For some dumb reason I was thinking that Target Index normalized on the Spec window, and I'm realizing now that it normalizes on the within sigma, which is a problem as I have a lot of mathematically significant signals that aren't practically significant. So, couple quick questions.
- If you provide a specified sigma will the Target Index use that instead of within? That will at least standardize the noramlizing factor
- The spec centered mean seems more in line with what I'm looking for, but its not in absolute terms. Is there a way to modify it to pull the absolute value into the process screening table?
Hi,
From the help documentation:
Target Index
The number of short-term standard deviations that the process average differs from the target value. This measures the ability of the process to hit the target value. The Target Index is calculated as 3(Cp - Cpk). A target index is considered poor if above 1, marginal if between 0.5 and 1, and adequate if less than 0.5. See White et al. (2018).
So as Target Index is calculated from the Cp and Cpk it is therefore a function of the size of the spec window.
Does that sound correct?
Regards,
Phil
So the thing is that while Cp and Cpk are technically in the formula, in practice they end up cancelling themselves out and the results are only dependent on sigma-within and the difference between the target value and the mean. It isn't affected at all by the spec limits themselves.
I tried walking through the math by hand and it looks like the USL and LSL don't show up in the final formula, but to be honest I am not the best at this kind of math and not super sure how to write it out here meaningfully anyways.
But just to show what I mean, take a look here
So in this case my system has a T = 0 with spec at +/- 2. The mean is at 0.03, and the PPK/CPK are both beautiful on this, but the target index is flagging.
Alternatively take a look at this. Same T same USL/LSL
In this case the Target Index is better (not great, but better), but the Mean is much much farther off target.
The reason why is because of the Sigma-Within in the first case is extremely narrow, wherease it's much worse in the second case.
Further proof. Let's change the USL/LSL size to +/- 3 for those two
Here is the first
Here is the second
Note that the PPK and CPK both improve, as would be expected since the spec window has opened up farther. Yet the Target Index did not change at all.
Therefore: The target index is independent of the spec window (assuming that the Target = (USL + LSL/2))
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This isn't to say that the Target Index isn't useful. But really you're effectively just z-scoring your data. How many sigma-withins is your mean away from your target. In my case the target is 0, so the Mean = x-bar.
So by that logic TI = Mean / Sigma-Within So in the TI = 1.58 case I have 0.0353/0.01933 = 1.5794
For the second case TI = Mean/Sigma-Within = 0.6648
Now if your target <> 0 then you would have to subtract the Target from the Mean. But either way USL and LSL are not part of the equation.
Edit: If anyone wants to test just use the Semiconductor Capability sample set. Change the USL/LSL however you want. As far as I can tell it doesn't affect the TI.
I went ahead and re-tried the derivation just to check. T = target. We're also assuming that the Target is centered in the process. That was needed for this derivation to work. Wasn't sure how it works with a non-centered target. Also I only solved it for Cpl, but I'm fairly certain the only difference on Cpu is that it flips the sign which is how TI always stays positive. I'd say there's a 50/50 chance i messed up the math here. But from what I can tell it looks like the USL/LSL fall out.
