Calculating Reliability with Partial Test Results

Getting answers before you are finished. Why are people always so impatient? Why can't they just wait until testing is complete before they ask for answers? I suppose it is just human nature, as I have heard that question any time I have been involved in reliability testing programs. And, although we would know much more if we waited for more data to roll in, there are times that we can evaluate where our project stands on the basis of partial test results. Think about it. You have probably noticed that in medical trials sometimes (rarely) just a little while into a multi-year investigation into the effectiveness of some drug, medical procedure, or device the trial is halted. That is because enough statistics have been collected to determine that the drug or procedure is harmful or extremely beneficial. Those are remarkable results to come so early. Researchers spend a large quantity of effort to ensure that the trials they design include the right amount of people and the right length of time to determine an answer. Ethics demand that experiments are not carried out on too many individuals over too long a period of time. So, what this tells us is that partial statistics from an ongoing test may be able to provide us with important information.

Let me describe the ideal situation in which you may have to provide an answer on partial test results. Many situations may provide even less data making the provision of any answer extremely tenuous at best based on your credibility as a reliability analyst. Let's say we are testing a population of units (20) in an accelerated life test. At the equivalent life of 27 cycles out of 100, 6 unit of our total of 20 have failed. From our previous testing we are expecting a beta weibull shape factor of approximately 2.4, and our time to failure data plotted on the exponential graph is consistent with that (see this page for an example). This factor will be a source of uncertainty until the test is completed. And, of course, we are assuming that our test is properly designed. [ad name="Adsense Small Horz Banner"] Now, using standard six sigma techniques (at least the basic ones), our data doesn't add up to much. No single unit has completed the test successfully, and so we will have little to say about whether or not any unit can even survive the duration of the test. But, we can fit our data to a weibull distribution curve given our percent failed values at a given point in time and our assumed beta value. Again, this will not exactly match what we calculate in the end, but it may provide useful information at this intermediate stage.

Using the free weibull calculator available on this site, I provide my input values and review the results. This is an excellent opportunity to test sensitivity of the results to your inputs, as our information is uncertain at this stage. Varying the inputs by 10% to 15% and quoting the preliminary results as a range of values based on that variance can provide more confidence that you have at least identified the region of the likely end values. The image below shows the results obtained from the calculator.Weibull Reliability Calculator Results for Partial Test with 30% failed at 27% Life Complete and a Beta of 2.4

As you can see, our results indicate that 99.97% of our units would be failed prior to 100 cycles, with a mean time between failures of about 42 cycles. That is not a good situation. We would be advised now to halt the test and improve our design, even though 70% of our test units are operating perfectly. In this case, we do have sufficient data at this stage of the process to make conclusions. If we continued the test, it is true, we would be able to make even more conclusions and perform more analysis, but why go on when we know the end of the story.

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