Sample Size for SPC Considering Alpha and Beta Risk

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    I have the luxury of population data for SPC purposes where sub-group sizes are in excess of 10,000 units. Can I use a sample size calculation that accounts for alpha and beta risk? If I use the population data I feel that the upper and lower control limits are overly sensitive (bearing in mind that I have different sized sub groups each period). Can I for example just use the standard hypothesis test approach to establishing sampling size?



    More detail may be useful in providing good advice, but it sounds like you have an issue with between-subgroup variability. Rather than mess with alpha and beta and treat a control chart like a hypothesis test, you likely should consider either your sampling plan or the variability between subgroups.

    The limits on the chart are based on the within subgroup variability, under the assumption that this is a good estimate of short-term variation that does not include process drift. Then, should your process drift off-target, it would get signalled. But when using a chart with subgroups, what can happen is that the variability between subgroups may be large relative to the variability within subgroups, and therefore you have tight limits that points regularly exceed. But that is a potential quality problem, and not necessarily a control problem as it may be common causes.

    If that sounds like your situation, you may just want to reconsider what kind of chart you use or how you subgroup.

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