How to read the control chart Typical trends of successive point position in the control chart that are considered undesirable are shown below. These trends may indicate that a ‘special cause’ variation source is affecting the process output and that action from the process operator is required to remedy the situation. These rules only provide a guideline. Take the process-specific variation into consideration when actually making process adjustments. Assuming that the upper and the lower control limits are 3 away from the center line, divide the control chart into six regions at intervals of 1 to apply the following rules. These rules are applicable to the True, Xbar control chart. Note that these 'trend rules for action' were formulated assuming a normal distribution. Rules can be formulated to suit any other distribution.
Specific examples of a process capability index (Cp) (bilateral tolerance)
LSL
USL
This process is barely capable. Process variation is exactly equal to the 6 sigma tolerance limits.
σ
A
Cp=1
6 σ
LSL
USL
This process is generally considered capable of producing outputs that consistently meet tolerance limits. Process variation is 1 sigma less than tolerance limits. This process is easily capable of producing outputs that consistently meet tolerance limits. Process variation is 2 sigma less than tolerance limits.
σ
Cp=1.33
X + 3 X + 2 X + 1 X−1 X−2 X−3 X + 3 X + 2 X + 1 X−1 X−2 X−3 X + 3 X + 2 X + 1 X−1 X−2 X−3
X + 3 X + 2 X + 1 X−1 X−2 X−3 X + 3 X + 2 X + 1 X−1 X−2 X−3
UCL
UCL
6 σ 8 σ
X
X
LSL
USL
LCL
LCL
2) Nine consecutive points are to one side of the center line.
1) There is a point beyond either of the control limit lines (±3 ).
σ
Cp=1.67
UCL
UCL
6 σ 10 σ
X
X
Note that Cp only represents the relationship between the tolerance limits and the process variation and does not consider the position of the process mean. Note : A process capability index that takes the difference between the process mean from the target process mean into consideration is generally called Cpk, which is the upper tolerance (USL minus the mean) divided by 3 (half of process capability) or the lower tolerance (the mean value minus LSL) divided by 3 , whichever is smaller. Control chart Controls the process by separating process variation into chance cause variation and common cause variation. The control chart consists of one center line (CL) and the control limit lines statistically determined above and below it (UCL and LCL). It can be said that the process is in a state of statistical control if all points are within the upper and lower control limit lines without notable trends when the characteristic values that represent the process output are plotted. The control chart is a useful tool for controlling process output, and therefore quality.
LCL
LCL
3) Six points consecutively increase or decrease.
4) 14 points alternately increase and decrease.
X + 3 X + 2 X + 1
UCL
UCL
X
X
X−1 X−2 X−3 5) Two of three consecutive points are over ±2 from the center line on either side.
LCL
LCL
6) Four of five consecutive points are over ±1 from the center line on either side.
X + 3 X + 2 X + 1
X + 3 X + 2 X + 1
UCL
UCL
X
X
X−1 X−2 X−3 7) There are 15 consecutive points within ±1 from the center line.
X−1 X−2 X−3 8) There are eight consecutive points over ±1 from the center line.
Upper control limit (UCL)
LCL
LCL
Center line (CL)
Lower control limit (LCL)
Note: This part of 'Quick Guide to Precision Measuring Instruments' (09-31 to 09-32) has been written by Mitutoyo based on its own interpretation of the JIS Quality Control Handbook published by the Japanese Standards Association.
1
2
3
4
5
6
7
Subgroup number
Common Cause Variation Common cause of variation is of relatively low importance. Common cause variation is technologically or economically impossible to eliminate even if they can be identified. X-R control chart The process control that provides the most information on the process. The X-R control chart consists of the X control chart that uses the mean of each subgroup for control to monitor abnormal bias of the process mean and the R control chart that uses the range for control to monitor abnormal variation. Usually, both charts are used together.
References - JIS Quality Control Handbook (Japanese Standards Association) Z 8101: 1981
Z 8101-1: 1999 Z 8101-2: 1999 Z 9020: 1999 Z 9021: 1998
A-32
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