# Control charts to trend data for multiple dependent variables? Hotelling's T^2 stat

D

#### Dan Armstrong

Multi-variable control charts?

Is it possible to use control charts to trend data for multiple dependent variables?
I need to trend the water conductivity for a purified water system, which wouldn't normally be a problem, except the specifications (USP - US Pharmacopeia) state that the conductivity measurement cannot be temperature compensated. The conductivity limit varies directly with increasing temperature.
How can I trend the data when the limit for one variable changes based on another variable?

D

#### Darius

Dan Armstrong said:
Is it possible to use control charts to trend data for multiple dependent variables? ....
The conductivity limit varies directly with increasing temperature.
How can I trend the data when the limit for one variable changes based on another variable?

It may be a nonesense but...

If the conductivity depends on the temperature, you can determinate the target and limits of the conductivity chart and change them acording to the temperature, or use "Short Run Charts", where each point is (IX - Taget_IX/Target_MR).

G

#### Graeme

Dan Armstrong said:
Is it possible to use control charts to trend data for multiple dependent variables?
...
How can I trend the data when the limit for one variable changes based on another variable?

Another way to do this is to use a multivariate control chart such as one based on Hotelling's T^2 statistic. It is a bit complex to go into here, but there are a number of Internet sites that discuss it. For example, see the NIST page at https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/hotell.htm or the NIST online statistics handbook at https://www.itl.nist.gov/div898/handbook/index.htm

Also, it appears that some statistical software programs have this built in, because a search for "hotelling" and "control chart" produced hits from companies such as Statsoft and Minitab.

D

#### Dan Armstrong

Thanks for the information. I'll give both answers a try.

Replies
25
Views
58K
J
Replies
12
Views
4K
Replies
11
Views
15K
G
Replies
26
Views
13K
Replies
6
Views
42K
suvk1
S