure: ordered usage from T0= 0 Data structure: superimposedMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 81b3a.

6 Fleet vs System Fleet failures and fleet time can stay random over time because of the mix of old and new systems in the fleet Failures for each individual system are tracked and composed additively on a cumulative timeline Cumulative timeline combines failures from different systems onto a single timeline Individual systems each provide usage data, and clustering of events becomes evident at similar usages Failures are superimposed onto a timeline Both use Power law statistically, but treat data differentlyMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 91b3b. Fleet vs Repairable SystemsXIXXXXS ystem 1 XIXXXXS ystem 2 XIXXXXS ystem 3 IXXXXS ystem nXIXXXXXXXXXXXXXXXXXXS uperimposeXIXXXXS ystem 1 XIXXXXS ystem 2 XIXXXXS ystem 3 IXXXXS ystem nXIXXXXXXXXXXXXXXXXXXC umulative TimelineRepairable Systems Systems age in patterns, characteristics are evident when viewing clustering of superimposed failuresNOTE: In repairable systems, failures for non-repairable elements are however failures for the system or element are dependentFleet Failures become random when time modeled because the fleet is composed of systems both new and old, , assumption of independent failures is not validMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 101c.

7 Overview: Analytical Flow Censored Data ?Test and Censoring Considerations(Test) Type I: Time Censoring test time fixedRight Censored lower bound known, upper bound not fully known for all data(Test)Type(Data)SuspensionsAnalyze as Complete DataYesAnalyze as Censored Data(Test) Type II: Failure Censoring number failures fixedLeft Censored only have the upper bound, not sure of exact time of failure NoInterval Censored all fail, have ideas of times but not exact measuresMTTF or MTBF?Expectations of RepairReplaceable = New = Non-repairable(MTTF)Repairable (MTBF)Analyze as MTTFM inimalNew or Like NewSuperimpose each SystemOrdered Usage from T=0 Identical conditionsData StructureRepair StructureCumulative TimelineFleetMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 112.

8 Data Censoring and Test Typea)Complete datab)Left censored data also called Interval datac)Right censored data also called Suspended datad)Singly censored datae)Multiply censored dataf)Interval, or grouped, datag)Test Type I also called Type I Censoringh)Test Type II also called Failure CensoringMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 122a. Complete data All units run to failure, have exact usage times for each Another way to say this is that each unit has run through its entire lifetime and is characterized exactly Examples include:Sample 1 of nSample 2 of nSample 3 of nSample 4 of nSample 5 of nSample n of nUsage (Time, Cycles, Distance, etc.) Complete DataIIIIIIFailFailFailFailFailFail.. Highly structured lab testing Fully accessible field data with high failure ratesMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 132b1.

9 Left Censored data Check performance at some time, t Observe the unit(s) have failed, do not know exactly when Examples include:Sample 1 of nSample 2 of nSample 3 of nSample 4 of nSample 5 of nSample n of nUsage (Time, Cycles, Distance, etc.) Left Censored DataII]I]IFailFail, not sure of exact usageFailFailFail, not sure of exact usageFail.. Testing or field data where data is not fully accessibleMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 142b2. Interval Censored data Different from left-censored in that all intervals do not start with zero usage Check performance at some time, t Observe the units have failed, do not know exactly when Examples include:Sample 1 of nSample 2 of nSample 3 of nSample 4 of nSample 5 of nSample n of nUsage (Time, Cycles, Distance, etc.)

10 Interval Censored Data]]]]]]Fail in intervalFail in interval..[[[[[[Fail in intervalFail in intervalFail in intervalFail in interval Testing or field data where data is not always accessible Minitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 152c. Right Censored (or Suspended) data Important to include usage of survivors in timelines Check performances at some time, t Observe some units have failed, while the remaining are still operational; record all usage Examples include:Sample 1 of nSample 2 of nSample 3 of nSample 4 of nSample 5 of nSample n of nUsage (Time, Cycles, Distance, etc.) Right Censored DataIIIO perationalOperationalFailFailFailOperati onal.. Most field data, especially those checked somewhat regularly Time truncated = Type I, failure truncated = Type IIMinitab Insights 9/13/2016 This document does not contain technology or Technical Data controlled under either the International Traffic in Arms Regulations or Export Administration RegulationsSlide 162d.