Control chart methodology was applied 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 was .054 inch. 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 15 minutes throughout its 16-hour daily production schedule and optically measured the gap. Data for 4 consecutive hours of production are presented in the accompanying table.

a. Construct an R-chart from these data.

b. Construct an xÌ…-chart from these data.

c. Apply the pattern-analysis rules to the control charts. Does 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?

d. Should the control limits be used to monitor future process output? Explain.

Time Gap Width (thousandths of an inch) 54.2 00:15 00:30 54.1 53.7 53.9 54.1 54.0 54.4 55.9 53.0 53.4 53.8 52.9 51.6 53.8 55.1 53.9 00:45 01:00 01:15 54.0 52.1 53.0 54.2 55.2 53.3 55.2 53.4 51.9 55.0 56.6 57.2 53.1 52.9 52.6 54.0 53.1 54.5 54.5 52.7 51.7 53.6 01:30 01:45 02:00 54.0 54.3 02:15 02:30 02:45 54.9 55.7 56.3 53.1 51.0 54.2 57.5 55.2 52.9 56.3 55.8 55.4 56.1 56.3 55.6 53.8 54.0 54.0 55.4 54.2 55.2 54.2 55.7 03:00 03:15 52.1 53.1 03:30 03:45 04:00 53.7 54.1 53.5 56.9 53.9 56.1 54.0 54.0 55.1 55.1 54.6 55.0 54.2 54.8 54.0