Control charts They are a graphical tool used to measure the variability of a process. It consists of assessing whether the process is under control or out of control, based on calculated statistical control limits. There are graphics for variables and to attributes. For the moment we will see the creation of control charts by variables.
In this article you will find:
Control charts by variables
They measure a continuous characteristic, that is, it can take infinite values within an interval. The most used in quality control is the X-R chart, which records the mean of the process and the path or range of each sample and is used to control and analyze a process using values related to product quality such as temperature, weight, volume, concentration, etc..
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In its construction, it is necessary to draw up a graph for the mean sample values and another graph for the routes. The first indicates whether there are changes in the central tendency of a process and the second
Steps to follow for its construction:
- Data collection and registration
It is necessary to collect the maximum possible number of data, at least 100 recent data on the characteristic that the process is controlled, however when you cannot have so much data, 50 or 20 data are enough. The sample size (n) and the number of samples (k) must be determined. - Calculate the mean and runs of the samples
The mean of each sample and the routes or ranges of each of them are calculated. Then the general average is determined with the means of each sample and the average route with the routes of each one. - Calculate control limits
For each graph we must calculate the upper and lower control limits. These control limits are calculated at plus minus 3 deviations from the average by considering that the distribution of means follows a normal distribution or close to it, when the sample has a size greater than 4.
For the mean graph:
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Central limit: equal to the average of the means
Upper control limit: mean of means + A2 * Average Ranks
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Lower Control Limit: Average of Means - A2 * Average Ranks
For the Ranges chart:
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Central limit: equal to the average of the Ranges
Upper control limit: D4 * Average Ranks
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Lower control limit: D3 * Average Ranks
Where to2, D4 and D3 are coefficients whose value depends on the size of the sample (n). The following table shows the values of these for the calculation of the 3sigma control limits of both graphs.
Control chart example:
