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# Statistical Probabilities - How To Calculate Sample Frequencies

Posted on 2013-01-24

Hi All,

I need some help with statistical calculations - I can't remember everything from 20 years ago!

Situation:

We have a production process that has to hit a mean size with a tolerance.

Mean = 100mm

Tolerance = +/- 2mm

So therefore, an item is 'good' if it is greater than or equal to 98mm and less than or equal to 102mm, and bad if it is outside that range.

We are willing to accept a maximum 1% chance, that in a run of 10,000 units, there will be at least one item that is bad.

The production process slowly gets out of alignment (due to vibration and other factors), and has to be periodically recalibrated. The misalignment is symmetrical in terms of which way it goes out (it is just as likely to lift the mean upwards as downwards).

In order to maintain the quality, we are proposing to do the following:

Define a range with mean = 100mm, Tolerance = +/- X

where X < 2 mm

We will then sample the production output once every Y items.

If an item sampled falls outside of +/- X then the production process gets stopped, and maintenance is done to recalibrate everything back to the original status, and then restart the production process.

Ultimately, I need to calculate the sampling frequency (Y) we have to use to deliver on the objective.

I would likely be doing the calculations by putting them into an excel spreadsheet, but that seems kind of secondary - that just happens to be the brand of calculator I am using.

I suspect I need to know the Standard Deviation of the actual outputs of the process when it is freshly calibrated. If so, then my first thought is that I would need to get a sufficiently large run (100 items - perhaps more, but it has to be practical, ideally this sample size could be a parameter in the calculation of probability), have them all manually checked, and from that data, calculate an actual mean and Standard Deviation. I have been *told* that the actual output mean is 100mm, but the production people could not give me a standard deviation figure.

What I need from you is:

1) What additional information is required, in order to do the calculation

2) what is the actual calculation that I have to do to determine Y.

Please do post any queries or clarifications required.

Thanks,

Alan.