Control charts
I wanted to help explore the implications of changing sample size for a quality control process aimed at determining the defect rate in multiple sites. Defect in this particular case is binary ie the products are either good or not. Much of the advice on this in the quality control literature strikes me as rather abstract and technical, while still not sufficiently detailed on what really needs to be done for power calculations. My idea was to instead let an end user see in advance what sort of thing they would see if they went into the exercise with different sample sizes.
The result was this interactive R/Shiny/ggvis web app:
I’m not an expert in statistical quality control by any means, but the statistics are straightforward. The “p-chart” is simply a time series of the proportion of recorded defects in samples taken over time, compared to horizontal lines for the central tendency of the process “under control” and upper and lower limits of acceptability before being seen as “our of control”. When they exceed some margin – typically three standard deviations, but see below – beyond some central acceptable target you conclude there’s strong evidence of something going wrong in that particular process at that particular point of time. Of course, about 3 times in 1,000 if the true defect rate is bang on the target you’ll still get that “three standard deviations too big” threshold, but that’s deemed an acceptable false positive rate.
3 x sigma versus exact binomial
Coming to this for the first time from a more general statistics backgroun, I raised an eyebrow at the “Six Sigma” approach of just making an Upper Control Limit (UCL) of 3 standard deviations away from the general population. This rule of thumb comes from …read more
Source:: r-bloggers.com