Exponential Chi-Squared Reliability Demonstration Test

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Exponential Chi-Squared Reliability Demonstration Test

This example validates the results for an exponential chi-squared reliability demonstration test design in Weibull++.

Reference Case

The data set is from Example 14.3 on page 362 in the book Practical Reliability Engineering by O’Connor and Kleyner, Wiley, 2012.


A component was tested for a total of 2,000 hours, and three failures were observed. The test was time-truncated. Assuming a constant failure rate, what is the demonstrated 90% lower confidence limit on reliability at 100 operating hours?


The book shows that the demonstrated MTBF is 299.36, and the demonstrated reliability is 71.6%.

Results in Weibull++

For the MTBF the result is 299.36 hours, as shown next.

Exponential RDT MTBF.png

For reliability, the result is 71.6%, as shown next.

Exponential RDT.png

Both results show that 2,000 tests are needed to demonstrate the required reliability of 71.6% or MTBF of 299.36.