Engineers are developing a new type of insulation. They want to determine the sample sizes necessary to estimate the 10th percentile when the distance from the lower bound to the estimate is within 100, 200, or 300 hours. The engineers will perform reliability tests on small specimens for 1000 hours. They use the following information for the test plan:

- Approximately 12% of the specimens are expected to fail in the first 500 hours of the test.
- Approximately 20% of the specimens are expected to fail by the end of 1000 hours.
- The failure times for the insulation follow a Weibull distribution.

- Choose .
- Under Parameter to be Estimated, select Percentile for percent, and enter
`10`. - From Precisions as distances from bound of CI to estimate, select Lower bound, and enter
`100 200 300`. - From Assumed distribution, select Weibull.
- In the upper Percentile box, enter
`500`. In the upper Percent box, enter`12`. - In the lower Percentile box, enter
`1000`. In the lower Percent box, enter`20`. - Click Right Cens. In Time censor at, enter
`1000`. - Click OK in each dialog box.

To calculate the sample sizes, Minitab uses a Weibull distribution with a scale of 6464.18 and a shape of 0.8037. With a censoring time of 1000 hours and a target confidence level of 95% for a one-sided confidence interval, the calculated sample sizes for each precision value are as follows:

- 354 units must be tested to estimate a lower bound for the 10th percentile within 100 hours.
- 61 units must be tested to estimate a lower bound for the 10th percentile within 200 hours.
- 15 units must be tested to estimate a lower bound for the 10th percentile within 300 hours.

Because each sample size is rounded to the nearest integer value, the actual confidence levels are slightly higher than the target confidence level of 95%.