Periodic Control Charts

[Bastiaans Jan <Jan.Bastiaans@marshalls.co.uk>]

Dear Denizens,

Although I have followed the DEN for some years and have learned a lot from
it, I have so far never asked a question nor answered someone else's. For my
first email, it is a lengthy one and probably a confusing one at that. It
relates to the use of a particular control chart I hope to use. I have an
Excel spreadsheet available if anybody wishes to look into this deeper.
Please send me an email at jan.bastiaans@marshalls.co.uk if you wish to
receive this spreadsheet. Here goes...

I have a question relating to control charts that display periodicity (if
that's the correct word). As the energy manager of the company I work for,
one of my duties is to check for abnormal energy use, for which I'd like to
use a control chart. The problem is that the energy used each day varies
according to what day of the week it is. To be more precise, the consumption
on a weekday (full production) is different to a weekend (when only part of
the plant is running). 

I have tried a XbarR chart (sub group of seven), but found that this was not
quite sensitive enough, so I tried a XmR chart that calculates the average
(Xbar), UCL, LCL and average moving range per weekday. So all Mondays are
grouped together and all values are calculated, the same is done for
Tuesdays, etc. The question I have relates to the appropriateness of the
method I use for calculating moving range. 

At present, the moving range is calculated by looking at the difference
between this Monday and the previous Monday. The next moving range value is
the difference between this Tuesday and the previous Tuesday, etc. The
average moving range is then calculated by weekday. The dataset is then
plotted in chronological order, complete with the averages and control
limits. Is this method of calculating moving range appropriate?

I also have a further question. Please feel free to stop reading here as
this is the point at which things starts to get confusing (for me that is).

The resulting graph looks confusing, as even the average moves up and down
according to which day of the week it is. It is very hard to make much sense
it. In an effort to improve the graph, I decided to 'index' the energy
consumption (X) as well as the averages and the limits for each day. This
should allow a plot that looks the same as a normal XmR chart, without
(hopefully) losing any information. In order to do so, I used the following
formulas:

For X:		(X - Xbar) / mRbar
For Xbar:	Xbar / Xbar - 1
For UCL:	(UCL - Xbar) / mRbar
For LCL:	(LCL - Xbar) / mRbar
For mR:		mR / mRbar
For mRbar:	mRbar / mRbar
For mR UCL:	mR UCL / mRbar

This is probably sacrilege, and if it is I'd like to know why. At present,
this method seems appropriate for what I am trying to do, but not being an
expert I might be making some obvious mistakes. I would value your comments.

Thank you for your time and effort. I appreciate it.

Regards,

Jan Bastiaans
Energy Management Co-ordinator
Marshalls plc
++44 (0)1422 306353