Operations Models:

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Example 12.2

• Operations Models
• Demings Experiment

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Quality

• Tampering with a stable process
• Ford, GM, Xerox persuaded to change Quality
  philosophy after this
• Therefore important in SOM

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Background Information

• Suppose that you are in the business of drilling
  a tiny hole in the exact center of a square piece
  of wood.
• In the past, the holes you have drilled were, on
  average, in the center of the wood, and the x-
  and y-coordinates each had a standard deviation
  of 0.1 inch.
• Also, the drilling process has been stable that
  is, the holes average being in the center of the
  square, and the deviations from the center of the
  square follow a normal distribution with mean 0
  and standard deviation 0.1 inch.

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Background Information -- continued

• This mean, for example, that the x-coordinate is
  within 0.1 inch 95 of the holes, and the
  x-coordinate is with 0.3 inch of the center for
  99.7 of the holes.
• This describes the inherent variability in the
  drilling process.
• Without changing the hole-drilling process, you
  must live with this amount of variation.
• Now suppose that you drill a hole and its x- and
  y- coordinates are x0.1 and y0.

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Background Information -- continued

• A natural reaction is to reduce the x-setting of
  the drill by 0.1 to correct for the fact that the
  x-coordinate was too high.
• Then if the next hole has coordinates x -0.2
  and y 0.1, you might try to increase the
  x-coordinate by 0.2 and decrease the y-coordinate
  by 0.1.
• Demings funnel experiment shows that this method
  of continually readjusting a stable process he
  calls it tampering will actually increase the
  variability of the coordinates of the position
  where the hole is drilled. In other words,
  tampering will generally make a process worse!

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Background Information -- continued

• To illustrate the effects of tampering, Deming
  placed a funnel above a target on the floor and
  dropped small balls through the funnel in an
  attempt to hit the target.
• As he demonstrated, many balls did not hit the
  target. His goal, therefore, was to make the
  balls fall as close to the target as possible.
• Deming proposed four rules for adjusting the
  positioning of the funnel.

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Demings Rules

1. Never move the funnel
2. After each ball is dropped, move the funnel
   relative to its previous position to compensate
   for any error. To illustrate, suppose the target
   has coordinates (0,0) and the funnel begins
   directly over the target. If the ball lands at
   (0.5,.1) on the first drop, we compensate by
   repositioning the funnel at (0-0.5,0-0.1)
   (-0.5,-.1). If the second drop has coordinates
   (1,-2), we then reposition the funnel at
3. (-0.5 1, -0.1 (-2)) (-1.5, 1.9).

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Demings Rules -- continued

1. Move the funnel relative to its original
   position at (0,0) to compensate for any error.
   For example, if the ball lands at (0.5,0.1) on
   the first drop, we compensate by repositioning
   the funnel at (0-0.5, 0-0.1) (-0.5, -1). If the
   second drop has coordinates (1, -2), we then
   reposition the funnel at (0, -1, 0 (-2))
   (-1,2).

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Demings Rules -- continued

• Always reposition the funnel directly over the
  last drop. Therefore, if the first ball lands at
  (0.5,1), we position the funnel, (0.5, 1). If the
  second drop has coordinates (1, 2), we position
  the funnel at (1, 2). This rule might be
  followed, for example, by an automobile
  manufacturers painting department. With each new
  batch of paint, they attempt to match the color
  of the previous batch regardless of whether the
  previous color was correct.
• Do you believe any of the latter three rules will
  outperform rule 1, the leave it alone rule? If
  so, read on you might be surprised.

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Solution

• To see how these rules work, we assume that the
  x-coordinate on each drop is normally distributed
  with mean equal to the x-coordinate of the funnel
  position and standard deviation of 1.
• A similar statement holds for the y-coordinate.
  Also, we assume that the x- and y- coordinates
  are selected independently of one another. These
  assumptions describe the inherent variability in
  the process of dropping the balls.

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Solution -- continued

• To see how the rules work, let F0, X0, F1 be
  respectively, the x-coordinates of the funnel
  position on the previous drop, the outcome of the
  previous drop, and the repositioned funnel
  position for the next drop.
• Then rule 1 never repositions, so that F1 F0.
  Rule 2 repositions relative to the previous
  funnel position, so that F1 F0 X0. Rule 3
  repositions relative to the original position (at
  0), so that F1 0 X0 -X0. Finally rule 4
  repositions at the previous drop, so that F1
  X0. Similar questions hold for the y-coordinate.

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Solution -- continued

• For the simulation model, we simulate 50
  consecutive drops of the ball from each of the
  four rules.
• Our single output measure is the (straight-line)
  distance of the final drop from the target.
• A rule is presumably a good one if the mean
  distance is small and the standard deviation of
  this distance is also small.

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FUNNEL.XLS

• Given the repositioning equations for the rules,
  the simulation model is straightforward.
• In fact, we use a RISKSIMTABLE function to test
  all four rules simultaneously.
• The spreadsheet model appears on the next slide.
• This file contains the model.

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Developing the Simulation Model

• The model can be developed with the following
  steps.
• Rule. Enter the formula RISKSIMTABLE(1,2,3,4)
  in cell B3 to indicate that we want to simulate
  all four rules. Note that if individual values
  are listed in RISKSIMTABLE, they must be enclosed
  in curly brackets. No curly brackets should be
  used if the list is referenced by a range.
• Position funnel. Enter 0 in cells B7 and C7 to
  indicate that the original funnel position is
  above the target at (0,0). Then implement the
  positioning equations by entering the formula
  IF(Rule1,B7,IF(Rule2,B7-D7,IF(Rule3,-D7,D7)))
  in cell B8 and copying it to the range B8C56.
  Note how this formula references the location of
  the previous drop. The IF function captures the
  logic for all four rules.

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Developing the Simulation Model -- continued

• Simulate drops Simulate the positions of the
  drops by entering the formula RISKNORMAL(B7,1)
  in cell D7 and copying it to the range D7E56.
  This says that the balls drop position is
  normally distributed with mean equal to the
  funnels position and standard deviation 1.
• Distance. Calculate the final distance from the
  target in cell C58 with the formula RISKOUTPUT(
  ) SQRT(SUMSQ(D56E56)). Here we have used SUMSQ
  function to get the sum of squares for the
  distance formula. We have also indicated that
  this is an output cell for _at_Risk.

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Using _at_RISK

• We set the number of iterations to 1000 and the
  number of simulations to 4.
• Selected summary measures for the final distance
  from the target for all four rules appears in the
  table shown here.
• We also show histograms of this distance for
  rule, 1, 2, 3 on the next three slides.

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Using _at_RISK -- continued

• These results prove Demings point about
  tampering.
• Rule 2 might not appear to be too much worse than
  rule 1, but its mean distance and standard
  deviation of distances are both about 40 higher
  than rule 1.
• Rules 3 and 4 are disastrous. Their mean
  distances are more than seven times higher than
  for rule 1, and their standard deviations are
  also much higher.
• The moral of the story, as Deming preached, is
  that you should not tamper with a stable process.
  If the process is not behaving as desired, then
  fundamental changes to the process are required,
  not a lot of tinkering.