X-bar, R-bar, p-bar, C-bar charts

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Bar Charts Assignment HelpThe control charts most often associated with statistical process control, (SPC), are the X-Bar and Range or R charts. X-Bar is just a fancy word for mean, also known as average. Range charts are just that, the range that the sample lay between. You should always set up the Range or R-Bar control charts first.

The charts are compared with control limits. Control limits, are typically calculated based on the number of original samples, or first samples, taken on any given process. (see upper control limit, lower control limit and Pre-Control Limit) The number of samples to start with will vary based on any given process, but should be sufficient to represent the population of the widget being manufactured. Motorola in the 1980’s require their suppliers to supply 75 pieces of data for first article inspection.

Once you have taken the data using a stratified sampling plan, the control limits are established by using a factor scale that will estimate the sigma, or standard deviation. Using this estimate, you can add and subtract 3 times one sigma to get your control limits and zones.

Remember that the bell of a bell-shaped curve is +/- 3 sigma. A different factor is used for the range control limits. Note that if the numbers of observations are less than 7, then the lower control limit on the range charts is always zero, (0). For more information on how to calculate upper control limits and lower control limits, including the factor tables, see our glossary. 

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