Question: Fill levels of jelly jars are of interest. Every half hour, three jars are taken from a production line and net contents measured and recorded. The range and average of these three measurements are calculated and plotted on charts. One of these charts is intended to monitor location of the fill distribution, and the other is useful in monitoring the spread of the fill distribution.
(a) What is the name for the chart used to monitor location of the fill-level distribution?
(b) What is the name for the chart used to monitor spread of the fill-level distribution?
(c) What is the name and value of the tabled constant used to make retrospective control limits for process location?
(d) What are the names and values of the two tabled constants used to make retrospective control limits for process spread or short-term variability?
(e) In this context, what constitutes a natural subgroup?
(f) Give an expression for the usual estimate of process short-term variability (σ) based on an average of subgroup ranges.