I have sample of daily historical usage data for part numbers at a factory. There are hundreds of part numbers in my data set.

I want to use the historical usage to calculate a forecast of the next 18 months of usage such that the value has 95% probability of not exceeding the actual usage in the future 18 month period. I am using left-tailed formula using Z=1.65 so that the area to the left is 5%.

mu = x-bar (sample average) - Z * (std dev/square root (n-number of points in sample))

My question is how to convert to the 18 month estimate.

Here is some sample data for a 180 day period:

Date Usage

6/11/2020 300

6/29/2020 300

6/30/2020 400

7/6/2020 300

7/14/2020 200

7/20/2020 300

7/28/2020 300

7/31/2020 200

8/11/2020 300

8/17/2020 400

8/18/2020 200

8/20/2020 500

8/26/2020 300

9/9/2020 300

9/18/2020 200

9/22/2020 200

10/30/2020 300

N = 17

Total usage over 180 days = 5,000

Average/30 days = 833.3

X-bar = 291.1

noStd Dev = 171.3

mu = 225.6

My interpretation is that 225.6 is the value that the true mean over the 180 days has a 95% probability of being 225.6 or greater.

QUESTION 1: Can I use mu of the sample (225.6) to extrapolate to 18 months, e.g. X-bar (18 months) = 75,000 and mu = (75,000 x (225.6/291.1)) = 58,124? Note that for some of my data mu is negative since the sample size is small.

QUESTION 2: At what number N should I not use the normal distribution? Is there alternative formula/approach where N is less than 20 or 10?

I appreciate any help you can provide.