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Two types of data
• Variables----Continuous
• Attributes—Discrete, Countable– Two types of attributes data
• You can count occurrences and non-occurrences.• You can only count occurences.
Examples?????
Decide on type of data
Continuous
(Variables)
Data
Discrete (Attributes)
Data
More than one observation per
subgroup?
< 10 observations
per subgroup?
Can both occurrences &
non-occurrences be
counted?
Are there equal area
of opportunity
?
Are the subgroup
sizes equal?
Yes
Yes
Yes
Yes
Yes
No
NoNo
No
No
–R –s XmR c-chart u-chart p-chart np-chart
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”
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.
“Standard Deviation”
• Based on sample estimate of population standard deviation.
• Based on moving ranges.
• Based on ranges.
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
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– β risk is too high
• When you have 200 observations– α risk is too high
• Can use T-Sigma Limits
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.
Choosing Charts1. Continuous
A. Only 1 observation per subgroup—use iChart B. More than 1 observation/subgroup
i) Less than 10 observations/subgroup—use Xbar-Rii) 10 or more observations/subgroup--use Xbar-Sigma
2. AttributesA. Occurrences (heads) and non-occurrences (tails) can
be counted.i) Subgroups of equal size—use np-ChartIi) Subgroups of unequal size—use p-Chart
B. Only occurrences can be counted.i) Equal area of opportunity (denominators)—use c-Chartii) Unequal area of opportunity– use u-Chart
Decide on type of data
Continuous(Variables)
Data
Discrete (Attributes)
Data
More than one observation per
subgroup?
< 10 observations
per subgroup?
Can both occurrences &
non-occurrences be counted?
Are there equal area of opportunity?
Are the subgroup
sizes equal?
Yes
Yes Yes
Yes
Yes
No
NoNo
No
No
–R –s XmR c-chart u-chart p-chart np-chart
See Flow Chart onpage 72 of Carey and Lloyd