As this question is being asked more and more frequently, the origin of the target values for capability indices should be explained here. (1,33; 1,67; 2,00)
A classic normal distribution is considered. If we were to calculate the normal distribution using the classic formula, this would be the formula for the C value: The tolerance width divided by 6 times the standard deviations:
Now you make an assumption: you want the tolerance to be as wide as 8s. This means that 8s should at least fit within the tolerance. In other words, 99.9937% of the measured values should at least be within the tolerance.
The s can be shortened, and the 8/6 becomes 4/3 becomes 1.33
So if the specification limits are exactly on the +-4s quantile limits, the capability of 1.33 has been achieved exactly:
Or there is the requirement that the tolerance should be at least as wide as 10s (i.e. 99.99994266% of the values should be at least within the tolerance)
So if the specification limits are exactly on the +-5s quantile limits, the capability of 1.67 has been achieved exactly:
This is the answer to the frequently asked question "But we wanted to calculate our C values with +-4s?" That is not possible. The denominator of the formula cannot be changed. But the target value to be achieved can.