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Calculation
a) Standard Deviation (s) is calculated as follows:
√∑(X - Xi)2
n-1
For bilateral tolerances:
i) Capability Index (Cp) = USL - LSL / 6s
ii) Performance Index or Centering of Process (CmK) =
Minimum of USL- X or X - LSL
3s 3s
For single sided tolerances:
i) Performance Index or Centering of Process (CpK) =
a) Find out minimum observed value from the data values.
b) Find out Z = X - Minimum Observed Value
s
c) Corresponding to the arrived value of 'Z' above, choose the value of 'k' from Table given in Annexure-I.
d) Find out CmK = USL - X or X - LSL
ks ks
as the case may be.
USL for runout, roundness, surface finish etc.
LSL for Min. Hardness
M.Ananthakrishnan
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What is the definition of Cp and Cpk in Statistical process control?
Cp is the capability of a process and Cpk is the actual capability of a part running in the process. The only way Cp = Cpk is if the process mean is exactly centered which is seldom the case in manufacturing. Therefore, Cp > or = to Cpk.
Relation between control limits and specification limits?
There is no direct relationship between control limits and specification limits. By saying that I mean that one measure has no effect on the other. However, the comparison of these two ranges can tell you a lot about your ability to meet specification. These terms are most often used, and are thus easiest to explain, in terms of manufacturing a part. Let us assume that we need to cut a piece of metal bar to a length of one inch. Specification limits tell us what variance is acceptable, either to us or our customer, when we produce the said part. The request for such a part would be accompanied by tolerances and might look something like 1.00" +/- 0.005". This means a part that is between 0.995" and 1.005" in length would be considered acceptable. The two acceptable extremes just cited would be our spec limits. Subtracting one from the other we arrive at a spec width of 0.010". Now, control limits are strictly a function of the natural variation of the process in question and are calculated using the measured standard deviation of that process. If the control limits fall inside the spec width, let us say we have an LCL of 0.998" and an UCL of 1.002" for our example, then we have process that is very capable of producing in spec parts almost every time. However, if the control limits fall outside the spec limits, maybe 0.990" and 1.010", then the natural variation present in our process causes us to make many parts that will not fall within the required specification. In other words, the process is not capable. The question about the relationship between spec limits and control limits really comes down to a question about process capability. This was just the briefest of intros to the subject. I suggest further reading (or googling) on the subject of capability (Cp &Cpk).
