Multivariate Control Chart: Upper Control Limit

Question

Hi there,

In the chapter of "Multivariate Control Charts" > "Ungrouped Data" > "Phase 1 - Obtaining Targets" I couldn't get the UCL value of 11.03 by following the formula shown in "Statistical Details".

Is there anyone out there kind enough to clarify?

Cheers,
CGC.

unknown · Answer

Yeah that's the value we could get by following the charting procedures but you wouldn't be able to get the same result by calculating it using the formulae given.

unknown · Answer

You're right Michael, I was first confused with the "n" notation, the type of "function of beta distribution" and the "first argument" of the function. The technical support team admitted the mistakes and confirmed "n" to be the total sample size, the "function" beta quantile function and the "first argument" (1-alpha).

There are errors in the documentation for Phase 2 as well, fyi.

mpb · Answer

With n=28 and p=6 and alpha=0.05 the one sided level of risk, the following formula agrees with the JMP multivariate control chart output (i.e. 11.03):

(((n-1)^2) / n) * beta quantile(1-alpha, p/2, (n-p-1)/2)

There seem to be a couple of issues with the documentation.
1. n is incorrectly defined for ungrouped data. It should be the number of data points, not the group sample size
2. The definition of alpha in the docs is not made clear but appears to be what I have written as 1-alpha with alpha the one sided level of risk

Michael