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An EXCEL Add-In for Comparing Two Exponential Distributions

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Presentation on theme: "An EXCEL Add-In for Comparing Two Exponential Distributions"— Presentation transcript:

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

2 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)

3 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

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

5 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

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

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

8 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

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

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

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

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

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

14 Summary Simple procedures provided to compare two exponential distributions Excel add-in availability at

15 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

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