X-bar and R-charts

The principal types of control charts used to analyze variables data are X-bar and R-charts. X-bar and R-charts are used in conjunction with each other. The measurements describe a process characteristic and are reported in small subgroups of constant sizes (usually two to five measurements per subgroup). Construction and use of these types of charts typically involve the following steps:

Select the size, frequency, and number of subgroups.
Assemble the data for the periods of interest.
Calculate the average (X-bar) and the range R of each subgroup.
Plot the averages and ranges on the control charts.
Calculate the central line control limits; plot them on the control chart.
Study the charts for stability and/or trends.

X-bar and s-charts

X-bar and s-charts (sample standard deviation) are also used in conjunction with each other and are measured from process characteristics. The sample standard deviation is a more efficient indicator of process variability, especially with larger sample sizes. However, it is more difficult to calculate and is less sensitive in detecting special causes of variation that cause only a single value in a subgroup to be unusual. Construction and use of these types of charts typically involve the following steps:

Select the size, frequency, and number of subgroups.
Assemble the data for the periods of interest.
Calculate s, s-bar (average), and the control limits for both the X-bar and s chart, and the X-double bar chart.
Plot the data on the control charts.
Calculate the central line control limits; plot them on the control chart.
Study the charts for stability and/or trends.

X-charts

Unlike X-bar and R-charts, which collect and evaluate subgroups of data, X-charts (sometimes referred to as individuals charts) involve the analysis of individual measured quantities for indications of process control or unusual variation. The standard deviation for X-charts is calculated using a moving range.

The following process should be used in developing and analyzing X-charts:

Assemble data for the periods of interest.
Calculate the average of the individual values.
Calculate the individual moving ranges (all ranges will be positive numbers).
Average the ranges.
Calculate the standard deviation and subsequent control limits for the individual values.
Plot the average and limit lines for the individual values and analyze for trends.

C-chart

The c-chart is the principal type of control chart used to analyze attributes data. C-charts (sometimes referred to as "count" charts) are used in dealing with counts of a given event over consecutive periods of time. The following process should be used in developing and analyzing c-charts:

Assemble data for the periods of interest.
Calculate the data central line.
Calculate the upper and lower control limits.
Plot central line, and control limits.
Study the charts for stability and/or trends.