 Example 3
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Life Data Analysis

Given the data in the file "Demo2.dat",

A. Does the product represented in the data meet a requirement of 99% reliability with 80% confidence at time = 40?

B. At what time does the product meet the requirement of 99% reliability with 80% confidence?

### Solution

1. Open the file using the file open icon or the "File" menu.
2. Select "Weibull" then   "Probability Plot" from the "Parameter Estimation" menu to obtain a probability plot estimation.  Then click the "Plot" button to obtain the plot.  This plot indicates that the Weibull distribution is a good model for the population.
3. Since maximum likelihood estimation is more accurate than probability plotting, MLE will be used for all calculations since the goodness-of-fit has be verified using probability plotting.  To estimate the parameters of the Weibull distribution using maximum likelihood estimation select "Weibull" and "Maximum Likelihood (MLE)" from the "Parameter Estimation" menu.
4. Select "Weibull" from the "Predictions" menu.  Change the confidence level from 90% to 80% in the "Confidence Level" frame at the upper left hand of the screen.   The confidence level being used is shown in the title bar of the spreadsheet at the bottom of the screen.  Click the spreadsheet in the first row under the "Reliability" column and enter 0.99.  After entering 0.99 press the down cursor or press the "Enter" key.  The lower confidence limit for reliability at reliability = 0.99 is 34.41.  The product does not demonstrate 99% reliability with 80% confidence at time = 40. The product does demonstrate 99% reliability with 80% confidence at time = 34.41.
5. If the product lower 80% confidence limit for the time to fail when reliability = 0.99 is 34.41, then the lower 80% confidence limit for reliability at time = 34.41 should be 0.99.  To verify this enter 34.41 in the second row of the spreadsheet under the column titled "Time" and press the "enter" key.  The resulting 80% lower confidence limit for reliability is 0.9858.  The values do not agree because when the sample size is small the confidence limits are approximate.  If time = 31.9 is entered the lower 80% confidence interval for reliability is 0.99.  It is recommended to enter time and compute reliability since this is the more conservative method.