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Cp (capability process)
The Cp index describes process capability; it is the number of times the spread of the process fits into the tolerance width. The higher the value of Cp, the better the process.
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Example: if Cp = 2.5, the spread of the process fits 2½ times into the tolerance width, while Cp = 1 means that the spread is equal to the tolerance width.
Note that even if the spread is off-centre, it is still the same size (Cp index). The figure takes no account of where the spread is positioned in relation to the upper and lower tolerance limits, but simply expresses the relation ship between the width of the spread and the tolerance width (see Fig. 3).
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Cm (capability machine)
The Cm index describes machine capability; it is the number of times the spread of the machine fits into the tolerance width. The higher the value of Cm, the better the machine.
Example: if Cm = 2.5, the spread fits 2½ times into the tolerance width, while Cm = 1 means that the spread is equal to the tolerance width.
Note that even if the spread is off-centre, it is still the same size (Cm index). The figure takes no account of where the spread is positioned in relation to the upper and lower tolerance limits, but simply expresses the relation ship between the width of the spread and the tolerance width (see Fig. 1).
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Cpk (capability process index)
If you also want to study the position of the process in relation to the tolerance limits, you use the Cpk index, which describes the process capability corrected for position. It is not much use having a high Cp index if the process setting is way off centre in relation to the middle of the tolerance range.
A high Cpk index means, then, that you have a good process with a small spread in relation to the tolerance width, and also that it is well centred within that width. If Cpk is equal to Cp, the process is set to produce exactly in the middle of the tolerance range (see Fig. 4).
A normal requirement is that Cpk should be at least 1.33.
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Cmk (capability machine index)
If you also want to study the position of the machine’s capability in relation to the tolerance limits, you use the Cmk index, which describes the capability corrected for position. It is not much use having a high Cm index if the machine setting is way off centre in relation to the middle of the tolerance range.
A high Cmk index means, then, that you have a good machine with a small spread in relation to the tolerance width, and also that it is well centred within that width. If Cmk is equal to Cm, the machine is set to produce exactly in the middle of the tolerance range (see Fig. 2).
A normal requirement is that Cmk should be at least 1.67.
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Control limits
Control limits are an important aspect of statistical process control. They have nothing to do with tolerance limits, because they are designed to call your attention when the process changes its behaviour.
An important principle is that control limits are used along with the mean value on the control graph to control the process, unlike tolerance limits, which are used along with individual measurements to determine whether a given part meets specifications or not.
The function of control limits is to centre the process on the target value, which is usually the same as the middle of the tolerance width, and to show where the limit of a stable process lies. This means, in principle, that you have no reason to react until the control chart signals certain behaviour.
A commonly used control graph is the XR graph, where the position and spread of the process are monitored with the help of sub groups and control limits.
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If a point falls outside a control limit on the X graph, the position of the process has changed (see Fig. 16).
If a point falls outside a control limit on the R graph, the spread of the process has changed (see Fig. 17).
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