- Collect samples over time

- Compute the mean: X-Bar = (x1 + x2 + .... xn) / n

- Compute the range: R = max {x1, x2, ..... xn} & min {x1, x2, ..... xn} as a proxy for the variance

- Average across all periods

* average mean

* average range

- Normally distributed

- n will be the sample size

* determines the values for A2, D3, D4, and factor to estimate standard deviation, z, which is notated by d2

- we want z (standard deviation) to be 3 for SPC, which is 99.7% confidence - All normal distributions are characterized by two parameters, μ = mean and σ = standard deviation

- All normal distributions are related to the standard normal, Z, where μ = 0 and σ = 1.

- For example:

* Let Q be the order quantity, and (μ, σ) the parameters of the normal demand forecast. Let D be a random variable representing demand.

* P{D ≤ Q} = P{Z ≤ z}, where z = (Q - µ) / σ or Q = z + (µ x σ)

- (The above are two ways to write the same equation, the first allows you to calculate z from Q and the second lets you calculate Q from z.)

- Look up P{Z ≤ z} in a Standard Normal Distribution Function Table (also called a z-table).

- in an example: if asked what the probability than x is less than a given number, z is in the lower tail (nothing needs to be done with the probability). however, if asked what the probability that x is more than a given number, z is in the upper tail and the probability should be subtracted from one ;