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R = x max - x min. The normal distribution is the basis for the charts and requires the following assumptions: The quality characteristic to be monitored is adequately modeled by a normally distributed random variable; The parameters μ and σ for the random variable are the same for each unit and each unit is independent of its predecessors or ...
The X-bar chart is always used in conjunction with a variation chart such as the ¯ and R chart or ¯ and s chart. The R-chart shows sample ranges (difference between the largest and the smallest values in the sample), while the s-chart shows the samples' standard deviation. The R-chart was preferred in times when calculations were performed ...
As with the ¯ and R and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [5] Thus, the s chart is examined before the x ¯ {\displaystyle {\bar {x}}} chart; if the s chart indicates the sample variability is in statistical control, then the x ¯ {\displaystyle {\bar {x}}} chart is examined to ...
Distribution-free control chart; DOE mean plot; ... Fan chart (statistics) Fan chart (time series) ... X̅ and R chart; X̅ and s chart; X-bar chart
Generalizing the ¯ notation, we can write a horizontal bar over an expression to indicate the average value of that expression over the set of samples. For example: ¯ = =. This notation allows us a concise formula for r xy:
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Statistical graphics have been central to the development of science and date to the earliest attempts to analyse data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in the 18th century.
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