Suppose I want to predict how many machine are going to fail in the next three years. The data collected are in days, so we want to predict no. of fails in next 1095 days.
All the machines (100 of them) started from, say, 1975 and until today, only 13 have failed. Now, I want to predict how many are going to fail in the next three years.
Some of the issues I encountered, in my opinion:
Ideally, we have the fixed time to run the tests on these machines, BUT in this case, we don't have the fixed time. I can assume today's date as the final date, that is, my testing time interval is [1975, Today's date]
So, I have to put all the other machines that didn't fail as Censored observation.
BUT when I do that, the data does not follow, I believe, Weibull distribution, a standard process to analyze failure times (Weibull analysis).
Do we have enough data to come up with an appropriate model? And if this is what we have to work with, how can we do that?
Can we still use Weibull analysis approach for this case, and estimate the scale and shape parameter and use it to find the expected no. of failures given by:
where a is the scale parameter and b is the shape parameter; n is the population of machines which began operating continuously at the same time t=0
Here are some of the arbitrary failure times ( I cannot share the data due to confidentiality issues):
10162, 8300, 11110, 11520, 11520, 8460, 7320, 11424, 11112, 11321, 11584, 10436, 9560
These are given in days from, say Jan 1, 1975. These are the machines that are built to last, so it is not uncommon to see these kind of minimal failure rates.