## Q

be used to develop the x chart (rather than the x chart and the range chart is developed by using the "moving range" concept discussed in Subsection

The assumptions of Shewhart charts are:

• The distribution of the data is approximately Normal.

• The sample group sizes are equal.

• All sample groups are weighted equally.

• The observations are independent.

### Describing Variation

The location or central tendency of a variable is described by its mean, median, or mode. The spread or scatter of a variable is described by its range or standard deviation. For small sample sizes (n < 6, n=number of samples), the range chart or the standard deviation chart can be used. For larger sample sizes, the efficiency of computing the variance from the range is reduced drastically. Hence, the standard deviation charts should be used when n > 10.

One or more observations may be made at each sampling instant. The collection of all observations at a specific sampling time is called a sample. The convention on summation and representation of mean values is where m is the number of samples (groups) and n is the number of observations in a sample (sample size). The subscripts . indicate the index used in averaging. When there is no ambiguity, average values are denoted in the book using only x and x. For variables that have a Normal distribution: