Proving Process Capability of a Packing Machine

Solitude

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We are looking at proving capability on an packing process. There must be a certain quantity in a box with no variance, e.g. 50 off or 100 off. Overs (and unders) are not allowed.

I think that we should conduct a binomial study as the pack either conforms or it doesn't.

We have had some discussions about could we prove the capability over different pack sizes, but this still relies on a binomial data set really, as there is no tolerance; it either conforms or it doesn't.

Is there anything else we could do to prove or demonstrate how capable the process is please? Thanks.
 

Miner

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You could do a binomial capability and obtain a percent nonconforming as a capability. However, I would find it more useful to collect data on the actual quantities (raw or # off target). That would allow you to determine whether there was a high or low bias to the quantities as well as a frequency between miscounts. You could always convert that into binomial later and calculate a percentage.
 

Solitude

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We have run 100 boxes through the process, and we have had no defects, i.e. all boxes contain 100off items.

There is no variation in the data, so everything that gets calculated is zero, and putting the data through Minitab throws an error. Any ideas on the best way to present the data would be appreciated.
 

Miner

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Binomial capabilities take a very large sample size. With a sample size of 100, you may state that p_bar = 0 with an 95% upper confidence limit of 0.036 (3.6% nonconforming).

Increasing your sample size to 500 would reduce this to 0.007 (0.7%). Increasing to 1000 would reduce it to 0.004 (0.4%)
 

Solitude

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Thanks Miner. Could you point me in the direction of how I can calculate or work this this information out please. Thanks for your help.
 

Miner

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Attached is the method used by Minitab's Power and Sample Size calculator.
 

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