Control limits are used to analyze production processes and represent the widest variation considered statistically normal. The limits are calculated by determining the standard deviation and are used as a signal for potential production issues. Companies may also set their own thresholds for quality or practical reasons.
Control limits are a tool used in the graphical analysis of a production process. Control limits represent the widest variation in the results of the production process that would be considered statistically normal; a violation of these limits suggests a likely problem with the production process. Control limits are different from the arbitrary limits a company can set to ensure quality or customer satisfaction.
The use of control limits simply involves measuring individual results from a production process that are intended to be consistent. For example, a widget factory might measure its widgets to ensure that they are all the same size, or at least very similar. Depending on the company’s resources, it can measure all widgets or simply collect a representative sample. This sample would have to cover all possible input variables such as different machines, different batches of raw materials and different operating staff.
Calculating the control limit first involves calculating the standard deviation. This is a mathematical process based on a large sample of data, for example a whole batch of widgets. Standard deviation uses a mathematical formula that calculates the average degree to which a single unit varies from the overall mean. In this example, it would be the average amount by which the size of any randomly selected widget varies in size relative to the average of the entire batch. Therefore, the standard deviation indicates how close is identical or how much varies an entire lot.
The control limit is plus or minus three times the mean change. If the average widget is 10 inches (25.4 cm) wide and the standard deviation is 0.1 inches (2.5 mm), then the control limits are 10.3 inches (26.2 cm) and 9.7 inches (24.6 cm). Statistically, with any production process – not just this widget example – 99.73% of the units will fall within the control limits.
The idea of these limits is to act as a signal that the results are statistically unusual and therefore there may be a production problem. Every time a result falls outside the limits, it acts as a signal. Therefore, if any widget is measured larger than 10.3 inches or smaller than 9.7 inches, it should initiate an investigation into potential issues.
It is important to remember that the definition of control limits is a purely statistical process: a product that exceeds the limits is not necessarily of good or bad quality. Companies often set their own thresholds to monitor based on qualitative or quantitative factors. The widget company may decide to keep all widgets between 9.7 inches (24.6 cm) and 10.3 inches (26.2 cm) for the sake of quality. As a separate example, the company may be forced to keep all widgets between 9.9 inches (25.1 cm) and 10.1 inches (25.6 cm) because otherwise they would not fit into the used widget packages. for delivery. These limits, chosen by the manufacturer, are known as tolerance limits or simply specifications.
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