Shewhart control chart

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The Shewhart control chart is one of the oldest quality control charts for statistical process control, which was developed by the American physicist of the Bell Telephone Company Walter A. Shewhart in 1924. It is used for quality control in controlled processes, in order to maintain the prevailing state and to indicate changes that occur.

history

Overview

20s Start of using statistics in industry and quality control based on the principles of WA Shewhart and RA Fisher (1890–1962). These include statistical design of experiments (DOE) and statistical quality control.
1931 Publication of the work "Economic Control of Quality of Manufactured Product" by WA Shewhart.
1932 WA Shewhart gives lectures at the University of London on statistical methods in production and quality control cards.
Second World War The US military procurement offices called for the introduction of the statistical method for process control in the arms industry and its suppliers. This was the beginning of the diffusion of process control by statistical methods in industry.

development

The decisive factor for Shewhart's findings was the discovery by Carl Friedrich Gauß that the deviations of the individual values ​​from the mean value are subject to a certain regularity. Shewhart applied this knowledge to the individual values ​​of an ongoing production process and noticed that not all deviations were subject to this law. This led him to the realization that the cause of the deviations must have two reasons, on the one hand random influences ("chance causes") and on the other hand systematic influences ("assignable causes"). The random influences are part of the normal distribution and cannot be changed, while the systematic influences are errors in production. These had to be identified and eliminated in order to obtain an optimal production process. The result is the ideally mastered process. However, first of all it is necessary to differentiate between the systematic and the random influences. Shewhart achieved this by developing a "control chart". To do this, he collected samples from an ongoing production process, which he graphically displayed together with the mean value and the deviations in chronological order. The results from a previous process provided him with the basis for calculating limit values. If a test value was within the limit, it could be assumed that its deviation from the mean value was subject to a random influence. However, if the test value was above or below the limit values, the probability that it was a systematic error was high. Exceeding a limit value was therefore a clear indication of an error in production. These findings resulted in great progress in measurement and control technology . Without it, it would not be possible today to quantitatively measure the ongoing production processes in-line and in-time and thus intervene during the ongoing process.

use

Shewhart quality control cards are used for controlled processes which are already considered satisfactory and whose condition should continue to be maintained. The state is viewed as the target state and the quality control card is used to display changes that occur. Either the mean or the median acts as the position parameter, while the standard deviation or the range are used as the parameter for the variance . Shewhart quality control charts are also used when the process mean is constant or changes randomly or predictably. The Shewhart quality control card reacts sensitively to large and short-term changes.

Types of Shewhart Control Charts

  1. Shewhart quality control cards for meter characteristics
    • np chart (quality control chart for the number of defective units in samples)
    • p chart (quality control chart for the proportion of defective units in samples)
    • c-chart (quality control chart for the number of defects per sample)
  2. Shewhart quality control charts for continuous features
    • X̅ track (mean value track)
    • x̃ track (median track)
    • X track (original value track)
    • s-trace (standard deviation trace)
    • R-track (span-width track)

Structure of a Shewhart control chart

Samples of a certain size n are taken at specified times at regular intervals. Quality features are measured . The measured values ​​X of these quality features are either summarized in a vector x as individual values and thus also used further or they are condensed into a sample function, such as E.g .: the mean, the median, the standard deviation or the range. On the form, the serial numbers of the samples are shown on the abscissa and the measured values ​​or the sample function on the ordinate. The coordinate system on the form also usually contains a center line M. This can be described as the target value to which the process is to be controlled. This value can be determined in various ways. On the one hand, the target value can be a setpoint value from predetermined regulations. On the other hand, it can be an empirical value from earlier investigations of the undisturbed process. Or it can be an estimate from a preliminary run. The warning and action limits are an important part of the quality control card. There are quality control cards with one or two warning and action limits each. One is below and the other above the center line. Due to the position of the entered test values ​​in relation to the warning and action limits, there are three options that involve various actions that must be specified beforehand. Most of the time one proceeds as follows:

1. The sample finding is within the warning limit
The manufacturing process is undisturbed, no intervention is necessary.
2. The sample finding lies between the warning and action limits
There is a suspicion of a disruption in the process. The manufacturing process is now subject to increased attention. To investigate the suspicion, additional
Samples are taken. If these are between the warning limits, the suspicion is not confirmed. However, if the additional sample finding is outside the warning limit, the suspicion is confirmed and the process is interfered with.
3. The sample finding is outside the control limits
It can be assumed that the manufacturing process is disrupted and intervention is necessary. You may also need the products since the last sample was taken
be checked again.
Example image: Structure of the Shewhart control chart

Create a Shewhart control chart

The two most important points to consider when creating a quality control chart are that you choose a suitable sample size and a reasonable time interval in which the samples are taken. It is also important to set sensible warning and action limits. When choosing the sample size and the time intervals, the costs play an important role. If, for example, the distances are selected too short, the test costs increase, as do the costs incurred in the event of an interruption in production due to an intervention. If the intervals are too long, however, increased costs can arise due to undetected faults. If the sample size is too large, the testing costs would also increase. Mostly one orientates oneself here on the experience values.

With the warning and action limits, the difficulty lies in the position of the limits to the center line M. If they are too close to M, the probability of a blind alarm is increased. But if they are too far away from M, the probability increases that a disturbance will be recognized too late. Here one orientates oneself mostly on pure statistical criteria.

As a rule, the warning limits are set in such a way that the test values ​​lie within the warning limit with a probability of 95%. The control limits are set in such a way that the test values ​​lie within the control limits with a probability of 99%. This results in the probability α with which the test values ​​reach or exceed the limits, 0.05 for the warning limits and 0.01 for the control limits. If you set two limits, an upper and a lower limit, which should have the same distance from M (in this case the expected value ), the probability α / 2 results for each of them. This would result in a probability of 0.025 for the upper and lower warning limits and a probability of 0.005 for the upper and lower control limits.

Another possibility is to set the warning and action limits using the standard deviation. With a sample function Y, which has an expected value µY (value of M) and a standard deviation ơY in an undisturbed process, the warning limits result from the values ​​µY ± 2ơY and the control limits from the values ​​µY ± 3ơY.

literature

  • Shewhart control chart. at: faes.de , accessed on June 5, 2016.
  • German Society for Quality eV (publisher): SPC2 quality control card technology (DGQ writing No. 16-32). 4th edition. Beuth Verlag, Berlin / Cologne 1992, ISBN 3-410-32827-0 .
  • Gerhard Linß: Quality management for engineers. 3. Edition. Hanser Verlag, 2011, ISBN 978-3-446-41784-7 .
  • Herbert Vogt: Methods of Statistical Quality Control. BG Teubner, Stuttgart 1988, ISBN 3-519-02627-9 .
  • Horst Rinne, Hans-Joachim Mittag: Statistical methods of quality assurance. Hanser Verlag, Munich / Vienna 1989, ISBN 3-446-15503-1 .
  • Tilo Pfeifer, Robert Schmitt: Masing handbook quality management. 6th edition. Hanser Verlag, 2014, ISBN 978-3-446-43431-8 .

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