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Capability for low sample sizes

Capability for low sample sizes

Capability for low sample sizes

Are there any correction factor for calculating capability when samples sizes are low?

Here I am talking about 10~12 samples. The industry I am operating produces parts at a rate of 10~12 per month. So, waiting for 30 parts is taking too long a time to assess capability.



RE: Capability for low sample sizes

You may want to look at an "individuals control chart".  It uses a moving range of two successive observations to estimate the process variability.

RE: Capability for low sample sizes

The more samples you have the smaller the window of uncertainty.  I wrote a quality control monitoring system for a press once.  I used a circular queue of readings.  The queue length was determined by tightly or small a window I needed.  The advantage I had was that I could update the mean and the standard deviation after each part.  That provided very quick response. Even so my test was not what I would do now.  Now I would take into account the rate of change in the mean readings.

It would be better if you said exactly what you wanted to do.

RE: Capability for low sample sizes

Hello everybody,

I am looking for calculating Cpk or Ppk with limited  (10~12) data points.

I do understand about Individuals control chart, which I plan to use for assessing the out of control situations. But that will not tell me much about capability. And also it is a very long process considering our output rate of 10~12 pcs per month.



RE: Capability for low sample sizes

Admittedly, I haven't bothered to review the calculations for process capability (C/Pp, C/Pk, & C/Ppk) is quite some time, but from what I remember, the calculations are based on the number of sample.  In other words, you should be able to get a value with 10-12 samples.

It also depends on your USL and LSL, right?  If your LSL is 0.00 and your USL is 10.00, and you measure 10 pieces that are normally distributed about 5.00 with a standard deviation of 0.25, the C/Ppk value may be close to your overall process C/Ppk (assuming NOTHING changes in your system).  However, if you are butted right up to one of the spec limits, then you will need to bite the bullet and wait for more samples.  I understand you want to get the answer right away, but you need the appropriate amount of data to do your job, right?

Confidence is directly proportional to number of data points.  The more valid data you can analyze, the higher the confidence in the calculated values.

RE: Capability for low sample sizes


I think you need to go back to whoever is asking for this and check that they really know what they are asking for.

You can certainly do some maths to indicate process capability and potential with such a small sample size, but your confidence that it is a good estimate will be low.

Process potential for a stable bilateral process is just the tolerance band divided by (the standard deviation of the measurements times a fudge factor (6)) is it not?

Process capability is similar using the mean and the closest tolerance limit, and a fudge factor of 3.

All from memory. Then you can do some heavy stats to indicate the confidence of your answer, at which point you will decide that plotting a run chart and a histogram has as much information and a lesser veneer of bullshit.

For a start - how can you prove that your process is stable with only 12 samples? How can you prove that your process is normally distributed with only 12 samples? You can't and you can't, so you shouldn't even be using normal SPC tools.



Greg Locock

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RE: Capability for low sample sizes

GregLocock is absolutely correct. Before you can do a capability study you have to determine if the process is under control. If the process is not under control all the calculations for SPC are meaningless.

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