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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 ...
Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
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A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart and has been identified as the prototype of charts. [1]
Each bar can also have a comment, such as "comment7=xx" to show "(xx)" after the number in bar 7. For a 2-column bar chart, the 2nd column items have prefix "col2_" such as scale maximum, col2_data_max=110, and col2_data3=67 with col2_comment3=zz. See below: "Example with two data columns". Each bar chart can be formatted typically within 1/5 ...
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 ...
The EWMA chart is sensitive to small shifts in the process mean, but does not match the ability of Shewhart-style charts (namely the ¯ and R and ¯ and s charts) to detect larger shifts. [ 2 ] : 412 One author recommends superimposing the EWMA chart on top of a suitable Shewhart-style chart with widened control limits in order to detect both ...