More Control Charts

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More Control Charts

• Module 6

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Why?

• There are many probability distributions in our
  world

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The Binomial Distribution, The distribution of
coin tosses.
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Two types of data

• Variables----Continuous
• AttributesDiscrete, Countable
• Two types of attributes data
• You can count occurrences and non-occurrences.
• You can only count occurences.

Examples?????
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Some Variables Shewart Charts

• X-mR aka i-Chart, Individuals Chart
• X-bar-range
• X-bar-sigma

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Some Attributes Shewart Charts

• p-Chart
• np-Chart
• u-Chart
• c-Chart

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Decide on type of data
Continuous (Variables) Data
Discrete (Attributes) Data
Yes
No
Yes
No
Yes
No
Yes
Yes
No
No
?R
?s
XmR
c-chart
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Example Individuals Chart
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Example X-Range Chart
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Example X-Sigma Chart
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How did they do that?
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The basic pattern.

• Plot observed measurements over time.
• Measurements, counts, rates
• Plot Centerline
• Average measurement or count, pooled rate.
• Plot Control Limits
• Centerline /- Multiplier X Standard Deviation

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Multiplier does 3 Things

• Determines the number of sigmas
• usually 3
• Converts standard deviations to standard errors
  (variables data).
• Can include factor to adjust for unusually small
  or large number of subgroups or time intervals.

Note How multiplier is constructed and used
varies by author.
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Standard Deviation

• Based on sample estimate of population standard
  deviation.
• Based on moving ranges.
• Based on ranges.

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The i-Chart or XmR Chart

• Calculate average of all individual values x
• Calculate all the moving ranges (MRi)
• MRi xi-xi-1
• Calculate the average MR Rbar
• Calculate control limits xbar /- 2.66Rbar
• Plot xbar
• Plot control limits
• Plot individual values, points

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The Xbar-Range Chart
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The Xbar-Sigma Chart
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The Xbar-Sigma Chart (Part II)
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Is 3 always OK?

• Notice 3 is multiplied by the SD.
• This gives /- 3 Sigma Control Limits.
• Designed for 25 observations.
• When you have only 7 observations
• ß risk is too high
• When you have 200 observations
• a risk is too high
• Can use T-Sigma Limits

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T-Sigma Limits
No. of Plotted Points T
2 1.5
3-4 2.0
5-9 2.5
10-34 3.0
35-199 3.5
200-1500 4.0
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How to use T-Sigma Limits

• Substitute the T-Sigma limit from the table for
  the 3 in A3, B3, and B4 above.
• For attributes charts, simply substitute the
  T-Sigma Limits for the multiplier in front of the
  standard error.

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The attributes Shewart Charts

• p-Chart
• np-Chart
• u-Chart
• c-Chart

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Example p-Chart
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Example np-Chart
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Example u-Chart
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Example c-Chart
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How did they do that?
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The p-Chart
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The np-Chart
Pooled over all subgroups
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The c-Chart
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The u-Chart
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Choosing Charts

• Continuous
• A. Only 1 observation per subgroupuse iChart
• B. More than 1 observation/subgroup
• i) Less than 10 observations/subgroupuse Xbar-R
• ii) 10 or more observations/subgroup--use
  Xbar-Sigma
• 2. Attributes
• A. Occurrences (heads) and non-occurrences
  (tails) can be counted.
• i) Subgroups of equal sizeuse np-Chart
• Ii) Subgroups of unequal sizeuse p-Chart
• B. Only occurrences can be counted.
• i) Equal area of opportunity (denominators)use
  c-Chart
• ii) Unequal area of opportunity use u-Chart

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See Flow Chart onpage 72 of Carey and Lloyd
Decide on type of data
Continuous (Variables) Data
Discrete (Attributes) Data
Yes
No
Yes
No
Yes
No
Yes
Yes
No
No
?R
?s
XmR
c-chart