RE: Shewhart's Maximum Control

[Steven_S_Prevette@RL.gov]

I can supply a few points on cycle time, in response to the question "I find
that in all of the work that I have done in the last few years regarding
cycle time that the data is always very skewed to the right."

There are some theories out there on cycle times, especially if talking time
between failures.  "Memoryless" systems (it doesn't matter how long you have
been in the cycle, the probability that the cycle completes in the next
minute is the same) are exponential.  Light bulb failures (ignoring the
initial transient of energizing the bulb) tend to be exponential.

In failure rates, there may be a "burn in" period (an initially high failure
rate due to manufacturing flaws) and a "burn out" period (the item is so old
that it has a higher rate of failure).  The failure rate, plotted with life
of the item, takes on what is called a "bathtub" curve.

And yes, cycle times are generally skewed right as no cycle time can be less
than zero.  The beta and gamma distributions can be utilized to model these.
They can look like the normal distribution, but have been cut off at zero.

However, having said all that, remember that control charting does not rely
upon distribution shape.  No matter how skewed the distribution, the
Tchebychev Inequality still holds (no more than 1 / n-squared of the data
will be outside n standard deviations from the average).  Shewhart's work
was not dependent upon the distribution of the data, and he did much testing
with different distribution shapes.  I am told that Dr. Wheeler has also
done some testing, and claims that in almost all cases, 98 to 99% of the
data will fall within 3 standard deviations of the average (note the
Tchebychev Inequality gives a worst case of 89%).

Steve Prevette
ESH Planning and Performance
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371
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