From: Stan Hilliard shilliard@samplingplans.com
Date: 31 Oct 2002
Time: 11:51:33
It is possible to determine sample size based on MTBF target and Confidence Level using TP781.
Example: Target MTBF=3.8, CL=70%. You have to add two additional pieces of information in order to calculate a sample size from this specification.
First convert the existing spec to sampling nomenclature:
AQL_mtbf=3.8 years, Beta=(100-70)/100=0.30
The two new values are:
Alpha=0.05, or whatever value that you pick for the risk of rejecting when the phase MTBF is on target.
RQL_mtbf=1.0 year, or whatever value that you pick for the phase MTBF that, if true, will have a beta=0.3 chance of being accepted with the decision rule.
I don't usually post answers from TP781 here because I would rather sell the program, and also there are several options that you can run and examine. For example, you can reduce the amount of running time by using a sequential sampling plan. Having said that, the solution for this example is:
Total Cycles = 5 years, accept on 3 failures.
Note: The assumption with the exponential distribution is constant failure rate - no wear-in and no wear-out. If that assumption is reasonable in this application, you can divide-up the Total Cycles among multiple devices, like 5 devices for one year each.
The matched sequential plan would be:
TotalCycles Ac Re
1 to 1 * 3 (*=cannot accept)
2 to 3 0 4
4 to 5 1 5
6 to 6 2 5
7 to 7 4 5
Thus with a sequential sampling plan, if the product is reliable enough to give you zero failures in two years, you can stop testing and accept at that point -- having demonstrated that the product meets the specification.
Once some test results are obtained, they (TotalCycles, #failures) can be entered into TP781 to calculate confidence limits on MTBF, or for the program, on the reliability of attaining the Reliable_Life. Confidence limits can be two-sided, one-sided upper, or one-sided lower. You specify the percent confidence. Confidence limits, at your specified percent confidence can be calculated for any actual sample size, so they can be calculated and reported on an on-going basis as the project continues.