Engineers determine that early transmission failures occurring on a track-type tractor are due to the failure of a ball bearing. The failure times for this ball bearing follow a Weibull distribution with a shape of 1.3 and scale of 1,000 hours. The engineers have 3 redesigned units available for testing and must determine how long to test each unit using a 0-failure test plan. The engineers want to show that the time until about 63.2% of the redesigned ball bearings fail exceeds 1,000 hours. In other words, the scale parameter of the Weibull failure time distribution for the redisigned ball bearings exceeds1,000.
A 0-failure test plan results in the smallest sample size and test time. However, if just one failure occurs, the demonstration test fails and you cannot conclude that you have achieved the desired reliability. For more information, go to What is the difference between an m-failure test and a 0-failure test?.
- Choose .
- From Calculate, select Testing times for each unit.
- In Sample sizes, enter 3.
- In Maximum number of failures allowed, enter 0.
- In Distribution, select Weibull. In Shape, enter 1.3.
- Under Demonstration test goal, select The true scale parameter exceeds this value. In Value, enter 1000.
- Select OK.
Interpret the results
At a 95% level of confidence, the testing time required to demonstrate that the scale of the new system exceeds 1000 hours is 998.906 hours.
The probability of passing graph shows that the probability that the 0-failure test will pass increases steadily as the ratio of improvement increases from 0 to 10. However, even at a ratio as high as 10, the test has just over an 80% chance of passing.
If the (unknown) true scale parameter were 4000, then the ratio of improvement = 4000/1000 = 4, and the test has a probability of passing of approximately 61%.
Because the likelihood of passing this demonstration test is not very high, even when the ratio of improvement is fairly high, the engineers may want to increase the sample size, or increase the maximum number of allowable failures.
Test Plans
| Failure Test | Sample Size | Testing Time |
|---|---|---|
| 0 | 3 | 998.906 |
