Quality control card

The control chart ( QCC ) or short control chart (Engl. "[Quality] control chart", where "chart" not really "card", but rather "graph" or "sheet" means) is in quality managementused to evaluate test data. The aim is to evaluate processes with regard to their constant quality over time (process stability). If the process changes significantly, the quality control card indicates the direction in which the change is taking place (increase in the quality spread and / or change in the position of the quality feature). For this purpose, statistical sample values (e.g. sample mean value and sample standard deviation of the quality characteristic) and warning, intervention and tolerance limits are graphically displayed.

Control charts are essential tools for statistical process control (SPC - English statistical process control ) for the optimization of production and service processes.

Types of control charts

Basically, there are control charts for the type of to be examined characteristics in control charts for variable features and control charts for attribute characteristics.

Control charts for variable characteristics

The control charts for variable characteristics include a.

the original value card
the Shewhart control chart (ImR chart according to Walter A. Shewhart)
the pre-control control card (process control cards ) and

the acceptance card

Process control cards

The process control card is a control card that does not start from predetermined limit values. The upper and lower warning limit as well as the upper and lower action limit are calculated from the existing process data; they do not reflect the tolerance range, but only the observed frequency distribution of the sample parameter monitored with the respective diagram. The warning and action limits are recalculated periodically based on the most recent process data. The process data collected on process control cards form the basis for the process capability study , in which the frequency distribution of the observed feature is compared with the tolerance range.

The main process control cards are:

Process control cards	English derivation	Graphic representation (chart) of the	mathematically	also
ImR card	I ndividual and m oving R is	Individual values over their sliding range	${\ displaystyle XmR}$	XmR card
Xbar card	X with bar (= dash )	Mean values as individual values	${\ displaystyle {\ bar {X}}}$	Xbar chart
XbarR card	Xbar and R	Mean values over their range	${\ displaystyle {\ bar {X}} R}$	Xbar R chart
XbarS card	Xbar and S	Mean values over their standard deviation	${\ displaystyle {\ bar {X}} S}$	Xbar S chart
EWMA card	E xponentially W eighted M oving A verage	exponentially weighted moving averages	${\ displaystyle EWMA}$
CUSUM control chart	Cu mulative SUM	Cumulative sums	${\ displaystyle CUSUM}$
Three-way card	Three-way chart	Interactions of three different influencing factors
z-card	z-chart		${\ displaystyle z}$	Z diagram

Control charts are also used to analyze position and scatter .

Acceptance control cards

The acceptance control card is a control card in which the action and warning limits are calculated using specified tolerance limits. The tolerance limit values indicate the maximum deviations a product may have in order to still be usable. The use of acceptance control cards contradicts the principle of continuous improvement.

Control charts for attribute characteristics

The main attribute control charts are:

Attributive control charts	English derivation	Graphic representation (chart) of the	Sample size	mathematically
p card	Proportions	Proportions, e.g. B. Proportion of defective units in a sample	variable	${\ displaystyle p}$
np card	n umber of p roportions	Number of proportions, e.g. B. Number of defective units in a sample	constant	${\ displaystyle np}$
c card		Number of events , e.g. B. Number of errors within a constant event range	constant	${\ displaystyle c}$
u card	U nit	Shares or events, e.g. B. Errors per unit examined	variable	${\ displaystyle u}$

Limit values

Warning limits and action limits

Limit values in quality control charts are represented by horizontal lines that are highlighted by color or line thickness. A distinction is made between warning and action limits , which are each above and below the mean value of the process to be controlled, which is defined as optimal.

Designation DE	Abbreviation DE	Designation EN	Abbreviation EN	Line style below
Upper control limit	OEG	Upper control limit	UCL	red, bold dashed line
Upper warning limit	OWG	Upper warning limit	UWL	red, thin dashed line
Average	${\ displaystyle {\ bar {X}}}$	Middle value	${\ displaystyle {\ bar {X}}}$	green solid line
Lower warning limit	UWG	Lower warning limit	Fiber optic	red, thin dashed line
Lower control limit	LEL	Lower control limit	LCL	red, bold dashed line

${\ displaystyle {\ bar {X}}}$ Quality control card

The distance between the two warning limits (±) and the two control limits (±) from the mean value is the same, whereby the following relationships apply if the measured value distribution obeys the Gaussian normal distribution :

UWG to OWG	95.45%	Mean value ± 2 sigma of the frequency distribution of the sample parameter shown
LEL to OEG	99.73%	Mean ± 3 sigma of the frequency distribution of the sample parameter shown

The eleventh measuring point (fifth from the right) in the control chart shown is above the upper warning limit . If an action limit were exceeded, it would be possible that the process has gotten out of control at this point. In just under 3 of approx. 1000 cases, however, the control limit is exceeded for statistical reasons (in the 3-sigma range defined above) without this necessarily meaning that the process or its parameters have changed ( ). If the warning limits are exceeded , possible, unintentional changes in the process must be looked for and, if necessary, suitable remedial measures must be taken to bring the process back into its proper state. Ideally, the process can be corrected before it gets out of control and possibly defective parts are produced. ${\ displaystyle 1-0 {,} 9973 = 0 {,} 0027}$

Decision rules

If a characteristic value z occurs within the warning limits (UWG <z <OWG), then no malfunction is to be assumed.
If a characteristic value z occurs between the warning and action limits (LEL <z <= UWG or OWG <= z <OEG), then there is a suspicion of a malfunction. Therefore, another sample is taken immediately.
If a characteristic value occurs outside the control limits (z <= LEL or z> = OEG), a malfunction is suspected and action is taken. The measures that must be taken depend on what knowledge is available about the process to be controlled and the type of fault displayed.

Tolerance limits

Tolerance limits (upper limit value (OGW) and lower limit value (UGW)) are generally not drawn on process control cards because they apply to individual characteristic values and not to the parameters shown on the control cards (sample mean values, sample ranges, etc.).

Indicator for the process

The quality control chart is also an indicator of the process in and of itself. When evaluating a quality control card, a distinction is made between random and systematic influences. Random influences lead to a scattering of the test data on the quality control card; they are caused by influencing factors such as small temperature fluctuations or material properties and are to be regarded as a normal, always present part of the process. Systematic influences can lead to a slow shift of the test data on the quality control card or to sudden, drastic process changes; they are caused by special influencing factors such as tool wear or incorrectly set machines.

Indicator for the product

The course of the measuring points of the examined parts shows the quality of the parts from the sample. This allows conclusions to be drawn about the quality of the total number of parts.

Evaluation of control charts

Systematic deviations are subject to laws. These regularities can be inferred from the course of the measuring points on the quality control card.

One speaks of a “trend” when at least seven measuring points show an almost linear gradient in the direction of a limit. There may be a strong increase in tool wear, which will soon cause the intervention or warning limit to be exceeded.

A "pattern" is a non-random curve, e.g. B. the periodic "swing" around the mean line. It can mean temperature fluctuations that cause sometimes larger and sometimes smaller parts in production.

One speaks of a run when there are 7 points drawn above or below the mean value line. In this case the process mean has probably shifted. This can e.g. B. indicate that a tool cutting edge has suffered damage and the parts are now being made larger or smaller.

So the control limits are not the only signs of potential problems; the arrangement of the measuring points must also be observed. If more than 90% of the points drawn are in the middle third of the area between the control limits or less than 40% of the points in this third, it can also be assumed that a systematic (not random) influence could be present.

Web links

Commons : Quality Control Cards - collection of images, videos and audio files

literature

Edgar Dietrich, Alfred Schulze: Statistical procedures for machine and process qualification . 6th, completely revised edition. Carl Hanser Verlag, Munich / Vienna 2009, ISBN 978-3-446-41525-6 .
Hans-Joachim Mittag: Quality control cards . Carl Hanser Verlag, Munich a. a. 1993, ISBN 3-446-17661-6 .

Individual evidence

↑ Dietrich, Schulze (2009), p. 219.
↑ Example of a Shewhart control chart
↑ QS-9000, SPC Guide
↑ Three-way chart example (PDF; 2.0 MB) Boeing
↑ Z-diagram in the ISI glossary of statistical terms
↑ Dietrich, Schulze (2009), p. 271

[1] Dietrich, Schulze (2009), p. 219.

[2] Example of a Shewhart control chart

[3] QS-9000, SPC Guide

[4] Three-way chart example (PDF; 2.0 MB) Boeing

[5] Z-diagram in the ISI glossary of statistical terms

[6] Dietrich, Schulze (2009), p. 271