Reliability & Life Testing Handbook, Volume 2

In sequential testing three decisions are of importance:
Decision D 1: The units have a scale parameter, ?, or characteristic life when ? = 0, which is equal to a minimum acceptable value of ? L 1 with a confidence level of (1 - ?).
Decision D 2: The units have a scale parameter, ?, which is equal to an upper limit of ? U 1with a confidence level of (1 - ?).
Decision D 3: There is insufficient information to decide whether Case 1 or Case 2 prevails, and the test has to be continued until a decision favoring either Case 1 or Case 2 is made.
The risk involved in arriving at the decision of Case 1 is ?, which is the probability that units are accepted, as a result of the sequential test, which have a characteristic life equal to or lower than ? L 1.
The risk involved in arriving at the decision of Case 2 is ?, which is the probability that units are rejected, as a result of the sequential test, which have a characteristic life equal to or greater than ? U l.
Decision D 1 is made that ? = ? L 1 when [1]
| (8.1) | |
where
| r | = | number of failures, |
| T i | = | times to failure, |
| ?* | = | Weibull distribution's shape parameter, |
and
| k | = |