The quality control technician grew weary of measuring pistons that came off the line, so he decided to make a fixture that would tell him whether the piston fell within product specifications

Question

The fixture had two holes, one the exact width of the upper specification (24 cm) and one slightly smaller than the lower specification (21 cm). If the piston fit through the smaller hole, it would be too small and therefore rejected. If the piston didn't fit through the larger hole, it was too large and would be rejected. Just to test his idea, he used the traditional measurement system and his new system on the next eight samples. The data and the two charts he constructed are shown below. Why aren't the plotted points forming similar shapes between the two graphs? Evaluate the advantages and disadvantages of his proposed system.

Sample 1 29.5 23 20.9 24.9
Sample 2 22.9 20.1 23.7 26.9
Sample 3 25.9 23.6 23 24.3
Sample 4 25.3 23.2 29.8 22.3
Sample 5 24.7 25.1 20.6 23
Sample 6 28.4 29.7 27.1 23.7
Sample 7 21.9 23.5 24.9 24.2
Sample 8 26.9 21.1 28.1 20.2
Sample 9 25.5 27.6 26.3 27.2
Sample 10 23.9 28.6 21.7 20.6

Answer 1

The points don't form similar shapes due to the nature of the data generating functions. The x-bar chart is from a process that creates a continuous random variable stream. The c-chart takes the same data and converts it to attribute data that can generate signals (errors) for being either too high or too low. The judgments made by the go/no-go gauge are accurate and this approach is often faster than taking a continuous measurement and meticulously recording the observations. The speed comes at the expense of information about the process. With the c-chart, an observer can tell that defects are being produced, almost three per sample, but there is no way to tell if the output is consistently too large, too small, or a mix of the two. The x-bar chart will provide information as to the direction of the production error, thereby providing process troubleshooting with some focus.