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x-bar and R charts

x and R charts are the control charts used for continuous data, e.g., the weigth or lenght of a product, the time to produce an item or reply a phone call...

x charts 

x charts show changes in the mean tendence of the process. 

Upper control limit (UCL) Central line Lower control limit (LCL)

UCL

x-bar-bar

UCL

Where:

x̿ is the mean of the samples;

Sigma sub x-bar is the standard deviation of the process (σ) divided by the square root of the elements per sample (n);

and typical values for z are 2 (more restrictive) or 3 (less restrictive).

X-bar chart

R charts 

R charts show changes in the dispersion of the process.

Upper control limit (UCL) Central line Lower control limit (LCL)

UCL

x-bar-bar

UCL

Where:

R is the average range of the samples;

and D4 and D3 are taken from the 3-sigma table.

R Chart

Building x and R charts 

  1. Take 20-25 samples of 4-5 pieces/products each one. Calculate mean and range for each sample.
  2. Calculate global mean and range (x-bar-bar and R-bar).
  3. Fix desired limits (generally 3σ) and calculate actual control limits
  4. Draw samples in the chart.
  5. Analyze the results and research for the possible causes of variation

Explanatory video