RE: stable system?

[Steven_S_Prevette@rl.gov]

Let's say I have a production process, with the goal of
producing ingots of lead that weigh 302 grams each. I have taken 10 samples
off the line in sequence as follows. Each number below is an average of the
weights in the sample. . . .

++++

Some observations:  
	1.  Ten is a relatively small number of values to work with, I would
prefer 25.  These numbers are said to be averages of samples - what are the
individual values?  That would automatically give more data.  We are losing
considerable information by only using the average of the samples.

	2.  True, the statistical sigma calculations give a standard
deviation of 1.97, giving the UCL and LCL listed in the original message.
However, 5 of the 10 points (285's and 290's) are indeed outside one
standard deviation from the average.  So I don't think the data are that
bad.  In only 10 points, I wouldn't necessarily expect any points outside 2
standard deviations.

	3.  Using average moving range (1.0), you get an even higher
standard deviation - 2.66.  However, the range between the 285 and 289 (a
range of 4.0) is higher than the R UCL of 3.27.  If you recalculate the
standard deviation from the moving range without the 4, you get an average
moving range of 0.625, giving a standard deviation of 1.67.

	4.  So the standard deviation is somewhere between 1.5 and 2.5, and
the jump from 285 to 289 may be significant.

	5.  Besides the small number of points, I think there may be another
player here - the rounding off of the data to the nearest gram.  With such
small standard deviations, I think you should try to get data to the nearest
tenth of a gram and that may give more enlightenment.

	6.  Even further, it was stated that the goal was to make ingots of
302 grams.  Not only is the average much less than 302, but all ten of the
ingots weigh less than 302 grams, and 302 appears to be higher than any of
the UCL's from any of the standard deviation calculations.  The process does
not appear to be capable of making a 302 gram ingot.

Steve Prevette
QA Engineer, ESH Radiological Compliance
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371