Your company works in the steel processing industry. You do mostly subcontracting work for your customers. One of your key resources is an old laser cutting machine for which it's manufacturer has promised a tolerance of +-0,026 mm. Recently, you have started to doubt if the machine is still working as good as it should be working. This is due to the fact that there recently was a decision stating that all manufacturing processes have to be working within the capability index of 1,33 at minimum.

You decide to test the capability of the machine. While at it, you also want to see if there's any reason to suspect that any special cause variation might exist in the cutting process itself. At the moment you have an active production order where one part of the cutting operation requires you to cut holes of 10 mm in diameter. After the cutting process is finished for the first batch, you take it aside and measure the diameters to a high accuracy. Below are your measurements and a run chart you've constructed of the measurements (in the order of parts manufactured).

Is there reason to suspect special cause variation exists in the laser cutting process? Also, is the cutting process capable?

Think: would control charts be better for testing for special cause variation in this case? Why? (no answer need for these last two questions)

a. The amount of runs is within limits of normal cause variation. In general, the process is not capable but does not fail the two sided capability test (the process fails only on the LSL).

b. The amount of runs is not within limits of normal cause variation, though it is at the high end of what is allowed. In general, the process could be considered capable but it does not meet the required capability index of the company (1,33).

c. The amount of runs is within limits of normal cause variation, though it is at the high end of what is allowed. In general, the process is not capable and fails on the two sided capability tests as well.

d. The amount of runs is within limits of normal cause variation, though it is at the high end of what is allowed. In general, the process is capable (although not meeting the company requirement of 1,33) but fails on the two sided capability tests on the USL.