RE: Deming/SPC case study question

[Steven_S_Prevette@rl.gov]

I will take this email to strictly answer the SPC question involved, but it
certainly sounds like this furniture scenario is straight out of The New
Economics and Out of the Crisis.  Read the story on page 290-291 of Out of
the Crisis and you will find many similarities, and a good idea on how to
move forward.

I will put a disclaimer on my SPC answer in that without a reasonable
operational definition of what is acceptable or not acceptable, the data may
be meaningless.  Yes, we can detect shifts in the numbers, but the source of
the shifts may simply be differences between inspectors (still, this may be
useful information after all).

You mention a shift from 40% to 60% rejections, so I will assume about a 50%
rejection rate.  The formula for the binomial standard deviation is the
square root of pavg times ( 1 - pavg) divided by the number of items in the
sample.  To simply get to where you have a lower control limit greater than
0%, and an upper control limit less than 100%, you must solve for n:

	0.5 / 3 = sqrt ( 0.5 x ( 1 - 0.5) / n)

or n = 9 (actually, it requires very little math to do this).  A check of
650 pieces per week seems rather excessive, especially with a 50% reject
rate.  Seems like the effort should be put into reducing the sources of the
rejection.  I am reminded of the 3 inspectors involved in the Red Bead
Experiment doing nothing but being sure there is a good measurement.  A
sample size of 650 gives you the failure rate to within plus or minus 2% if
the overall rate is around 50%.  Definite overkill, if the information is
only being used for defect rate.  I assume though that all defects found are
"fixed".

However, only checking 2 per week is insufficient, especially if you want to
demonstrate if you have improved.   I do get the feeling that the "increase"
from 40% to 60% could just be random noise, if your inspection rate is that
low.

Myself, I would choose about 20 to 25 per week, and work to fix the system
to get the reject rate down. 

Steve Prevette
Site Technical Authority for Statistical Trending
Environment, Safety and Health
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371