Control Charts as a tool in SQC
(Statistical Quality Control)

Overview

This page has been designed to help in understanding and learning the use, design and analysis of Control Charts, which is the most important tool of Statistical Quality Control.

The information has been formatted in the form of a tutorial, which will guide you through the process. It includes the history, background information, the uses, the types with examples, analysis of patterns, related software and additional sources of information about control charts.

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History

Control charting is one of the tools of Statistical Quality Control(SQC) It is the most technically sophisticated tool of SQC. It was developed in the 1920s by Dr. Walter A. Shewhart of the Bell Telephone Labs.

Dr. Shewhart developed the control charts as an statistical approach to the study of manufacturing process variation for the purpose of improving the economic effectiveness of the process. These methods are based on continuous monitoring of process variation.

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Background Information

A typical control chart is a graphical display of a quality characteristic that has been measured or computed from a sample versus the sample number or time. The chart contains a center line that represents the average value of the quality characteristic corresponding to the in-control state. Two other horizontal lines, called the upper control limit(UCL) and and the lower control limit(LCL) are also drawn. These control limits are chosen so that if the process is in control, nearly all of the sample points will fall between them. As long as the points plot within the control limits, the process is assumed to be in control, and no action is necessary.

However, a point that plots outside of the control limits is interpreted as evidence that the process is out of control, and investigation and corrective action is required to find and eliminate the assignable causes responsible for this behavior. The control points are connected with straight line segments for easy visualization.

Even if all the points plot inside the control limits, if they behave in a systematic or nonrandom manner, then this is an indication that the process is out of control.

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Uses of Control charts

Control chart is a device for describing in a precise manner what is meant by statistical control. Its uses are
  1. It is a proven technique for improving productivity.
  2. It is effective in defect prevention.
  3. It prevents unnecessary process adjustments.
  4. It provides diagnostic information.
  5. It provides information about process capability.

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Types of control charts

  1. Control charts for Attributes.
    1. p chart
    2. c chart
    3. u chart
  2. Control charts for Variables.
    1. X bar chart
    2. R chart

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Analysis of Patterns on Control Charts

A control chart may indicate an out-of-control condition either when one or more points fall beyond the control limits, or when the plotted points exhibit some nonrandom pattern of behavior.

The process is out of control if any one or more of the criteria is met.

  1. One or more points outside of the control limits. This pattern may indicate:
    • A special cause of variance from a material, equipment, method, or measurement system change.
    • Mismeasurement of a part or parts.
    • Miscalculated or misplotted data points.
    • Miscalculated or misplotted control limits.
  2. A run of eight points on one side of the center line. This pattern indicates a shift in the process output from changes in the equipment, methods, or materials or a shift in the measurement system.
  3. Two of three consecutive points outside the 2-sigma warning limits but still inside the control limits. This may be the result of a large shift in the process in the equipment, methods, materials, or operator or a shift in the measurement system.
  4. Four of five consecutive points beyond the 1-sigma limits.
  5. An unusual or nonrandom pattern in the data.
    1. A trend of seven points in a row upward or downward. This may show
      • Gradual deterioration or wear in equipment.
      • Improvement or deterioration in technique.
    2. Cycling of data can indicate
      • Temperature or other recurring changes in the environment.
      • Differences between operators or operator techniques.
      • Regular rotation of machines.
      • Differences in measuring or testing devices that are being used in order.
  6. Several points near a warning or control limit.

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Software

The March issue of Quality Progress contains a directory of software packages available from different suppliers and arranged in different application categories.

The Journal of Quality Technology has published computer programs in either BASIC or FORTRAN since 1969. A selected list of programs, related to control charts, published through 1989 are in the following table. 

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                                               Volume     Page
Program Capability                             & year     
Reference
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1.  Plotting X bar and R charts                 1/1969        149

2.  Plotting p and np charts            	1/1969      
  217

3.  Plotting c and u charts             	1/1969      
  285 

4.  Economic design of X bar charts       	2/1970         40

5.  Plotting cumulative-sum control       	2/1970         54
    charts

6.  Plotting exponentially weighted       	5/1973         84
    moving average control charts

7.  ARL for cumulative-sum control        	18/1986       189
    charts for controlling normal means

8.  ARL for combined individual           	19/1987       103
    measurement and moving-range charts

9.  ARL for exponentially weighted        	19/1987       161
    moving-average control charts

10. New limits for X bar and R charts    	20/1988       149
    sample size is changed

11. Optimal design parameters of joint    	21/1989        65
    X bar and R charts
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Source : Introduction to Statistical Quality control 

by Douglas C. Montgomery, page 252-254.

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Ordinary spreadsheets like Microsoft Excel and Lotus 123 can also be used for creating the above control charts. The charts presented in the examples have been created in Microsoft Excel.

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Tutorial Index

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Tutorial Composed by :
Sedrick Sweat (BSIE )
Krishna Terala (MSME '96)
Kris Troha (BSME)
Kilby Williamson (MSIE )
Inspired by Dr. Del Kimbler