A product being designed will have a failure-free warranty requirement of 1 year and the Engineers are planning a series of tests to estimate our warranty exposure.
Based on the binomial confidence interval analysis procedure described in section 7.2.4.1 of the NIST/SEMATECH e-Handbook of Statistical Methods I have computed the following in advance of the test. I used the exact intervals for small numbers of failures.
- If out of a random sample of 20 units, 4 units fail the 1 year warranty simulation test, I believe we can say that we are 90% confident that the population defect rate will lie between 7.1% and 40.1%
- If out of a random sample of 20 units, 1 unit fails the 1 year warranty simulation test, I believe we can say that we are 90% confident that the population defect rate will lie between 0.26% and 21.6%
- If out of a random sample of 20 units, 0 units fail the 1 year warranty simulation test, I believe we can say that we are 90% confident that the population defect rate will be 13.9% or less.
- If out of a random sample of 1 unit, zero units fail the 1 year warranty simulation test, I believe we can say that we are 90% confident that the population defect rate will be 95% or less.
Now assuming no failure occurs at the 1 year point in the test(s), continuing the test(s) beyond the 1 year warranty period with a some corresponding benefit in confidence would be desirable as the test units are costly to build. Can the above analysis procedure be extended to answer the following questions when the simulation test time exceeds the actual warranty period?
At the 90% confidence level, what are the upper and lower limits of the population defect rate if a 1.5 year warranty simulation test is run on 1 unit and that unit does not fail?
At the 90% confidence level, what are the limits of the population defect rate if 2 units are warranty simulated. One unit fails at 1.5 years and the other fails at 4 years?
Can Monte Carlo be used here to help answer/validate these questions?
Many thanks for any guidance.