# Tolerance Interval of large Time Series data

I have a time series Temperature data coming from a sensor which is collected at a irregular frequency. The data size is ~100K. I have to find the Lower and Upper Bounds for this data to find the normal operating Temp. range. I am planning to follow below steps for computing these Bounds:

1. Get a Sample data(size 5K) which is normally Distributed

2. Find the Tolerance Interval of this sample size

My Question: Is this a correct approach to find the Upper and Lower Bounds of data? if not then Statistical Quality Process Control charts should be used here. I am afraid to do that as this data is collected at irregular frequency.

Would be nice to know your data in order to give you a more appropriate answer, but with no more clues, I'll do my best to give you an answer.

1. Get a sample does not guarantee that the variable, in this case, temperature, is normally Distributed it could have another distribution. The sample size would be more than enough to guarantee that the mean temperature could be model by a normal distribution.

With that said, if you want to compute the tolerance interval for the mean temperature your approach would be correct.

1. But if the variable temperature doesn't distribute as a normal distribution you would have to first:
• i) Make a histogram for the data
• ii) Fit the correct distribution to the data.
• iii) Compute the desired interval based on the previously fitted distribution.

If the distribution doesn't look normal or similar you would have to choose another approach to compute intervals. Bootstrap is a very good choice for this type of situation.

1. As your variable is temperature it's most probable that successive measurements would be correlated, so, the independence assumption would be violated and data has to be managed with Time Series techniques. You could check independence assumption by doing a correlogram.

Hope this will be useful