You should not try to force fit the data to a Normal. The distribution is enherited of the process, so if it is not normal, you should use your six sima knowledge to apply it to the actual distribution of your data. Six sigma is not limited to normal distributions.
Build a confidence interval on the parameter, based on the distribution of your data. It can be constructed for any distribution, the normal is just the most documented test. Process capability will seem pretty straight forward once you build your confidence interval… make sure you understand the percentiles obtained from your distribution fit.
In addition, you can make your cualitative information very quantitative by using any of these:
– Number of successes or failures to comply within a fixed standard
– Time between failures
– Average cycle time
– % of occurrences within time standards
– % of occurrences within (or outside) customer-defined “good, bad, medium”
– Cost and/or…[Read more]
There is a special case for what you are tryin to do. Arrivals are best studied by its reciprocal, the time between arrivals, which ties up with another interesting effect (which you have discussed earlier, with other words – the effect of the day, hour – peak interval): stationary rates of arrival. To fully understand your process, y…[Read more]
Then, you must certainly perform a process capability study based on individual information. Most QA texts will tell you how to do this if the population is distributed normal. There are twists, not so complicated, to the formulae in order find the capability of any process distribution, but you must perform a goodness of fit test. My…[Read more]
As very well noted by Robert, there may be some other distributions that you can use to build process capability study. Let me check, but I don’t know how convenient a non-parametric may be, specially for a filling process, which – I guess – may be a good candidate for a parametric index. A quick way to overcome the limitation on…[Read more]
In theory, yes. Nevertheless, increasing significance implies getting more and more demanding on the results of the test. In other words, it will require a bigger sample size and fewer observations out of the “normal” bins, for instance, for a chi-square goodness of fit test. What the general formulae ensure is that, given a significance level,…[Read more]
Your assumptions about the fit are somehow misleading. Your type II error, yes it is not controllable, however all documented tests for normality rely basically in minimizing this type of error. So you can actually perform, to a ceirtain degree of confidence, some goodness of fit test knowing that your type II error has already been minimized (by…[Read more]