Shewhart Charts And Serially Recorded Data

摘要

In the early 1920s Walter Shewhart began to use statistical tools to solve product quality problems. Mass produced items were randomly sampled and measured by hand, and the observations averaged. These averages became points sequentially plotted on a chart that, when combined with a measure of common cause variability, allowed quality technicians to monitor and judge future sample averages. Thus, the Shewhart chart was born, and it continues to be a widely employed statistical tool. Eighty years have now passed, and the ability to measure has changed profoundly. Today it is often possible to forgo sampling and, instead, measure every sequentially produced item or sample frequently at fixed intervals. What influence does this ability to produce time series data have on today's applications of statistics by the quality technician? Begin with the simple model y = η + ε (for the moment with no subscripts) where y is a single observation. The quantity η (eta) is the observation's mean, its deterministic component. The quantity ε (epsilon) is a random variable, the observation's noise, its stochastic or scatter component. We now have the statistician's two-model problem.