Help with Capability Issue

Hi PH,
Are you sure you are not confusing CONTROL limits with SPECIFICATION limits?
Cp is calculated from specification limits (i.e. the tolerance limits usually defined by the customer). Cp = (USL – LSL)/(6 x sigma)
Control limits (LCL/UCL) are usually calculated as part of a control chart to determine whether the process is in statistical control or not and have nothing to do with process capability.
Bear in mind also that the calculation of both Cp and your control limits require that your data be normally distributed.

means you have a lot of variation in the process and possibly a bi modal distribution. can you uplolad the data file on this forum?

What is your target value – what are you shooting for?

Hi,
looking a bit more at the data, could it be that you took the measurements during the startup of the process? It sure looks  like some kind of transient to me.
Regards
Sandor

Hi PH
As others have said, there is a “problem” with oscillation in this data, however you never said that the data was actually time-ordered.
A more fundamental problem is that you have spec limits expressed to 2 decimal places and data accurate to only 1 decimal place.
It also strikes me as very odd that your minimum measure is 1.3 (your LSL rounded to 1dp) and your maximum measure is 2.8 (your USL rounded to 1dp). With 80 measures in your sample this strikes me as more than coincidental.
Is your process actually capable of producing a measurement outside these spec limits?
Is whoever is taking the measures perhaps rejecting out-of-spec parts without your knowledge?
Have you already performed a Gage R&R on  your measurement system?
Personally I think your data are suspect and I would fix that before worrying about capability or any other apparent issue (e.g. the oscillation).
Perhaps if you posted a bit more background about your process and measurement system?

I agree Adrian…this data somehow seems to be “made up” …. or the measurement system needs refinement. But to answer your original question, the Cp that you calculated was correct but the distribution is not normal, so you cannot really use Normal dist.

Ok, looks like we’re back in business.
  1. If we assume the data is time ordered then the pattern that emerges is interesting in that the process seems to be converging to a target of around 2. 
   2. Even if the data isn’t time ordered the distribution is definitely truncated.  The truncation makes the data non-normal, however, the truncation also answers the questions raised in the initial post – all of the data for this “sample” is indeed between the limits however, the capability calculation is assuming a normal distribution.  If this is a truncated normal then the actual process will make a lot of product outside the limits.  This high probability of out of spec material is reflected in the initial capability calculations.
  I agree with the other posters – the odd nature of the data suggests you need to do a lot more investigation before you try to do a capability calculation.

you took all the measurements yourself ?????? That woudnt be a R&R then…It would be more like capability study…

just checking !!!!

PH:

PH: This is fascinating problem. You can get your process to Cp
~ 1.25 – 1.36 without much effort. You have a clear drift of the position of a
labels that is masked by the way the data was collected.. 1)     
Your data has some negative kurtosis. The tails of the
distribution are fatter then you would expect for a normal distribution. This
will result in a standard deviation that is larger than it would be for a
normal distribution with about the similar range.2)     
This may be due to a natural limit on the low side of 1.3 and
on the high side at 2.7. The tails are a bit chopped off.3)     
The entire set of data has a great deal of autocorrelation.
Calculate the partial autocorrelation in Minitab to see that the Pearson’s
correlation is –0.846 (p-value 0.000).
This shows up in the run chart as the oscillation. This is a natural
consequence of taking measurements on both sides of the same label.4)     
There is ‘some’ problem with the resolution of the gauge, but
it is not a serious one. The problems would only get a bit more clear with an
extra decimal place.5)     
Label the measurements as “left” and “right” for each
measurement of the label.6)     
Do a probability plot broken out by left/right and you will
see the lurking problem. The distribution of each measurement subgroup is much
tighter than then the overall dataset. 

N

Mean

StDev

Cp

Entire set

40

1.9738

0.4046

0.42

Left

20

2.3100

0.2468

1.36

Right

20

1.6375

0.1970

1.25

7)     
When you use the entire dataset, you have two normal
distributions on either side of the target that combine to make a wide,
somewhat uniform distribution. It is well centred, but wide because you are
combining both left and right measurements.8)     
The sum of the two measurement (left and right) is fairly
constant, as you would expect.9)     
The difference of the two measurements, however, shows a clear
trend, the centre of the labels has drifted 0.90 mm from the beginning to the
end of the run. Send me an email address to [email protected] and I can send you
the entire session file from Minitab14. Cheers, BTDT

Cp only focuses on the process spread without considering the spec limits. Compute for Cpk to see how it fits with the spec limits.
Also, you may want to check how you have gathered the data. It must not combine apples with oranges, only for those with same parameters.
Aside from that, check the normality of the data, it seems not to be normal.