POD Tutorial Part I I Review of ahat versus a Strategies
|
|
- Ethelbert Whitehead
- 6 years ago
- Views:
Transcription
1 POD Tutorial Part I I Review of ahat versus a Strategies William Q. Meeker wqmeeker@iastate.edu Center for Nondestructive Evaluation Department of Statistics Iowa State University 1
2 Overview versus a data â Bolt hole example Distributions of signals and noise Statistical model for the signal POD from the ROC â MINITAB example â versus a regression model 2
3 ˆ versus a a Data Each inspection on a flaw gives an indication of signal strength (e.g. % full screen height on an oscilloscope) Find a statistical model to describe the distribution of signal strength as a function of flaw characteristics (especially size). We use â to denote the signal response We use a to denote the true flaw size (e.g., crack length or flaw area) 3
4 Bolt Hole aˆ versus a Data (from MIL-HDBK 1823) a aˆ a aˆ a aˆ < < < > >
5 Noise and Signal Distributions 5
6 POD with Threshold 1.3 6
7 Key References MIL-HDBK-1823 (1999), Non-Destructive Evaluation System Reliability Assessment. Meeker, W. Q. and Escobar, L. A. (1998), Statistical Methods for Reliability Data, John Wiley and Sons, New York. R. B. Thompson, W.Q. Meeker, M. Keller, J. Umbach, C.P. Chiou, Y. Wang, R. Burkel, W. Hassan, K. Smith, T. Patton, and L. Brasche, Update of Default Probability of Detection Curves for the Ultrasonic Detection of Hard-Alpha Inclusions in Titanium Alloy Billets, report in preparation for the FAA William J. Hughes Technical Center, Atlantic City, NJ 7
8 MIL-HDBK 1823 Written by a group of POD experts in the 1980 s. Became official in Covers design of studies, data analysis methods, and methods to estimate POD Hit-miss data data aˆ versus a Presently being revised by Chuck Annis 8
9 Analysis of aˆ versus a Data Simple linear regression model Some observations may be censored (in which case special software is needed--- e.g., MINITAB or JMP) 9
10 Bolthole ˆ versus a a Data Size Signal Status Left Left Exact Left Exact Exact Exact Exact Exact Exact Right Right Exact Exact 10
11 Bolthole Data 11
12 Bolthole Data with Threshold and Saturation Level 12
13 PICTORIAL REPRESENTATION OF POD DETERMINATION When distribution is normal, POD for a given flaw size a is determined by: Mean of log amplitude Standard deviation of log amplitude Decision threshold 13
14 The aˆ versus a Regression Model â is used to denote the observed signal (e.g. measured amplitude). The simple linear regression model can be expressed as: Pr(log(Signal) < y) = μ = β + β log( a) 0 1 log(y) - μ Φ σ σ is constant (does not depend on flaw size a) 14
15 Probability of Detection from the aˆ versus a Regression Model (1823 notation) POD( a) = Pr(Signal> a ) = Pr( Y > log( a )) log( ath) ( β0 + β1log( a)) = 1 Φ δ log( a) - μ =Φ (for symmetric Φ) σ Y = log(signal) = log( aˆ ) μ = ( log( ath) β0) / β1 σ = δ / β 1 th th 15
16 POD with Threshold
17 POD with Different Thresholds 17
18 Receiver Operating Characteristic (ROC) Curves 18
19 MINITAB Estimation of Censored Data Regression Model Parameters The MINITAB Regression with life data procedure will estimate the parameters β0 and β1. After the parameters have been estimated, POD (and possibly confidence intervals) could be obtained by Writing a MINITAB macro Importing results to Excel and writing a macro or procedure there Using other simple software (e.g. MATLAB). 19
20 MINITAB Worksheet with the Bolthole Data Size SignalL SignalR Status Log10Size Exact * 1.0 Left * 1.0 Left * 1.0 Left Exact Exact Exact Exact Exact Exact Exact Exact * Right * Right Exact Exact
21 Censored Data Regression Output from MINITAB Regression with Life Data: SignalL versus LogSize Response Variable Start: SignalL End: SignalR Censoring Information Count Uncensored value 16 Right censored value 2 Left censored value 3 Estimation Method: Maximum Likelihood Distribution: Lognormal Relationship with accelerating variable(s): Linear Regression Table Standard 95.0% Normal CI Predictor Coef Error Z P Lower Upper Intercept Log10Size Scale Log-Likelihood =
22 Probability of Detection from the MINITAB Computer Output Note and warning: MINITAB ver 14 and other statistical programs use base e (natrual) logs for its lognormal distribution (log of signal) POD ˆ ( a) = Pr(Signal> a ) log( a) - ˆ μ =Φ ˆ σ ˆ μ = (log( a ) ) / ˆ σ = ˆ δ / ˆ β = / = th th 22
23 POD with Threshold ˆ log( a) - ˆ μ log( a) - ( ) POD( a) =Φ ˆ =Φ σ μ = = ˆ (log 10(1.3) ) / ˆ σ = ˆ δ / ˆ β = / = POD Crack Size a 23
POD(a) = Pr (Y(a) > '1').
PROBABILITY OF DETECTION MODELING FOR ULTRASONIC TESTING Pradipta Sarkar, William Q. Meeker, R. Bruce Thompson, Timothy A. Gray Center for Nondestructive Evaluation Iowa State University Ames, IA 511 Warren
More informationQuantile POD for Hit-Miss Data
Quantile POD for Hit-Miss Data Yew-Meng Koh a and William Q. Meeker a a Center for Nondestructive Evaluation, Department of Statistics, Iowa State niversity, Ames, Iowa 50010 Abstract. Probability of detection
More informationIMPROVED METHODOLOGY FOR INSPECTION RELIABILITY ASSESSMENT FOR DETECTING SYNTHETIC HARD ALPHA INCLUSIONS IN TITANIUM
IMPROVED METHODOLOGY FOR INSPECTION RELIABILITY ASSESSMENT FOR DETECTING SYNTHETIC HARD ALPHA INCLUSIONS IN TITANIUM William Q. Meeker, Shuen-Lin Jeng, Chien-Ping Chiou, R. Bruce Thompson Center for Nondestructive
More informationAdvanced statistical methods for analysis of NDE data
Retrospective Theses and Dissertations 2006 Advanced statistical methods for analysis of NDE data Yurong Wang Iowa State University Follow this and additional works at: http://lib.dr.iastate.edu/rtd Part
More informationModel-Assisted Probability of Detection for Ultrasonic Structural Health Monitoring
4th European-American Workshop on Reliability of NDE - Th.2.A.2 Model-Assisted Probability of Detection for Ultrasonic Structural Health Monitoring Adam C. COBB and Jay FISHER, Southwest Research Institute,
More informationPractical Methods to Simplify the Probability of Detection Process
Practical Methods to Simplify the Probability of Detection Process Investigation of a Model-Assisted Approach for POD Evaluation Eric Lindgren, John Aldrin*, Jeremy Knopp, Charles Buynak, and James Malas
More informationGeneric Bolt Hole Eddy Current Testing Probability of Detection Study
Generic Bolt Hole Eddy Current Testing Probability of Detection Study NRC-IAR, DND, TRI/Austin Catalin Mandache NDE Group, Structures and Materials Performance Laboratory Outline Background Project objectives
More informationAFRL-ML-WP-TR
AFRL-ML-WP-TR-2001-4010 PROBABILITY OF DETECTION (POD) ANALYSIS FOR THE ADVANCED RETIREMENT FOR CAUSE (RFC)/ENGINE STRUCTURAL INTEGRITY PROGRAM (ENSIP) NONDESTRUCTIVE EVALUATION (NDE) SYSTEM DEVELOPMENT
More informationThe Relationship Between Confidence Intervals for Failure Probabilities and Life Time Quantiles
Statistics Preprints Statistics 2008 The Relationship Between Confidence Intervals for Failure Probabilities and Life Time Quantiles Yili Hong Iowa State University, yili_hong@hotmail.com William Q. Meeker
More informationSample Size and Number of Failure Requirements for Demonstration Tests with Log-Location-Scale Distributions and Type II Censoring
Statistics Preprints Statistics 3-2-2002 Sample Size and Number of Failure Requirements for Demonstration Tests with Log-Location-Scale Distributions and Type II Censoring Scott W. McKane 3M Pharmaceuticals
More informationChapter 9. Bootstrap Confidence Intervals. William Q. Meeker and Luis A. Escobar Iowa State University and Louisiana State University
Chapter 9 Bootstrap Confidence Intervals William Q. Meeker and Luis A. Escobar Iowa State University and Louisiana State University Copyright 1998-2008 W. Q. Meeker and L. A. Escobar. Based on the authors
More informationACCELERATED DESTRUCTIVE DEGRADATION TEST PLANNING. Presented by Luis A. Escobar Experimental Statistics LSU, Baton Rouge LA 70803
ACCELERATED DESTRUCTIVE DEGRADATION TEST PLANNING Presented by Luis A. Escobar Experimental Statistics LSU, Baton Rouge LA 70803 This is jointly work with Ying Shi and William Q. Meeker both from Iowa
More informationMahdi karbasian* & Zoubi Ibrahim
International Journal of Industrial Engineering & Production Research (010) pp. 105-110 September 010, Volume 1, Number International Journal of Industrial Engineering & Production Research ISSN: 008-4889
More informationSimultaneous Prediction Intervals for the (Log)- Location-Scale Family of Distributions
Statistics Preprints Statistics 10-2014 Simultaneous Prediction Intervals for the (Log)- Location-Scale Family of Distributions Yimeng Xie Virginia Tech Yili Hong Virginia Tech Luis A. Escobar Louisiana
More informationINFERENCE FOR REGRESSION
CHAPTER 3 INFERENCE FOR REGRESSION OVERVIEW In Chapter 5 of the textbook, we first encountered regression. The assumptions that describe the regression model we use in this chapter are the following. We
More informationMLC Quality and Reliability Data 2777 Route 20 East Cazenovia, New York, Phone: (315) Fax: (315)
MLC Quality and Reliability 777 Route East Cazenovia, New York, Phone: () 6-87 Fax: () 6-87 www.knowlescapacitors.co m Reliability General Manufacturing Process At each manufacturing step, defined process
More informationSimple Linear Regression: A Model for the Mean. Chap 7
Simple Linear Regression: A Model for the Mean Chap 7 An Intermediate Model (if the groups are defined by values of a numeric variable) Separate Means Model Means fall on a straight line function of the
More informationWeibull Reliability Analysis
Weibull Reliability Analysis = http://www.rt.cs.boeing.com/mea/stat/reliability.html Fritz Scholz (425-865-3623, 7L-22) Boeing Phantom Works Mathematics &Computing Technology Weibull Reliability Analysis
More informationStatisical method and simulation on detecting cracks in vibrothermography inspection
Graduate Theses and Dissertations Iowa State University Capstones, Theses and Dissertations 2010 Statisical method and simulation on detecting cracks in vibrothermography inspection Chunwang Gao Iowa State
More informationNotebook Tab 6 Pages 183 to ConteSolutions
Notebook Tab 6 Pages 183 to 196 When the assumed relationship best fits a straight line model (r (Pearson s correlation coefficient) is close to 1 ), this approach is known as Linear Regression Analysis.
More informationAccelerated Testing Obtaining Reliability Information Quickly
Accelerated Testing Background Accelerated Testing Obtaining Reliability Information Quickly William Q. Meeker Department of Statistics and Center for Nondestructive Evaluation Iowa State University Ames,
More informationEstimating Probability of Detection Curves Related to Eddy Current Sender Receiver Probes
5 th European-American Workshop on Reliability of NDE Lecture 9 Estimating Probability of Detection Curves Related to Eddy Current Sender Receiver Probes Anders ROSELL 1, 2, Gert PERSSON 2, Håkan WIRDELIUS
More informationDistribution Fitting (Censored Data)
Distribution Fitting (Censored Data) Summary... 1 Data Input... 2 Analysis Summary... 3 Analysis Options... 4 Goodness-of-Fit Tests... 6 Frequency Histogram... 8 Comparison of Alternative Distributions...
More informationA Tool for Evaluating Time-Varying-Stress Accelerated Life Test Plans with Log-Location- Scale Distributions
Statistics Preprints Statistics 6-2010 A Tool for Evaluating Time-Varying-Stress Accelerated Life Test Plans with Log-Location- Scale Distributions Yili Hong Virginia Tech Haiming Ma Iowa State University,
More informationBayesian Knowledge Fusion in Prognostics and Health Management A Case Study
Bayesian Knowledge Fusion in Prognostics and Health Management A Case Study Masoud Rabiei Mohammad Modarres Center for Risk and Reliability University of Maryland-College Park Ali Moahmamd-Djafari Laboratoire
More informationData: Singly right censored observations from a temperatureaccelerated
Chapter 19 Analyzing Accelerated Life Test Data William Q Meeker and Luis A Escobar Iowa State University and Louisiana State University Copyright 1998-2008 W Q Meeker and L A Escobar Based on the authors
More informationBayesian Methods for Accelerated Destructive Degradation Test Planning
Statistics Preprints Statistics 11-2010 Bayesian Methods for Accelerated Destructive Degradation Test Planning Ying Shi Iowa State University William Q. Meeker Iowa State University, wqmeeker@iastate.edu
More informationAccelerated Destructive Degradation Tests: Data, Models, and Analysis
Statistics Preprints Statistics 03 Accelerated Destructive Degradation Tests: Data, Models, and Analysis Luis A. Escobar Louisiana State University William Q. Meeker Iowa State University, wqmeeker@iastate.edu
More informationBayesian Life Test Planning for the Weibull Distribution with Given Shape Parameter
Statistics Preprints Statistics 10-8-2002 Bayesian Life Test Planning for the Weibull Distribution with Given Shape Parameter Yao Zhang Iowa State University William Q. Meeker Iowa State University, wqmeeker@iastate.edu
More informationInference for Regression Inference about the Regression Model and Using the Regression Line
Inference for Regression Inference about the Regression Model and Using the Regression Line PBS Chapter 10.1 and 10.2 2009 W.H. Freeman and Company Objectives (PBS Chapter 10.1 and 10.2) Inference about
More informationRadiation Belt Analyses: needs, data and analysis
Radiation Belt Analyses: needs, data and analysis Hugh Evans 03/09/2017 ESA UNCLASSIFIED - For Official Use Effects Requirements What are we looking for? Dose (TID/TNID) Solar cell degradation: Internal
More informationStatistical Prediction Based on Censored Life Data. Luis A. Escobar Department of Experimental Statistics Louisiana State University.
Statistical Prediction Based on Censored Life Data Overview Luis A. Escobar Department of Experimental Statistics Louisiana State University and William Q. Meeker Department of Statistics Iowa State University
More informationUnit 10: Planning Life Tests
Unit 10: Planning Life Tests Ramón V. León Notes largely based on Statistical Methods for Reliability Data by W.Q. Meeker and L. A. Escobar, Wiley, 1998 and on their class notes. 11/2/2004 Unit 10 - Stat
More informationLARGE NUMBERS OF EXPLANATORY VARIABLES. H.S. Battey. WHAO-PSI, St Louis, 9 September 2018
LARGE NUMBERS OF EXPLANATORY VARIABLES HS Battey Department of Mathematics, Imperial College London WHAO-PSI, St Louis, 9 September 2018 Regression, broadly defined Response variable Y i, eg, blood pressure,
More informationUnit 20: Planning Accelerated Life Tests
Unit 20: Planning Accelerated Life Tests Ramón V. León Notes largely based on Statistical Methods for Reliability Data by W.Q. Meeker and L. A. Escobar, Wiley, 1998 and on their class notes. 11/13/2004
More informationn =10,220 observations. Smaller samples analyzed here to illustrate sample size effect.
Chapter 7 Parametric Likelihood Fitting Concepts: Chapter 7 Parametric Likelihood Fitting Concepts: Objectives Show how to compute a likelihood for a parametric model using discrete data. Show how to compute
More informationAppendix A The Wave Energy Approach for Computing Group Velocity
Appendix A The Wave Energy Approach for Computing Group Velocity In this Appendix an energy approach is used to derive the equation for the group velocity. This derivation is different to that given in
More informationThe simple linear regression model discussed in Chapter 13 was written as
1519T_c14 03/27/2006 07:28 AM Page 614 Chapter Jose Luis Pelaez Inc/Blend Images/Getty Images, Inc./Getty Images, Inc. 14 Multiple Regression 14.1 Multiple Regression Analysis 14.2 Assumptions of the Multiple
More informationLecture 18: Simple Linear Regression
Lecture 18: Simple Linear Regression BIOS 553 Department of Biostatistics University of Michigan Fall 2004 The Correlation Coefficient: r The correlation coefficient (r) is a number that measures the strength
More informationDefect Detection Using Hidden Markov Random Fields
Electrical and Computer Engineering Publications Electrical and Computer Engineering 5 Defect Detection Using Hidden Markov Random Fields Aleksandar Dogandžić Iowa State University, ald@iastate.edu Nawanat
More informationEDDY CURRENT DETECTION OF SUBSURFACE CRACKS IN ENGINE DISK BOLTHOLES
EDDY CURRENT DETECTION OF SUBSURFACE CRACKS IN ENGINE DISK BOLTHOLES R. Palanisamy and D. O. Thompson Ames Laboratory, USDOE Iowa State University Ames, IA 50011 and G. L. Burkhardt and R. E. Beissner
More information1 Introduction to Minitab
1 Introduction to Minitab Minitab is a statistical analysis software package. The software is freely available to all students and is downloadable through the Technology Tab at my.calpoly.edu. When you
More informationChapter 17. Failure-Time Regression Analysis. William Q. Meeker and Luis A. Escobar Iowa State University and Louisiana State University
Chapter 17 Failure-Time Regression Analysis William Q. Meeker and Luis A. Escobar Iowa State University and Louisiana State University Copyright 1998-2008 W. Q. Meeker and L. A. Escobar. Based on the authors
More informationBusiness Statistics. Lecture 9: Simple Regression
Business Statistics Lecture 9: Simple Regression 1 On to Model Building! Up to now, class was about descriptive and inferential statistics Numerical and graphical summaries of data Confidence intervals
More informationLinear Regression In God we trust, all others bring data. William Edwards Deming
Linear Regression ddebarr@uw.edu 2017-01-19 In God we trust, all others bring data. William Edwards Deming Course Outline 1. Introduction to Statistical Learning 2. Linear Regression 3. Classification
More informationApplications of Reliability Demonstration Test
Applications of Reliability Demonstration Test Winson Taam Applied Statistics, NST, BR&T Jun 3, 2009 BOEING is a trademark of Boeing Management Company. EOT_RT_Sub_Template.ppt 1/6/2009 1 Outline Concept
More informationA Simulation Study on Confidence Interval Procedures of Some Mean Cumulative Function Estimators
Statistics Preprints Statistics -00 A Simulation Study on Confidence Interval Procedures of Some Mean Cumulative Function Estimators Jianying Zuo Iowa State University, jiyizu@iastate.edu William Q. Meeker
More informationSuppose we obtain a MLR equation as follows:
Psychology 8 Lecture #9 Outline Probing Interactions among Continuous Variables Suppose we carry out a MLR analysis using a model that includes an interaction term and we find the interaction effect to
More informationBayesian Life Test Planning for the Log-Location- Scale Family of Distributions
Statistics Preprints Statistics 3-14 Bayesian Life Test Planning for the Log-Location- Scale Family of Distributions Yili Hong Virginia Tech Caleb King Virginia Tech Yao Zhang Pfizer Global Research and
More informationUltrasonic Sol-Gel Arrays for Monitoring High- Temperature Corrosion
Center for Nondestructive Evaluation Conference Papers, Posters and Presentations Center for Nondestructive Evaluation 7-2016 Ultrasonic Sol-Gel Arrays for Monitoring High- Temperature Corrosion Thomas
More informationChapter Goals. To understand the methods for displaying and describing relationship among variables. Formulate Theories.
Chapter Goals To understand the methods for displaying and describing relationship among variables. Formulate Theories Interpret Results/Make Decisions Collect Data Summarize Results Chapter 7: Is There
More information3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value.
3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor 3 36.15??? Error??? Total 19 196.04 Completed table is: One-way
More informationWeibull Reliability Analysis
Weibull Reliability Analysis = http://www.rt.cs.boeing.com/mea/stat/scholz/ http://www.rt.cs.boeing.com/mea/stat/reliability.html http://www.rt.cs.boeing.com/mea/stat/scholz/weibull.html Fritz Scholz (425-865-3623,
More informationChapter 26 Multiple Regression, Logistic Regression, and Indicator Variables
Chapter 26 Multiple Regression, Logistic Regression, and Indicator Variables 26.1 S 4 /IEE Application Examples: Multiple Regression An S 4 /IEE project was created to improve the 30,000-footlevel metric
More informationTMA 4275 Lifetime Analysis June 2004 Solution
TMA 4275 Lifetime Analysis June 2004 Solution Problem 1 a) Observation of the outcome is censored, if the time of the outcome is not known exactly and only the last time when it was observed being intact,
More informationInterval Estimation for Parameters of a Bivariate Time Varying Covariate Model
Pertanika J. Sci. & Technol. 17 (2): 313 323 (2009) ISSN: 0128-7680 Universiti Putra Malaysia Press Interval Estimation for Parameters of a Bivariate Time Varying Covariate Model Jayanthi Arasan Department
More informationFormative Assignment PART A
MHF4U_2011: Advanced Functions, Grade 12, University Preparation Unit 2: Advanced Polynomial and Rational Functions Activity 2: Families of polynomial functions Formative Assignment PART A For each of
More informationNotes largely based on Statistical Methods for Reliability Data by W.Q. Meeker and L. A. Escobar, Wiley, 1998 and on their class notes.
Unit 2: Models, Censoring, and Likelihood for Failure-Time Data Notes largely based on Statistical Methods for Reliability Data by W.Q. Meeker and L. A. Escobar, Wiley, 1998 and on their class notes. Ramón
More informationCh 13 & 14 - Regression Analysis
Ch 3 & 4 - Regression Analysis Simple Regression Model I. Multiple Choice:. A simple regression is a regression model that contains a. only one independent variable b. only one dependent variable c. more
More informatione 4β e 4β + e β ˆβ =0.765
SIMPLE EXAMPLE COX-REGRESSION i Y i x i δ i 1 5 12 0 2 10 10 1 3 40 3 0 4 80 5 0 5 120 3 1 6 400 4 1 7 600 1 0 Model: z(t x) =z 0 (t) exp{βx} Partial likelihood: L(β) = e 10β e 10β + e 3β + e 5β + e 3β
More information23. Inference for regression
23. Inference for regression The Practice of Statistics in the Life Sciences Third Edition 2014 W. H. Freeman and Company Objectives (PSLS Chapter 23) Inference for regression The regression model Confidence
More informationExperimental Designs for Planning Efficient Accelerated Life Tests
Experimental Designs for Planning Efficient Accelerated Life Tests Kangwon Seo and Rong Pan School of Compu@ng, Informa@cs, and Decision Systems Engineering Arizona State University ASTR 2015, Sep 9-11,
More informationDegradation data analysis for samples under unequal operating conditions: a case study on train wheels
Degradation data analysis for samples under unequal operating conditions: a case study on train wheels Marta AFONSO FREITAS UNIVERSIDADE FEDERAL DE MINAS GERAIS DEPARTMENT OF PRODUCTION ENGINEERING marta.afreitas@gmail.com
More informationChapter 1. Modeling Basics
Chapter 1. Modeling Basics What is a model? Model equation and probability distribution Types of model effects Writing models in matrix form Summary 1 What is a statistical model? A model is a mathematical
More informationPWSCC Crack Growth Rate (CGR) Expert Panel Status Update
PWSCC Crack Growth Rate (CGR) Expert Panel Status Update Materials Reliability Program Industry-NRC Materials R&D Update Meeting June 2-4, 2015 Rockville, MD Introduction An international PWSCC Expert
More informationModel Building Chap 5 p251
Model Building Chap 5 p251 Models with one qualitative variable, 5.7 p277 Example 4 Colours : Blue, Green, Lemon Yellow and white Row Blue Green Lemon Insects trapped 1 0 0 1 45 2 0 0 1 59 3 0 0 1 48 4
More informationST505/S697R: Fall Homework 2 Solution.
ST505/S69R: Fall 2012. Homework 2 Solution. 1. 1a; problem 1.22 Below is the summary information (edited) from the regression (using R output); code at end of solution as is code and output for SAS. a)
More informationArrhenius Plot. Sample StatFolio: arrhenius.sgp
Summary The procedure is designed to plot data from an accelerated life test in which failure times have been recorded and percentiles estimated at a number of different temperatures. The percentiles P
More informationOptimal Cusum Control Chart for Censored Reliability Data with Log-logistic Distribution
CMST 21(4) 221-227 (2015) DOI:10.12921/cmst.2015.21.04.006 Optimal Cusum Control Chart for Censored Reliability Data with Log-logistic Distribution B. Sadeghpour Gildeh, M. Taghizadeh Ashkavaey Department
More informationSTA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #6
STA 8 Applied Linear Models: Regression Analysis Spring 011 Solution for Homework #6 6. a) = 11 1 31 41 51 1 3 4 5 11 1 31 41 51 β = β1 β β 3 b) = 1 1 1 1 1 11 1 31 41 51 1 3 4 5 β = β 0 β1 β 6.15 a) Stem-and-leaf
More informationDetection theory 101 ELEC-E5410 Signal Processing for Communications
Detection theory 101 ELEC-E5410 Signal Processing for Communications Binary hypothesis testing Null hypothesis H 0 : e.g. noise only Alternative hypothesis H 1 : signal + noise p(x;h 0 ) γ p(x;h 1 ) Trade-off
More informationWeek 2 Quantitative Analysis of Financial Markets Bayesian Analysis
Week 2 Quantitative Analysis of Financial Markets Bayesian Analysis Christopher Ting http://www.mysmu.edu/faculty/christophert/ Christopher Ting : christopherting@smu.edu.sg : 6828 0364 : LKCSB 5036 October
More informationConfidence Intervals, Testing and ANOVA Summary
Confidence Intervals, Testing and ANOVA Summary 1 One Sample Tests 1.1 One Sample z test: Mean (σ known) Let X 1,, X n a r.s. from N(µ, σ) or n > 30. Let The test statistic is H 0 : µ = µ 0. z = x µ 0
More informationInvestigating Models with Two or Three Categories
Ronald H. Heck and Lynn N. Tabata 1 Investigating Models with Two or Three Categories For the past few weeks we have been working with discriminant analysis. Let s now see what the same sort of model might
More informationTOWARD A VIABLE STRATEGY FOR ESTIMATING VIBROTHERMOGRAPHIC PROBABILITY OF DETECTION
TOWARD A VIABLE STRATEGY FOR ESTIMATING VIBROTHERMOGRAPHIC PROBABILITY OF DETECTION Stephen D. Holland, Christopher Uhl, Jeremy Renshaw^ ^Center for NDE and Aerospace Eng Dept, Iowa State Univ, Ames, Iowa
More informationThe Flight of the Space Shuttle Challenger
The Flight of the Space Shuttle Challenger On January 28, 1986, the space shuttle Challenger took off on the 25 th flight in NASA s space shuttle program. Less than 2 minutes into the flight, the spacecraft
More informationFULL LIKELIHOOD INFERENCES IN THE COX MODEL
October 20, 2007 FULL LIKELIHOOD INFERENCES IN THE COX MODEL BY JIAN-JIAN REN 1 AND MAI ZHOU 2 University of Central Florida and University of Kentucky Abstract We use the empirical likelihood approach
More informationSeminar on Case Studies in Operations Research (Mat )
Seminar on Case Studies in Operations Research (Mat-2.4177) Evidential Uncertainties in Reliability Assessment - Study of Non-Destructive Testing of Final Disposal Canisters VTT, Posiva Backlund, Ville-Pekka
More informationReview for Final Exam Stat 205: Statistics for the Life Sciences
Review for Final Exam Stat 205: Statistics for the Life Sciences Tim Hanson, Ph.D. University of South Carolina T. Hanson (USC) Stat 205: Statistics for the Life Sciences 1 / 20 Overview of Final Exam
More informationDepartment of Mathematics & Statistics Stat 2593 Final Examination 19 April 2001
Department of Mathematics & Statistics Stat 2593 Final Examination 19 April 2001 TIME: 3 hours. Total Marks: 60. Indicate your answers clearly. Show all work. Remember to answer as a statistician should.
More informationChapter 18. Accelerated Test Models. William Q. Meeker and Luis A. Escobar Iowa State University and Louisiana State University
Chapter 18 Accelerated Test Models William Q. Meeker and Luis A. Escobar Iowa State University and Louisiana State University Copyright 1998-2008 W. Q. Meeker and L. A. Escobar. Based on the authors text
More informationSMAM 314 Computer Assignment 5 due Nov 8,2012 Data Set 1. For each of the following data sets use Minitab to 1. Make a scatterplot.
SMAM 314 Computer Assignment 5 due Nov 8,2012 Data Set 1. For each of the following data sets use Minitab to 1. Make a scatterplot. 2. Fit the linear regression line. Regression Analysis: y versus x y
More informationIntroduction to Regression
Introduction to Regression Using Mult Lin Regression Derived variables Many alternative models Which model to choose? Model Criticism Modelling Objective Model Details Data and Residuals Assumptions 1
More informationReliability Growth in JMP 10
Reliability Growth in JMP 10 Presented at Discovery Summit 2012 September 13, 2012 Marie Gaudard and Leo Wright Purpose of Talk The goal of this talk is to provide a brief introduction to: The area of
More informationLogistic Regression Models to Integrate Actuarial and Psychological Risk Factors For predicting 5- and 10-Year Sexual and Violent Recidivism Rates
Logistic Regression Models to Integrate Actuarial and Psychological Risk Factors For predicting 5- and 10-Year Sexual and Violent Recidivism Rates WI-ATSA June 2-3, 2016 Overview Brief description of logistic
More informationLifetime prediction and confidence bounds in accelerated degradation testing for lognormal response distributions with an Arrhenius rate relationship
Scholars' Mine Doctoral Dissertations Student Research & Creative Works Spring 01 Lifetime prediction and confidence bounds in accelerated degradation testing for lognormal response distributions with
More informationENIQ TGR TECHNICAL DOCUMENT
Institute for Energy and Transport ENIQ TGR TECHNICAL DOCUMENT Influence of Sample Size and Other Factors on Hit/Miss Probability of Detection Curves ENIQ report No 47 Charles Annis & Luca Gandossi EUR
More informationCorrelation and Regression Analysis. Linear Regression and Correlation. Correlation and Linear Regression. Three Questions.
10/8/18 Correlation and Regression Analysis Correlation Analysis is the study of the relationship between variables. It is also defined as group of techniques to measure the association between two variables.
More informationSix Sigma Black Belt Study Guides
Six Sigma Black Belt Study Guides 1 www.pmtutor.org Powered by POeT Solvers Limited. Analyze Correlation and Regression Analysis 2 www.pmtutor.org Powered by POeT Solvers Limited. Variables and relationships
More informationComparisons of Approximate Confidence Interval Procedures for Type I Censored Data
Statistics Preprints Statistics 6-6-999 Comparisons of Approximate Confidence Interval Procedures for Type I Censored Data Shuen-Lin Jeng Ming-Chuan University William Q. Meeker Iowa State University,
More informationProbabilistic Quantitative Precipitation Forecasts for Tropical Cyclone Rainfall
Probabilistic Quantitative Precipitation Forecasts for Tropical Cyclone Rainfall WOO WANG CHUN HONG KONG OBSERVATORY IWTCLP-III, JEJU 10, DEC 2014 Scales of Atmospheric Systems Advection-Based Nowcasting
More informationApplied Regression Modeling
Applied Regression Modeling A Business Approach Iain Pardoe University of Oregon Charles H. Lundquist College of Business Eugene, Oregon WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS
More informationImprovement in Subsurface Fatigue Cracks under Airframes Fasteners Detection Using Improved Rotating Giant Magneto- Resistance Magnetometer Head
ECNDT 2006 - Th.4.1.2 Improvement in Subsurface Fatigue Cracks under Airframes Fasteners Detection Using Improved Rotating Giant Magneto- Resistance Magnetometer Head C. DOLABDJIAN, L. PEREZ, ENSICAEN
More informationCensored Data Analysis for Performance Data V. Bram Lillard Institute for Defense Analyses
Censored Data Analysis for Performance Data V. Bram Lillard Institute for Defense Analyses 4/20/2016-1 Power The Binomial Conundrum Testing for a binary metric requires large sample sizes Sample Size Requirements
More informationBasic Business Statistics 6 th Edition
Basic Business Statistics 6 th Edition Chapter 12 Simple Linear Regression Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of a dependent variable based
More informationMultiple Regression. Inference for Multiple Regression and A Case Study. IPS Chapters 11.1 and W.H. Freeman and Company
Multiple Regression Inference for Multiple Regression and A Case Study IPS Chapters 11.1 and 11.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 11.1 and 11.2) Multiple regression Data for multiple
More informationMULTIPLE LINEAR REGRESSION IN MINITAB
MULTIPLE LINEAR REGRESSION IN MINITAB This document shows a complicated Minitab multiple regression. It includes descriptions of the Minitab commands, and the Minitab output is heavily annotated. Comments
More informationIEC Reliability testing Compliance test plans for success ratio. Proposal for review of sequential tests
The Standard Institution of Israel Technion Israel Institute of Technology IEC-61123 Reliability testing Compliance test plans for success ratio Proposal for review of sequential tests המלצה לשיפור תקן
More informationConfidence Interval for the mean response
Week 3: Prediction and Confidence Intervals at specified x. Testing lack of fit with replicates at some x's. Inference for the correlation. Introduction to regression with several explanatory variables.
More information1; (f) H 0 : = 55 db, H 1 : < 55.
Reference: Chapter 8 of J. L. Devore s 8 th Edition By S. Maghsoodloo TESTING a STATISTICAL HYPOTHESIS A statistical hypothesis is an assumption about the frequency function(s) (i.e., pmf or pdf) of one
More information