# Applying One Tail Test to Daily Data to Estimate Monthly Values

#### Kaiser101

##### New Member
This is my first post in this forum so I apologize that if I am not formatting my question as seasoned forum users.

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?