Diagramme (Control Charts) als Hilfsmittel in der SQC(Statistischen-Qualitätskontrolle)


Diese Seite ist entworfen worden, um im Verstehen und im Lernen des Gebrauches, des Designs und der Analyse von Control Charts zu helfen, die das wichtigste Hilfsmittel der statistischen Qualitätskontrolle sind.

Die Informationen sind in Form eines Tutorial formatiert worden, der Sie durch den Prozeß führt. Es umfaßt die Geschichte, die Hintergrundinformationen, den Gebrauch, die Arten mit Beispielen, Analyse der Muster, in Verbindung stehende Software und zusätzliche Quellen über Control Charts.


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Control charting ist eins der Hilfsmittel der statistischen Qualitätskontrolle(SQC). Es ist das technisch am weitesten entwickelte Hilfsmittel von SQC. Es wurde in den zwanziger Jahren vom Dr. Walter A. Shewhart den Bell Telephone Labs entwickelt.

Dr. Shewhart entwickelte die Control Charts als statistisches Verfahren zur Studie der Variation in Herstellungsverfahren mit dem Ziel der Verbesserung der ökonomischen Wirksamkeit des Prozesses. Diese Methoden basieren auf der ununterbrochenen Überwachung der Prozeßvariation.

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Background Information

A typical control chart is a graphical display of a quality characteristic that has been measured or computed from a sample versus the sample number or time. The chart contains a center line that represents the average value of the quality characteristic corresponding to the in-control state. Two other horizontal lines, called the upper control limit(UCL) and and the lower control limit(LCL) are also drawn. These control limits are chosen so that if the process is in control, nearly all of the sample points will fall between them. As long as the points plot within the control limits, the process is assumed to be in control, and no action is necessary.

However, a point that plots outside of the control limits is interpreted as evidence that the process is out of control, and investigation and corrective action is required to find and eliminate the assignable causes responsible for this behavior. The control points are connected with straight line segments for easy visualization.

Even if all the points plot inside the control limits, if they behave in a systematic or nonrandom manner, then this is an indication that the process is out of control.

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Uses of Control charts

Control chart is a device for describing in a precise manner what is meant by statistical control. Its uses are

  1. It is a proven technique for improving productivity.
  2. It is effective in defect prevention.
  3. It prevents unnecessary process adjustments.
  4. It provides diagnostic information.
  5. It provides information about process capability.

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Types of control charts

  1. Control charts for Attributes.
    1. p chart
    2. c chart
    3. u chart
  2. Control charts for Variables.
    1. X bar chart
    2. R chart

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Analysis of Patterns on Control Charts

A control chart may indicate an out-of-control condition either when one or more points fall beyond the control limits, or when the plotted points exhibit some nonrandom pattern of behavior.

The process is out of control if any one or more of the criteria is met.

  1. One or more points outside of the control limits. This pattern may indicate:
  2. A run of eight points on one side of the center line. This pattern indicates a shift in the process output from changes in the equipment, methods, or materials or a shift in the measurement system.
  3. Two of three consecutive points outside the 2-sigma warning limits but still inside the control limits. This may be the result of a large shift in the process in the equipment, methods, materials, or operator or a shift in the measurement system.
  4. Four of five consecutive points beyond the 1-sigma limits.
  5. An unusual or nonrandom pattern in the data.
    1. A trend of seven points in a row upward or downward. This may show
    2. Cycling of data can indicate
  6. Several points near a warning or control limit.

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The March issue of Quality Progress contains a directory of software packages available from different suppliers and arranged in different application categories.

The Journal of Quality Technology has published computer programs in either BASIC or FORTRAN since 1969. A selected list of programs, related to control charts, published through 1989 are in the following table.

----------------------------------------------------------------                                               Volume     PageProgram Capability                             & year     Reference----------------------------------------------------------------1.  Plotting X bar and R charts                 1/1969        1492.  Plotting p and np charts            	1/1969        2173.  Plotting c and u charts             	1/1969        285 4.  Economic design of X bar charts       	2/1970         405.  Plotting cumulative-sum control       	2/1970         54    charts6.  Plotting exponentially weighted       	5/1973         84    moving average control charts7.  ARL for cumulative-sum control        	18/1986       189    charts for controlling normal means8.  ARL for combined individual           	19/1987       103    measurement and moving-range charts9.  ARL for exponentially weighted        	19/1987       161    moving-average control charts10. New limits for X bar and R charts    	20/1988       149    sample size is changed11. Optimal design parameters of joint    	21/1989        65    X bar and R charts-----------------------------------------------------------------Source : Introduction to Statistical Quality control 
by Douglas C. Montgomery, page 252-254.

Ordinary spreadsheets like Microsoft Excel and Lotus 123 can also be used for creating the above control charts. The charts presented in the examples have been created in Microsoft Excel.

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