# Statistical Quality Control Using Control Charts

### Introduction

Control charts are used to monitor a process for some quality characteristic such as e.g., thickness, weight, defective fractions, etc. The common elements of quality control charts are outlined below:

• The Y-axis (vertical axis)) is a value axis that is scaled according to the unit of the corresponding summary statistic (e.g., standard deviation, mean, etc.)
• The X-axis (horizontal axis) is categorical and represents sample ID, order, sequence, run time, site, etc.
• Each point represents a summary statistic based on computation results from subgroup measurements of a continuously varying quality characteristic.
• The center line displays the average of the summary statistic. The upper and lower control limit lines (UCL and LCL) display the range of expected variations in the summary statistic. Points above the UCL or below the LCL lines are out-of-control points, while points inside the UCL and LCL are in-control-points.

### Shewhart Control Charts for Variables

These charts are based on quality characteristics that can be measured and expressed numerically.

• Xbar (R) chart/LI>
• Xbar (S) chart/LI>
• R chart
• S chart
 An Xbar (R) Quality Control Chart An Xbar (S) Quality Control Chart

### Other Control Charts Used for Variables

The following control charts are also used for variables:

• Levey-Jennings control chart
• Individual measurements chart
• Moving range chart

#### Special Cause Variation (Westgard Procedure Rules)

The Westgard multi-rules procedure, published by Westgard et. al. (1981), is used to detect trends or shifts by examining individual values to determine the status of the measuring system.

• The multi-rules procedure is commonly used with Levey-Jennings chart. In the Levey-Jennings control chart shown here (the right-hand side image), with no points being outside 3s, the run is accepted.

Westgard Rules Applied to a Levey-Jennings Control Chart
 An Individual Measurements Chart A Moving Range Chart

### Shewhart Control Charts for Attributes

The QC charts for attributes are based on quality characteristics that are attributes and expressed categorically, for example "conforming" or "non-conforming", "defective" or "non-defective", etc.

• p chart
• np chart
• c chart
• u chart
 An Example of np Quality Control Charts An Example of u Quality Control Charts