Why use constants to calculate control limits

Question

I am refreshing some knowledge on 6s and currently go through the calculations for upper and lower control limits for quality control charts.

when i for example look at the xbar-Rm chart and I want to calculate the upper control limit the sources I am looking through give me the following calculation:

UCL = Average + constant E3 * AVG of moving Ranges

In theory the UCL is 3 sigma above the average and this is what the formula is trying to calculate but why do we use a constant and not the actual sigma value of all measured values?

I made an example with an average of around 4,946 and an average moving range of 0,0358 which results into an UCL of 5.042124. When I use the XLS STDEV.S function, I get a very similar result of around 5.041221

Again, why do we need to rely on constants that we have to look up and cannot memorize when we quickly wanna calculate something. what is the advantage of this?

Thanks in advance!

Answer 1

Unlike the variance, the standard deviation is a biased estimator. Thus, if you use a sample containing N data points and calculate it's standard deviation the result systematically deviates from the population standard deviation. In order to compensate for this bias we use the constants.