Theoretical Basis of Control Charts

Total Quality Management

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Theoretical Basis of Control Charts

Here we will revise our statistics in relation to SQC. The concept how statistics is helpful in control chart is explained by the following sketches. Reference

Control Charts for Variables

As the name indicates, these charts will use the variable data of a process. X Chart gives an idea of the central tendency of the observations. These charts will reveal the variations between sample observations. R chart gives an idea about the spread (dispersion) of the observations. This chart shows the variations within the samples.

X Chart and R Chart

Procedure to Construct X Chart and R Chart

Identify the process to be controlled.
Select the variable of interest.
Decide a suitable sample size (n) and number of samples to be collected (k)
Collect the specified number of samples over a given time interval.
Find the measurement of interest for each piece within the sample.
Obtain the mean ( X) of each sample. ( X =[∑ xi]/n) .
Also obtain the range R of each sample (R=Max xi – Min xi).
Then obtain x and R { x =[∑ X]/k, R = [∑ R]/k. 7. Establish the control limits for X and R chart.