Any production process is not perfect enough to produce all the products exactly the same.

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.

Procedure for

(i) Let *X*_{1},*X*_{2},
*X*_{3}, 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*
= *x*_{max} − *x*_{min}

Let *R*_{1},
*R*_{2}, *R*_{3}… 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 A_{2},
D_{3} and D_{4} are given in the table.

Tags : Statistical Quality Control (SQC) | Applied Statistics , 12th Business Maths and Statistics : Chapter 9 : Applied Statistics

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12th Business Maths and Statistics : Chapter 9 : Applied Statistics : Construction of X and R charts | Statistical Quality Control (SQC) | Applied Statistics

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