Applied Statistics : Statistical Quality Control (SQC)
Construction of and R charts
Any production process is not perfect enough to produce all the products exactly the same. Some amount of variation is inherent in any production process. This variation is a total of number of characteristics of the production process such as raw materials, machine setting, operators, handling new operations and new machines, etc. The chart is used to show the quality averages of the samples taken from the given process. The R chart is used to show the variability or dispersion of the samples taken from the given process. The control limits of the and R charts shows the presence or absence of assignable causes in the production process. Both and R charts are usually required for decision making to accept or reject the process.
The procedure for constructing and R charts are outlined below.
(i) Let X1,X2, X3, etc. be the samples selected, each containing ‘n’ observations (usually n = 4, 5 or 6)
(ii) Calculate mean for each samples 1 , 2 , 3 .... by using
total of ‘n’ values included in the sample Xi .
(iii) Find the mean () of the sample means.
total of all the sample means.
Calculate R = xmax − xmin
Let R1, R2, R3… be the ranges of the ‘n’ samples. The average range is given by
The calculation of control limits for chart in two different cases is
The calculation of control limits for R chart in two different cases are
The values of A2, D3 and D4 are given in the table.