This may seem like a simple statistics problem, but how do I construct a control chart that shows a changing average (e.g. counts per minute from a slowly decaying radioactive source)? In other words, after taking a number of readings, how do I determine the slope from the resulting scatter of readings and how do I get the chart to show the average, upper control limit and lower control limit as a slope?

This may seem like a simple statistics problem, but how do I construct a control chart that shows a changing average (e.g. counts per minute from a slowly decaying radioactive source)? In other words, after taking a number of readings, how do I determine the slope from the resulting scatter of readings and how do I get the chart to show the average, upper control limit and lower control limit as a slope?

In the example provided (radioactive decay) you are not so interested in the slope of the counts, as the counts decay logarithmically. If you want to know if the decay rate is stable, the best bet would be to do a logarithmic transform to plot the lambda (or if prefered, the half life) calculating this point to point. The lambda (or half life) can then be analyzed as a normal variable on a control chart.

:applause: The value of the Cove as a resource for diverse interests is nicely epitomized when someone with an arcane question regarding statistical control in nuclear physics can get a succinct answer thirteen minutes after posting.

:applause: The value of the Cove as a resource for diverse interests is nicely epitomized when someone with an arcane question regarding statistical control in nuclear physics can get a succinct answer thirteen minutes after posting.

You're welcome. Of course, please notice my byline - Hanford. We glow in the dark here (and I did spend 12 years in Navy submarines).

You're welcome. Of course, please notice my byline - Hanford. We glow in the dark here (and I did spend 12 years in Navy submarines).

That's my point--where else will you find answers from such a diverse field of knowledgeable people? The information you provided will be useful to a small minority of the people who see it, but that's precisely what makes it--and the Cove--so valuable.

Well, I mentioned radioactive source as an example. I've worked at nuclear power plants before (as a health physics technician :cool: ), so I'm aware that radioactive materals decay logarithmically. I could have said battery, which have a discharge rate which would have a sharper falloff after a steady discharge rate (inverse logarithmic curve?)

But in either case, imagine zooming in so the logarithmic curve approximates a slope (either a long half-life or a slowly discharging lithium battery), or think of any other process where the average is a straight line, but at a slope. How would I construct a control chart of that?

Speakin' o' decay, how would someone plot a control chart of that? Or any other logarithmically changing average? Or even an average that fluctuates up and down, like barometric pressure?

I guess what I'm looking for here is examples in Excel, Matlab, Scilab, Gnuplot, Dataplot, or whatever.

Control charts are used to show that "something" is in control, i.e. that the value is constant other than random fluctuations. Ususally the number that is (hopefully) constant is some sort of count (e.g. typos per page, defects per batch) or measurement (thickness of a part, resistance of a circuit).

If the "something" that you want in control is not the actual value, but instead is a function of time (e.g. tool wear, battery discharge, counts for nuclear decay), then you can transform the data so there is something constant to plot. If you expect a constant slope, then plot the slope itself on the control chart (this could just be a moving range chart which should be centered on a slightly negative value). If you expect exponential decay for nuclear decay, plot the slope of the log of the counts, which should be the decay constant lambda.

The battery discharge might be tougher, because I would have a hard time coming up with parameter that should be constant. Perhaps you could measure a bunch of batteries to come up with a "standard discharge curve". Then test a new battery and plot the difference between its discharge curve and the "ideal" discharge curve.

Tim F


P.S. Nuclear decay is typically called "exponential", not "logarithmic". You would take the log of the counts to get a straight line, but the function itself is exponential: N = N(0)exp[-lambda*t]

I guess what I'm looking for here is examples in Excel, Matlab, Scilab, Gnuplot, Dataplot, or whatever.

back in a January 2003 there was a similar thread...I posted an article by Donald Wheeler "can I have Sloping Limits" (Quality Magazine May 1999)
Also, you might want to check this out: Sarkar, Ashok, and Pal, Surajit, “Process Control and Evaluation in the Presence of Systematic Assignable Cause”, Quality Engineering, Volume 10, Number 2, 1997, pp. 383-388

I've used both techniques very successfully in the past.
hope this helps give you soem ideas...

I guess what I'm looking for here is examples in Excel, Matlab, Scilab, Gnuplot, Dataplot, or whatever.
How's this? This was a real example from Hanford.

P.S. (edit)
Tim Folkerts pointed out that the label on the chart was incorrect. The internal calculations were correct:

- ln ( counts2 / counts1) / (time2 - time1)

And yes, there were a mixture of isotopes in the samples, and we were trying to determine how long you needed to wait for short lived isotopes to decay off and be able to detect longer term isotopes.

back in a January 2003 there was a similar thread...I posted an article by Donald Wheeler "can I have Sloping Limits" (Quality Magazine May 1999)...........

That thread is:

SPC for hole size taking into account punch wear (http://elsmar.com/Forums/showthread.php?t=9961)