Example of Estimation Test Plan

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 Stat > Reliability/Survival > Test Plans > Estimation.
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.

Interpret the results

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.

Note

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%.

Type I right-censored data (Single Censoring)

Estimated parameter: 10th percentile

Calculated planning estimate = 393.094

Target Confidence Level = 95%

Precision in terms of a one-sided confidence interval that gives a lower bound for the parameter.

Planning Values

Percentile values 500, 1000 for percents 12, 20

Planning Distribution

Distribution	Scale	Shape
Weibull	6464.18	0.803708

Test Plans

Censoring Time	Precision	Sample Size	Actual Confidence Level
1000	100	354	95.0011
1000	200	61	95.0892
1000	300	15	95.1695