# Common patterns x and r charts trend or continuous

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Common Patterns x and R Charts Trend , or continuous movement in one direction Trends are usually due to a gradual wearing out or deterioration of a tool or some other critical process component. They can also result from human causes, such as operator fatigue or the presence of supervision.

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Common Patterns x and R Charts Stratification , or a tendency for the points to cluster artificially around the center line This pattern may also result when the sampling process collects one or more units from several different underlying distributions within each subgroup

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Control Charts x for and s

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Although and R charts are widely used, it is occasionally desirable to estimate the process standard deviation directly instead of indirectly through the use of the range R. This leads to control charts for and s, where s is the sample standard deviation
Generally, and s charts are preferable to their more familiar counterparts, and R charts, when either The sample size n is moderately large say, n>10 or 12. (Recall that the range method for estimating s loses statistical efficiency for moderate to large samples.) The sample size n is variable.

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Control Limits for s Chart
Control Limits for x Chart (for x and s charts)

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Example
Example

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x and s Control Charts with Variable Sample Size
Example

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Example
Example

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Summary of formulas for x, R and s Control Charts
Seatwork

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Control Charts for Attributes
• Fall '19
• Control Chart, Process capability, W. Edwards Deming, R Charts

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