I have a sample of measurements representing the number of defects at a certain time point. I have 74 measurements over the past year. In addition, I have a limit of the maximum number of defects allowed for a single measurements. I have calculated a descriptive statistics, showing that the maximum is lower than the specification limit, and I have produced graphs over time (like time series). I was thinking how to add something inferential. Can I use a tolerance interval if the sample is not random, but systematic (about 6 samples a month)? Is there any other tool I can use to show that my measurements are OK? Just to clarify, I am not even close to the limit. Thank you.
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It depends. Do you think time might deterministically affect your measurements or might be correlated to a variable that does? If so, then do not lump variation due to time in with variation due to random chance by treating all measurements as one sample. If you think that variation due to random chance is time-independent, what you could do is fit a deterministic function of time to your data, then you can treat the deviations of the data from that model as a single random sample. If you think that variation due to random chance is time-dependent, then you would have to treat each group of data at each time point as different random samples and construct simultaneous intervals for every sample.
