Transcript Attribute Charts and low defect rates.pptx

A problem with analysis you would like to have.
What happens when defect rates get very
low?
 For Poisson data, the distribution gets very skewed and
the usual three sigma limits are not valid.
 This occurs when λ≤20 and becomes very noticeable
when λ is close to zero.
 This also happens for Binomial data when p is small
and the sample size n is large. In this case the Binomial
is approximately Poisson (n*p*(1-p)≥10 usually means
it is a good approximation).
 For λ≤20 we can use table values to obtain control
chart limits.
Table values from Edition 2 of the text:
Problem solved?
 Almost.
 The potential problem (which every SPC text ignores),
is that when λ≤.1, if λ is small enough, the UCL should
be such that any value X≥1 should be evidence of an
out of control point.
 This violates the Shewhart principle that the ARL, or
time between false signals, should be approximately
equal to 100.
Is violating this Shewhart principle really a
problem here?
 According to Dr. Tom, “沒問題”.
 Why? According to Shewhart, the ARL of 100 (or false
signal rate of about 1%), was designed to keep the
Operator from reacting to false signals.
 With Attributes charts, at very low defect rates the
concepts of Special Cause and Defects overlap.
Is there another way to approach this
without violating that Shewhart principle?
 Sort of.
 In Edition 2 of the text, the author suggests increasing
the Area of Opportunity so that the ARL is still
approximately 100, i.e. the chance of a false signal
remains about 1%.
 The idea is that the chart may give false signals but
retains “sensitivity”.
Is there any problem with increasing the
Area of Opportunity here?
 According to Dr. Tom “很大問題”.
 If you increase the Area of Opportunity this way, it
may take a number of defects over a long period of
time in order to trigger a signal of Special Cause.
 By waiting it may make it more difficult to determine
the source of the problem because time may have
elapsed since one or more of the defects occurred,
making it more difficult to determine what was
“special” about the conditions when they happened.
So with defect rates that low one should?
 Look for the cause as soon as one knows about it.
 With low defect rates it is usually harder to find the
cause, since defects are so rare there is not likely to be
enough data to find a pattern in the conditions which
produced them.
 A designed experiment may be the best and most
economical way to reduce defects at this point.
 This is a problem you would like to have.