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- 1. Essen%als for Reliability Prac%%oners Dr. Andre Kleyner ©2013 ASQ & Presenta%on Kleyner hAp://reliabilitycalendar.org/webinars/
- 2. Essentials for Reliability Practitioners and Monte Carlo Simulation Simplified ASQ Reliability Division by Dr. Andre Kleyner Delphi Electronics & Safety March 14, 2013
- 3. Today’s Webinar:Objectives:1. Review of the fundamental body of knowledge for a reliability practitioner (prompted by a discussion on LinkedIn) and sources for Reliability Education.2. Learn the basics of Monte-Carlo simulation and how to perform it with a simple Excel spreadsheet. Outline Reliability Fundamentals (briefly) Practical Reliability Engineering by Patrick O’Connor and Andre Kleyner Substantial changes from Ed.4 to Ed.5 Monte Carlo simulation unleashed 2
- 4. Definition of Reliability Reliability is the probability that the item will perform its functions without failure in specified environments for a specified mission life. 3
- 5. Reliability Science: Integration of Two Disciplines: Physics of Failure (PoF) – This term is introduced in the early 1980-s. Began with the extensive study of solder joints fatigue life. Failure – Mix of mechanical engineering, material sciences, failure analysis, chemistry, etc. Analysis of failures on individual unit level. Environment – Mostly answers the questions “What? How?” (What failed, how the failure occurred?) Focus: failure modes and failure mechanisms. Addresses individual problems. Mission Life Probabilistic Reliability (Statistical Methods) – Based on statistical methods and study of the population (of products) in respect to failures. Does not address individual problems. Probability – Covers the issues of statistical analysis of validation test data, reliability demonstration, reliability prediction, estimating R=f(t), confidence intervals, Weibull life data analysis, etc. – Typically answers the question “How much, How many, How long ” (How many samples I need to test and for how long?) 4 How do I statistically estimate R(t) and at what confidence?
- 6. Need for a Comprehensive and Practical ReliabilityTextbook (and the new edition of this book) Few universities actually have reliability engineering programs, therefore there are many more reliability engineers than reliability engineering students. To name a few: University of Maryland, University of Arizona and a few smaller programs, like University of Tennessee. Fred Schenkelberg has the full list on his website, but this list is rather short Most reliability engineers are grown as opposed to trained. Reliability science is a growing field and we, reliability practitioners need to stay updated Certain gaps in the previous edition needed to be closed, such as acceleration models, Weibull Analysis, etc. 5
- 7. Practical Reliability Engineering, Edition 5, Wiley & Sons 2012Ch 1. Introduction to Reliability EngineeringCh 2. Reliability MathematicsCh 3. Probability PlottingCh 4. Monte Carlo Simulation (new chapter)Ch 5. Load-strength InterferenceCh. 6. Reliability Prediction and ModelingCh. 7. Design for ReliabilityCh. 8. Mechanical ReliabilityCh. 9. Electronic Systems ReliabilityCh. 10. Software ReliabilityCh. 11. Design of Experiments and Analysis of VarianceCh. 12. Reliability TestingCh. 13. Analyzing Reliability Data (Test, Field, and Warranty data)Ch. 14. Reliability Demonstration (new chapter)Ch. 15. Reliability in ManufactureCh. 16. Maintainability, Maintenance and AvailabilityCh. 17. Reliability Management
- 8. Key Subject Areas Covered:Probability and StatisticsDesign for ReliabilityTestingData AnalysisHighly correlated with the Body of Knowledge forASQ CRE Certification material. Usually asecond choice after the PrimerEach chapter has an extended Questions section(for course instructors and self practice) and thereis a Solutions Manual (not open to the public) 7
- 9. Probability and Statistics Reliability Mathematics – Probability Concepts – Key statistical distribution (Normal, Exponential, Weibull, etc.) Probability Plotting – Fitting Distribution to a data – Weibull analysis Monte Carlo Simulation (brand new chapter) Load-Strength Interference (Stress-Strength) 8
- 10. Design for Reliability– More Emphasis on designing things right.You can not test reliability in, it has to be ‘designed-in’ HASS, Control Charts, Re- 6. Monitor and Control validation, Audits, Look Across, Lessons Learned, ORT Design and Process Validation 5. Validate HALT, Accelerated Test. Reliability Demonstratio Evaluation Testing, DRBTR, Reliability Growth modeling, FEA, Warranty Data Change Point Analysis Analysis, DRBFM, Reliability 4. Verify 3. Analyze prediction Lessons Learned, Reliability Block Diagrams DFMEA, Cost trade-off analysis, 2. Design Lessons Learned Probabilistic design, Cost trade-offs, Tolerance Analysis QFD, Requirements definitions, Benchmarking, Product usage analysis 1. Identify Understanding of customer requirements and specifications
- 11. Product Testing and Data Analysis Reliability Testing – Accelerated Testing – HALT and HASS – Test planning and preparation Analyzing Reliability Data – Acceleration models – Accelerated data analysis – Repairable systems – Test, Field, and Warranty data Reliability Demonstration (new chapter) – Success Testing – Test to Failure – Degradation models – Reliability Growth 10
- 12. Substantial Changes from Edition 4 to Edition 5 Weibull Analysis – moving forward from Weibull Paper References and examples of reliability software Design for Reliability – focus on doing it early Reliability Prediction: moving away from MIL-HDBK-217 to the modern arsenal of methods Reliability Demonstration chapter Lead Free Solder in Electronics (+more updates on electronics) Acceleration Models Warranty Analysis and Management Highly extended Questions section More on repairable systems and maintenance 11
- 13. FOur world is no longer DeterministicExample: Stress Analysis B A A force F is applied to a rectangular area with dimensions A×B. F Stress: S= AB F is random and A and B have tolerances, therefore S is a random variable. If stress S needs to be evaluated and compared to a target - use Monte Carlo simulation. 12
- 14. Monte Carlo Diagram x1 x2 f(x1, x2, …, xn) y xn x1, x2, …, xn – inputs f(x1, x2, …, xn) – transfer function Sampling: runs, simulations, iterations It is a fairly simple mathematical procedure, with random inputs and random Very few cases with outputs: y = f(x1, x2, …, xn), where the analytical solutions input values are sampled and the output e.g. N1+N2=N3 values (reliability, profit, stress, failure rate) are recorded and analyzed
- 15. Monte Carlo Flow Diagram Monte Carlo is a “brute force” method relying on computer power. The result is the data generated as a large number of outputs. It can be 7. Analyse the Results represented in a basic statistic format, a histogram, fitted into a probability distribution function, or any other format needed for the 6 . analysis. i=m 3. Design 2. Create a 4. Generate random 5.Run the Simulation.1. Define the Parametric inputs. Sample Deterministic Define m – Problem Model model variables model. Collect number of y = f(x1, x2, ..., xq). xi1, xi2, ..., xiq Output Data yi runs
- 16. What do you need to run a Monte Carlo simulation? The latest XK6 Cray Supercomputer PhD in Statistics Specialized, very expensive $$$ Monte Carlo simulation software A regular PC (Mac will do too). Can’t use your cell phone. Yet. At least I haven’t tried. Basic understanding of statistical distributions (both discrete and continuous) Excel spreadsheet. (You don’t even need to know macros) 15
- 17. Excel: RAND( ) = [0;1]Rectangular Distribution 1 a≤ x≤b PDF : f ( x) = (b − a) 0 otherwise Excel: = a + (b-a)*RAND( ) =RANDBETWEEN(a, b) - Integers only
- 18. Triangular Distribution 2( x − a ) (b − a )(c − a ) for a ≤ x ≤ c PDF : f ( x) = 2(b − x) (b − a )(b − c) for c ≤ x ≤ b Symmetrical: Excel: =a+(b-a)*(RAND( )+RAND( ))/2 0 otherwise
- 19. Normal Distribution µ −σ +σExcel: =NORMINV(RAND( ), µ, σ ) 18
- 20. Lognormal Distribution 50% area x Median 95%-tile 2 1 ln x − µ 1 − 2 σ f ( x) = e xσ 2π Where µ = Mean(lnx) or location parameter σ = STD(lnx) or scale parameterExcel: =LOGINV(RAND( ), µ, σ) 19
- 21. Weibull Distribution β t − η R(t ) = e The Two-Parameter Weibull Distribution β β t βt − η f (t ) = e η η Where,η = scale parameter,β = shape parameter (or slope),20 Excel: =(η(-LN(1-RAND()))^(1/β)) η β
- 22. Exponential Distribution x − λt − λx R(t ) = e f ( x ) = λe λ Excel: =(-1/λ)*LN(RAND( ))Practical Reliability Engineering Ed.5 has a table of variouspdf and also explains how you can derive Excel equationpractically for any distribution 21
- 23. random force F applied to F a rectangular area withExample dimensions A×B. B AA: mean of 2.0 cm, tolerance ±1.0 mm (Triangular distribution)B: mean of 3.0 cm tolerance of ±1.5 mm (Triangular distribution)F can be statistically described by the 2-parameter Weibull with β =2.5and η =11,300 N (no connection with failure distributions)The structure is expected to function properly while within the elasticstrain range, therefore the probability of exceeding the yield strength of 30MPa (30×106 N/m2) needs to be estimated. 22
- 24. Example F B A F Stress: S= AB A, B, F are inputs and S is a transfer function = (11, 300( − LN (1 − RAND ())) (1/ 2.5) )S= =19+(21-19)*(RAND( )+RAND( ))/2 × [28.5+(31.5-2.85)*(RAND( )+RAND( ))/2] → S1, S2, ….S2000 Check how many times Si > 30MPa Excel Example 23
- 25. Additional Considerations for Monte-Carlo Simulation The M-C simulation process is quite simple. It can be performed with Excel, but there are excellent tools available: e.g. @Risk by Palisade Convergence of the M-C process is very important. Some models may not converge or require a large number of runs Model sensitivity can be very high (response to certain inputs) Watch out for correlated inputs 24

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