INTRODUCTION TO ENGINEERING ECONOMICS Chapter 1: Engineering Decision Making

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Control Charts for Moving Averages

• and R charts track the performance of
  processes that have long production runs or
  repeated services.
• Sometimes, there may be insufficient number of
  sample measurements to create a traditional
  and R chart.
• For example, only one sample may be taken from a
  process.
• Rather than plotting each individual reading, it
  may be more appropriate to use moving average and
  moving range charts to combine n number of
  individual values to create an average.

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Control Charts for Moving Averages

• When a new individual reading is taken, the
  oldest value forming the previous average is
  discarded.
• The new reading is combined with the remaining
  values from the previous average to form a new
  average.
• This is quite common in continuous process
  chemical industry, where only one reading is
  possible at a time.

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Control Charts for Moving Averages

• By combining individual values produced over
  time, moving averages smooth out short term
  variations and provide the trends in the data.
• For this reason, moving average charts are
  frequently used for seasonal products.

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Control Charts for Moving Averages

• Interpretation
• a point outside control limits
• interpretation is same as before - process is out
  of control
• runs above or below the central line or control
  limits
• interpretation is not the same as before - the
  successive points are not independent of one
  another

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Example Eighteen successive heats of a steel
alloy are tested for RC hardness. The resulting
data are shown below. Set up control limits for
the moving-average and moving-range chart for a
sample size of n3. Heat Hardness Average Range
Heat Hardness Average Range 1 0.806
10 0.809 2 0.814 11 0.808 3
0.810 12 0.810 4 0.820 13 0.812
5 0.819 14 0.810 6 0.815
15 0.809 7 0.817 16 0.807 8
0.810 17 0.807 9 0.811 18 0.800
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Example Eighteen successive heats of a steel
alloy are tested for RC hardness. The resulting
data are shown below. Set up control limits for
the moving-average and moving-range chart for a
sample size of n3. Heat Hardness Average Range
Heat Hardness Average Range 1 0.806
10 0.809 0.810 0.002 2 0.814 11
0.808 0.809 0.003 3 0.810
0.810 0.008 12 0.810 0.809 0.002 4
0.820 0.815 0.010 13 0.812 0.810
0.004 5 0.819 0.816
0.010 14 0.810 0.811 0.002 6 0.815
0.818 0.005 15 0.809 0.810 0.003
7 0.817 0.817 0.004 16 0.807
0.809 0.003 8 0.810 0.814 0.007
17 0.807 0.808 0.002 9 0.811
0.813 0.007 18 0.800 0.805 0.007
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Exponentially Weighted Moving Average (EWMA)

• The EWMA values are obtained as follows
• Control limits are set at
• Where

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Chart with a Linear Trend

• As the tool or die wears
• a gradual change in the average is expected and
  considered to be normal
• the measurement gradually increases
• the R chart is likely to remain in control - the
  estimate of ? may not change.
• The difference between upper and lower
  specifications limits is usually set
  substantially greater than 6? , to provide some
  margin of safety against the production of
  defective products

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Chart with a Linear Trend

• Step 1 A trend line is obtained for the
  chart. A simplified formula is available if
• there are an odd number of subgroups
• subgroups are taken at a regular interval and
• the origin is assumed at the middle subgroup

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Chart with a Linear Trend
Step 2 For each subgroup a separate pair of
control limits is obtained above and below
the trend line (so, the control limits are
sloping lines parallel to the trend line)
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Chart with a Linear Trend
Step 3 Estimate . For k 3, 4
etc. the initial aimed-at mean value, is
set k? above the lower specification limit and
the process is stopped for readjustment (a new
setup is made, tool/die is changed) when the
observed mean value reaches k? below the
upper specification limit.
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Text Problem 10.25 A certain manufacturing
process has exhibited a linear increasing trend.
Sample averages and ranges for the past 15
subgroups, taken every 15 minute in subgroup of 5
items, are given in the following table.
Fit the linear trend line to these data, and
plot a trended control chart with 3-sigma limits.
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Text Problem 10.26 Specifications on the process
in Problem 10.25 are 200?30. The process may be
stopped at any time and readjusted. If on
readjustment the mean is to be set exactly 4?
above the lower specification and the process is
to be stopped for readjustment when the mean
reaches a level exactly 4? below the upper
specification (a) Calculate the aimed-at
starting and stopping values of (b) Estimate the
duration of a run between adjustments
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Reading and Exercises

• Chapter 10 (moving average and linear trend)
• pp. 382-391 (Sections 10.6-7)
• 10.24, 10.27