# SPC Help - Probability of SL=CL

L

Spc

Hi all
I have a question, how about the probability of SL=CL in SPC study?
SL=specific limit CL=cernter limit

Any inputs appreciated.

K

#### ksanders

Do you mean specification limit? If so, is you question whether or not this can happen?

L

yes, that's my question.

#### SteelMaiden

##### Super Moderator
Trusted Information Resource
In simplest terms (don't want to fire up any big debates) yes, your process can be running and centered on your specification limit. It's not a good thing, but it could happen. If your process is centered on the spec limit, it means that (around) half of what you are producing is out of spec.

K

#### ksanders

With SPC, almost anything is possible. If the process average is shifted away from nominal to a point where it becomes equal to one of the specification limits, the result is a Cpk of zero (0), and 50% of the product is being produced outside of the specification limit. Take a look at the Cp value. If the Cp value is within normally acceptable limits (1.00 or larger), then there is hope. The process average can be shifted to the print nominal, and your process will again be producing most of it's product within specification. Further refinement of the process will result in larger values for both Cp and Cpk, increading your capability.

Basic rules for Capability Ratio's Cp and Cpk:

1. Cp tell the process potential (if it were centered). This is the best your process can do at it's current state.
2. Cpk tell you how your process is currently running against it's potential.
3. Cpk can never exceed Cp. If Cpk and Cp are equal, your process is perfectly centered within the specification. Any differences between the two, is an indication of how well your process is centered within specification.
4. A Cpk of 1.33 indicates that ±4 sigma are within the specification limits.
5. A Cpk of 1.00 indicates that ±3 sigma are within the specification limits.
6. A Cpk of zero (0) indicates that nominal is equal to one of the specification limits. (At least 50% nonconforming)
7. A negative Cpk indicates that nominal is outside the specification limits. (>50% nonconforming)

I hope this will help.

L

Originally posted by SteelMaiden
In simplest terms (don't want to fire up any big debates) yes, your process can be running and centered on your specification limit. It's not a good thing, but it could happen. If your process is centered on the spec limit, it means that (around) half of what you are producing is out of spec.

In this situation, how many Sigma does it imply?

K

#### ksanders

Sigma is based on the variation present in the samples collected and is used to calculate the capability indecies. Capability doesn't imply sigma, it is a result of sigma as it relates to the process tolerance. The larger the tolerance relative to sigma, the better the capability. The larger the sigma relative to the tolerance, the worse the capability.

L