## ASTM-E2587 › Standard Practice for Use of Control Charts in Statistical Process Control

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This practice provides guidance for the use of control charts in statistical process control programs, which improve process quality through reducing variation by identifying and eliminating the effect of special causes of variation.

This practice describes the use of control charts as a tool for use in statistical process control (SPC). Control charts were developed by Shewhart (2) 3 in the 1920s and are still in wide use today. SPC is a branch of statistical quality control (3, 4), which also encompasses process capability analysis and acceptance sampling inspection. Process capability analysis, as described in Practice E2281, requires the use of SPC in some of its procedures. Acceptance sampling inspection, described in Practices E1994, E2234, and E2762, requires the use of SPC so as to minimize rejection of product.

### Scope

1.1 This practice provides guidance for the use of control charts in statistical process control programs, which improve process quality through reducing variation by identifying and eliminating the effect of special causes of variation.

1.2 Control charts are used to continually monitor product or process characteristics to determine whether or not a process is in a state of statistical control. When this state is attained, the process characteristic will, at least approximately, vary within certain limits at a given probability.

1.3 This practice applies to variables data (characteristics measured on a continuous numerical scale) and to attributes data (characteristics measured as percentages, fractions, or counts of occurrences in a defined interval of time or space).

1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.

1.5 *This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.*

### Significance and Use

4.1 This practice describes the use of control charts as a tool for use in statistical process control (SPC). Control charts were developed by Shewhart (2)3 in the 1920s and are still in wide use today. SPC is a branch of statistical quality control (3, 4), which also encompasses process capability analysis and acceptance sampling inspection. Process capability analysis, as described in Practice E2281, requires the use of SPC in some of its procedures. Acceptance sampling inspection, described in Practices E1994, E2234, and E2762, requires the use of SPC so as to minimize rejection of product.

4.2 Principles of SPC—A process may be defined as a set of interrelated activities that convert inputs into outputs. SPC uses various statistical methodologies to improve the quality of a process by reducing the variability of one or more of its outputs, for example, a quality characteristic of a product or service.

4.2.1 A certain amount of variability will exist in all process outputs regardless of how well the process is designed or maintained. A process operating with only this inherent variability is said to be in a state of statistical control, with its output variability subject only to chance, or common, causes.

4.2.2 Process upsets, said to be due to assignable, or special causes, are manifested by changes in the output level, such as a spike, shift, trend, or by changes in the variability of an output. The control chart is the basic analytical tool in SPC and is used to detect the occurrence of special causes operating on the process.

4.2.3 When the control chart signals the presence of a special cause, other SPC tools, such as flow charts, brainstorming, cause-and-effect diagrams, or Pareto analysis, described in various references (4-8), are used to identify the special cause. Special causes, when identified, are either eliminated or controlled. When special cause variation is eliminated, process variability is reduced to its inherent variability, and control charts then function as a process monitor. Further reduction in variation would require modification of the process itself.

4.3 The use of control charts to adjust one or more process inputs is not recommended, although a control chart may signal the need to do so. Process adjustment schemes are outside the scope of this practice and are discussed by Box and Luceño (9).

4.4 The role of a control chart changes as the SPC program evolves. An SPC program can be organized into three stages (10).

4.4.1 Stage A, Process Evaluation—Historical data from the process are plotted on control charts to assess the current state of the process, and control limits from this data are calculated for further use. See Ref. (1) for a more complete discussion on the use of control charts for data analysis. Ideally, it is recommended that 100 or more numeric data points be collected for this stage. For single observations per subgroup at least 30 data points should be collected (6, 7). For attributes, a total of 20 to 25 subgroups of data are recommended. At this stage, it will be difficult to find special causes, but it would be useful to compile a list of possible sources for these for use in the next stage.

4.4.2 Stage B, Process Improvement—Process data are collected in real time and control charts, using limits calculated in Stage A, are used to detect special causes for identification and resolution. A team approach is vital for finding the sources of special cause variation, and process understanding will be increased. This stage is completed when further use of the control chart indicates that a state of statistical control exists.

4.4.3 Stage C, Process Monitoring—The control chart is used to monitor the process to confirm continually the state of statistical control and to react to new special causes entering the system or the reoccurrence of previous special causes. In the latter case, an out-of-control action plan (OCAP) can be developed to deal with this situation (7, 11). Update the control limits periodically or if process changes have occurred.

Note 1: Some practitioners combine Stages A and B into a Phase I and denote Stage C as Phase II (10).

### Keywords

common cause; control chart; control limits; rational subgroup; special cause; state of statistical control; statistical process control;

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03.120.30 (Application of statistical methods)

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### Document Number

ASTM-E2587-16

### Revision Level

2016 EDITION

### Status

Current

### Modification Type

Revision

### Publication Date

May 15, 2016

### Document Type

Practice

### Page Count

29 pages

### Committee Number

E11.30