# control chart

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## control chart

[kən′trōl ‚chärt]## Control chart

A graphical technique for determining whether a process is or is not in a state of statistical control. Being in statistical control means that the extent of variation of the output of the process does not exceed that which is expected on the basis of the natural statistical variability of the process. Several main types of control charts are used, based on the nature of the process and on the intended use of the data.

Every process has some inherent variability due to random factors over which there is no control and which cannot be eliminated economically. For instance, in a metal fabrication process random factors may include the distribution of impurities and structural faults among the metal molecules, vibrations of the fabrication equipment, fluctuations in the power supply that affect the speed and torque of the equipment, and variations in the operator performance from one cycle to the next. The inherent variability of the process is the aggregate result of many individual causes, each having a small impact.

The control chart technique is applicable to processes that produce a stream of discrete output units. Control charts are designed to detect excessive variability due to specific assignable causes that can be corrected. Assignable causes result in relatively large variations, and they usually can be identified and economically removed. Examples of assignable causes of variations that may occur in the example of metal fabrication include a substandard batch of raw material, a machine malfunction, and an untrained or poorly motivated operator.

A control chart is a two-dimensional plot of the evolution of the process over time. The horizontal dimension represents time, with samples displayed in chronological order, such that the earliest sample taken appears on the left and each newly acquired sample is plotted to the right. The vertical dimension represents the value of the sample statistic, which might be the sample mean, range, or standard deviation in the case of measurement by variables, or in the case of measurement by attributes, the number of nonconforming units, the fraction nonconforming, the number of nonconformities, or the average number of nonconformities per unit.

Typically a control chart includes three parallel horizontal lines (see illustration): a center line and two control limits. The center line (CL) intersects the vertical dimension at a value that represents the level of the process under stable conditions (natural variability only). The process level might be based on a given standard or, if no standard is available, on the current level of the process calculated as the average of an initial set of samples. The two lines above and below the center-line are called the upper control limit (UCL) and lower control limit (LCL) respectively, and they both denote the normal range of variation for the sample statistic. The control limits intersect the vertical axis such that if only the natural variability of the process is present, then the probability of a sample point falling outside the control limits and causing a false alarm is very small. Typically, control limits are located at three standard deviations from the center line on both sides. This results in a probability of a false alarm being equal to 0.0027.

The principle of operation of control charts is rather simple and consists of five general steps:

- 1. Samples are drawn from the process output at regular intervals.
- 2. A statistic is calculated from the observed values of the units in the sample; a statistic is a mathematical function computed on the basis of the values of the observations in the sample.
- 3. The value of the statistic is charted over time; any points falling outside the control limits or any other nonrandom pattern of points indicate that there has been a change in the process, either its setting or its variability.
- 4. If such change is detected, the process is stopped and an investigation is conducted to determine the causes for the change.
- 5. Once the causes of the change have been ascertained and any required corrective action has been taken, the process is resumed.

The main benefit of control charts is to provide a visual means to identify conditions where the process level or variation has changed due to an assignable cause and consequently is no longer in a state of statistical control. The visual patterns that indicate either the out-of-control state or some other condition that requires attention are known as outliers, runs of points, low variability, trends, cycles, and mixtures. *See* Control systems, Quality control