Refer to Exercise 12.16 (p. 712). in which a robotics clamp manufacturer was concerned about gap width.
a. Construct an R-chart for the gap width.
b. Which parameter of the manufacturing process does your R-chart provide information about?
c. What does the R-chart suggest about the presence of special causes of variation during the time when the data were collected?
Exercise 12.16
University of Waterloo (Canada) statistician S.H. Stciner applied control chart methodology to the manufacturing of a horseshoe-shaped metal fastener called a robotics clamp (Applied Statistics, Vol. 47,1998). Users of the clamp were concerned with the width of the gap between the two ends of the fastener. Their preferred target width is .054 inches. An optical measuring device was used to measure the gap width of the fastener during the manufacturing process. The manufacturer sampled five finished clamps every fifteen minutes throughout its 16-hour daily production schedule and optically measured the gap. Data for four consecutive hours of production are presented in the table below
a. Construct an 
-chart from these data.
b. Apply the pattern-analysis rules to the control chart. Docs your analysis suggest that special causes of variation are present in the clamp manufacturing process? Which of the six rules led you to your conclusion?
c. Should the control limits be used to monitor future process output'? Explain