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Statistical Process Control

Manufacturing engineers are often concerned with managing the variability of a process, which can be done with control charts. The ideas underlying the control chart are that the natural variability in any manufacturing process can be quantified with a set of control limits and that variation exceeding these limits signals a change in the process.

Shewhart Charts

Shewhart Control Chart with Multiple Control Limits
Shewhart Control Chart with Multiple Control Limits

The Shewhart chart was introduced in 1924 by Walter A. Shewhart (1891-1967), a physicist at the Bell Telephone Laboratories. In industry, the Shewhart chart is the most commonly applied statistical quality control method for studying the variation in output from a manufacturing process. Shewhart charts are typically used to distinguish variation due to special causes from variation due to common causes.

Special causes are local, sporadic problems such as the failure of a particular machine or a mistakenly recorded measurement. Common causes are problems inherent in the manufacturing system, such as inadequate product design or excessive humidity. Once the special causes have been identified and eliminated, the process is said to be in statistical control. When statistical control has been established, Shewhart charts can be used to monitor the process for the occurrence of future special causes and to measure and reduce the effects of common causes.

Cusum Charts

Two-Sided Cusum Chart with V-Mask
Two-Sided Cusum Chart with V-Mask

Cumulative sum control charts, or cusum charts, are used to decide whether a process is in statistical control by detecting a shift in the process mean. They display cumulative sums of the deviations of measurements or subgroup means from a target value. Cusum charts can be more sensitive to shifts in the process mean than Shewhart charts.

A one-sided cusum scheme, or decision interval scheme, detects a shift in one direction from the target mean. A two-sided cusum scheme, implemented with a V-mask, detects a shift in either direction from the target mean.

Moving Average Charts

Exponentially Weighted Moving Average Chart
Exponentially Weighted Moving Average Chart

Moving average charts can be used for deciding whether a process is in statistical control and for detecting shifts in the process mean. In contrast to a Shewhart chart, in which each point is based on information from a single subgroup, each point on a moving average chart combines information from the current sample and past samples. As a result, moving average charts are more sensitive to small shifts in the process average. On the other hand, it is difficult to interpret patterns of points on a moving average chart, since consecutive moving averages are usually highly correlated.

Each point on a uniformly weighted moving average chart, commonly called a moving average chart, represents the average of a specified number of the most recent subgroup means. Each point on an exponentially weighted moving average (EWMA) chart represents a weighted average of the most recent subgroup means.

You can also produce control charts with the SQC Menu System.