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Specific examples of a process capability index (Cp) (bilateral tolerance) How to Read the Control Chart
LSL USL Typical trends of successive point position in the control chart that are
considered undesirable are shown below. These trends are taken to mean
The process capability is that a ‘special cause’ is affecting the process output and that action from the A
barely achieved as the process operator is required to remedy the situation. These determination rules
Cp = 1 6 sigma process limits only provide a guideline. Take the process-specific variation into consideration
are coincident with the when actually making determination rules. Assuming that the upper and the
6 tolerance limits. lower control limits are 3s away from the centreline, divide the control chart
into six regions at intervals of 1s to apply the following rules. These rules
LSL USL are applicable to the X control chart and the X control chart. Note that these
'trend rules for action' were formulated assuming a normal distribution. Rules
Cp = 1.33 The process capability is can be formulated to suit any other distribution.
the minimum value that
6 can be generally accepted UCL X + 3 UCL X + 3
8 as it is no closer than 1 X + 2 X + 2
sigma to the tolerance X + 1 X + 1
limits.
X X
LSL USL
X - 1 X - 1
Cp = 1.67 The process capability X - 2 X - 2
is sufficient as it is no LCL X - 3 LCL X - 3
closer than 2 sigma to the (1) There is a point beyond either of (2) Nine consecutive points are to
tolerance limits. the control limit lines (±3). one side of the centreline.
6 UCL X + 3 UCL X + 3
10 X + 2 X + 2
X + 1 X X + 1
Note that Cp only represents the relationship between the tolerance limits
and the process dispersion and does not consider the position of the process X LCL X - 1
mean. (4) 14 points alternately increase X - 2
X - 1 and decrease. X - 3
X - 2
Notes: A process capability index that takes the difference between the LCL X - 3
process mean from the target process mean into consideration is (3) Six points consecutively increase
generally called Cpk, which is the upper tolerance (USL minus the or decrease.
mean) divided by 3s (half of process capability) or the lower tolerance
(the mean value minus LSL) divided by 3s, whichever is smaller. UCL X + 3 UCL X + 3
X + 2
Control Chart X + 1 X + 2
Used to control the process by separating the process variation into that due X X + 1
to chance causes and that due to a malfunction. The control chart consists of X
one centreline (CL) and the control limit lines rationally determined above and X - 1
below it (UCL and LCL). It can be said that the process is in a state of statistical X - 2 X - 1
control if all points are within the upper and lower control limit lines without LCL X - 3
notable trends when the characteristic values that represent the process (5) Two of three consecutive points are over X - 2
output are plotted. The control chart is a useful tool for controlling process ±2 from the centreline on either side. LCL X - 3
output, and therefore quality.
(6) Four of five consecutive points are over
±1 from the centreline on either side.
Upper control limit (UCL) UCL X + 3 UCL X + 3
X + 2
X + 1 X + 2
X X + 1
X
X - 1
X - 2 X - 1
LCL X - 3 X - 2
(7) There are 15 consecutive points within LCL X - 3
±1 from the centreline. (8) There are eight consecutive points over
±1 from the centreline.
Centreline (CL)
Lower control limit (LCL) Note: This part of 'Quick Guide to Quality Control' (A-21 to A-22) has been
written by Mitutoyo based on its own interpretation of the JIS Quality
12 34 567 Control Handbook published by the Japanese Standards Association.
Subgroup number
References
Chance Causes - JIS Quality Control Handbook (Japanese Standards Association)
These causes of variation are of relatively low importance. Chance causes are Z 8101: 1981
technologically or economically impossible to eliminate even if they can be Z 8101-1: 1999
identified. Z 8101-2: 1999
Z 9020: 1999
X-R Control Chart Z 9021: 1998
A control chart used for 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.
A-22
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