An EXCEL Add-In for Comparing Two Exponential Distributions

Slides:

Advertisements

Similar presentations

A General EXCEL Solution for LTPD Type Sampling Plans

Advertisements

Copyright 2004 David J. Lilja1 Comparing Two Alternatives Use confidence intervals for Before-and-after comparisons Noncorresponding measurements.

Reliability Engineering (Rekayasa Keandalan)

MODULE 2: WARRANTY COST ANALYSIS Professor D.N.P. Murthy The University of Queensland Brisbane, Australia.

1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 7.5 Estimation of a Population Variance This section presents methods.

Chapter 10 Comparisons Involving Means Part A Estimation of the Difference between the Means of Two Populations: Independent Samples Hypothesis Tests about.

1 SANS Technology Institute - Candidate for Master of Science Degree 1 A Preamble into Aligning Systems Engineering and Information Security Risk Dr. Craig.

5/18/2015CPE 731, 4-Principles 1 Define and quantify dependability (1/3) How decide when a system is operating properly? Infrastructure providers now offer.

Reliability 1. Probability a product will perform as promoted for a given time period under given conditions Functional Failure: does not operate as designed.

Jump to first page STATISTICAL INFERENCE Statistical Inference uses sample data and statistical procedures to: n Estimate population parameters; or n Test.

Getting results. Session summary and analysis The PRS software provides a set of tools to review and analyze classroom sessions With these tools, you.

Confidence Intervals for  With  Unknown

1 Doing Statistics for Business Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sandifer Chapter 7 Sampling.

Statistics 101 Class 9. Overview Last class Last class Our FAVORATE 3 distributions Our FAVORATE 3 distributions The one sample Z-test The one sample.

1 Fundamentals of Reliability Engineering and Applications Dr. E. A. Elsayed Department of Industrial and Systems Engineering Rutgers University

Comparing Means.  Comparing two means is not very different from comparing two proportions.  This time the parameter of interest is the difference between.

Statistical Methods in Reliability Diesel Generator Fan Failure Data Jesse Lesperance Spring 2008.

1 Sampling and Sampling Distributions Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS.

HSRP 734: Advanced Statistical Methods July 10, 2008.

On Model Validation Techniques Alex Karagrigoriou University of Cyprus "Quality - Theory and Practice”, ORT Braude College of Engineering, Karmiel, May.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 24 Comparing Means.

Integrated circuit failure times in hours during stress test David Swanick DSES-6070 HV5 Statistical Methods for Reliability Engineering Summer 2008 Professor.

1 SMU EMIS 7364 NTU TO-570-N Inferences About Process Quality Updated: 2/3/04 Statistical Quality Control Dr. Jerrell T. Stracener, SAE Fellow.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 8.2.

AP Statistics: ANOVA Section 2

Guide to Using Minitab 14 For Basic Statistical Applications To Accompany Business Statistics: A Decision Making Approach, 8th Ed. Chapter 8: Estimating.

HSRP 734: Advanced Statistical Methods July 17, 2008.

Lecture 8 Simple Linear Regression (cont.). Section Objectives: Statistical model for linear regression Data for simple linear regression Estimation.

Normal Distribution.

4s-1 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights.

STA 2023 Module 11 Inferences for Two Population Means.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 12.3.

Reliability Failure rates Reliability

4/25/2017 Reliability Chapter Ten Reliability Reliability.

1 In Microsoft Office 2007, click on the Windows button and select the Excel Options button on the lower right From Excel Options, select Trust Center.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.2.

Class 5 Estimating  Confidence Intervals. Estimation of  Imagine that we do not know what  is, so we would like to estimate it. In order to get a point.

Confidence Intervals for a Population Proportion Excel.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 8.3.

Chapter 8 Estimation ©. Estimator and Estimate estimator estimate An estimator of a population parameter is a random variable that depends on the sample.

Chapter 14 Single-Population Estimation. Population Statistics Population Statistics:  , usually unknown Using Sample Statistics to estimate population.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide

4s-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

EMIS 7300 SYSTEMS ANALYSIS METHODS FALL 2005

Using and Finding “Student’s t”

EXCEL: Multiple Regression

Inference about Two Means - Independent Samples

Two-Sample Hypothesis Testing

Copyright (c) 2005 John Wiley & Sons, Inc.

Chapter 23 Comparing Means.

Software Reliability PPT BY:Dr. R. Mall 7/5/2018.

Microsoft Official Academic Course, Microsoft Excel Core 2016

Chapter 8: Inference for Proportions

Software Test Termination

Counting Statistics and Error Prediction

Bootstrap Confidence Intervals using Percentiles

CONCEPTS OF ESTIMATION

Reliability Failure rates Reliability

CHAPTER 22: Inference about a Population Proportion

Statistical Process Control

T305: Digital Communications

Psych 231: Research Methods in Psychology

Chapter 24 Comparing Means Copyright © 2009 Pearson Education, Inc.

AP Statistics Chapter 12 Notes.

Counting Statistics and Error Prediction

Counting Statistics and Error Prediction

RELIABILITY THEORY Presented By S.ITHAYA EZHIL MANNA Assistant Professor In Mathematics St.Joseph’s College Trichy-2.

Microsoft Official Academic Course, Microsoft Excel Core 2016

Presentation transcript:

An EXCEL Add-In for Comparing Two Exponential Distributions David C. Trindade, Sun Microsystems, Inc. David Meade, AMD, Inc. 2000 Joint Statistical Meetings, Indianapolis

Reliability Analysis Problem Exponentially distributed times to failure Want to compare two MTTFs (non-repairable components) or MTBFs (repairable systems) Typically censored data (Time or Count censoring)

Statement of Problem Two exponentially distributed data sets of count censored data Let Ti be the total time on test, i = 1,2 The mean time to failure (MTTF) estimate is

Distributions of Statistics Ti has a distribution given by The ratio has an F-distribution with (2r1,2r2) degrees of freedom

Procedure Set up two-sided 100g% confidence interval for the ratio Confidence limits are If interval excludes 1, then q1 and q2 differ statistically at the specified significance level

Example (Count Censored) Two exponentially distributed data sets Ratio ( ) 1.43 95% CI: LCL 0.76 UCL 2.80 Interval includes 1. Not significantly different.

Time Censored Data The ratio has an F-distribution with (2r1+1,2r2+1) degrees of freedom.

Procedure Set up two-sided 100g% confidence interval for the ratio Confidence limits are If interval excludes 1, then q1 and q2 differ statistically at the specified significance level

Example (Time Censored) Two exponentially distributed data sets Ratio ( ) 2.18 95% CI: LCL 1.03 UCL 5.10 Interval excludes 1. Significantly different.

EXCEL Add-In This visual basic add-in makes the comparison of exponential distributions a snap!

Software Example Simply Execute Our User-friendly Macro By Using the Pull Down Menu Provided.

Software Example Cont. Select the Censoring Type. Fill In The MTBF and Number of Failures for Each Distribution, as shown below.

Software Example Cont. Click the “OK” Button, and Let the Software Do the Rest. We Do All of the Calculations For You!

Summary Simple procedures provided to compare two exponential distributions Excel add-in availability at www.trindade.com/mttf.htm

References Bain, L.J. and Englehardt, M. (1991) Statistical Analysis of Reliability and Life-Testing Models, 2nd Ed., Marcel Dekker, New York Lee, E. T. (1992) Statistical Methods for Survival Data Analysis, 2nd Ed., John Wiley and Sons, Inc., New York Nelson, W. (1982) Applied Life Data Analysis, John Wiley and Sons, New York Lawless, J.F. (1982) Statistical Models & Methods for Lifetime Data, John Wiley and Sons, New York