Question

Zero Defects & On-target: There are two manufacturing philosophies of manufacturing. Zero-defects is primarily practiced by American manufacturers and on-target is generally adopted by Japanese companies. Taking an example for an assembly, show how you will choose the target dimensions if you want to be close to the ideal by one SD, two SDs, and three SDs for both manufacturing philosophies. You may assume any adequate SD dimension.

Example: Say the dimension and tolerance given to you is 100 mm (+2 mm / -0 mm). This means the dimension will have the lower specification limit (LSL) of 100 mm and the upper specification limit (USL) of 102 mm, with a needed target of 100 mm. Now say you ran the parts on the machine and found the SD for a set of 30 parts to be 0.03 mm.

With this information you can now attempt to find what target you should aim the machine at.

Ideally the target will be 100 mm but because of the variation in the process, it cannot be 100 mm, but we can be as close to it as possible. The distance we can be away from it for 68% of the output to be good will be 1x SD, for 95% it will be 2 x SD and for 99.73% it will be 3 x SD.

Hence the targets will be as follows:

1) 68% will be 100 + 1x SD = 100 + (1 x 0.03) = 100.03 mm

2) 95% will be 100 + 2x SD = 100 + (2 x 0.03) = 100.06 mm

3) 99.73% will be 100 + 3x SD = 100 + (3 x 0.03) = 100.09 mm

Answer 1

Assuming the target of the machine to be normally distributed, with mean and std deviation of , we know that about 68% of the times the target can be expected to be within 1 std deviation from the mean, 95% of the times it can be expected to be within 2 std deviations from the mean, and 99.73% of the times it can be expected to be within 3 std deviations from the mean.

Hence, given a mean target of, say 1000 mm, with a std deviation of 1 mm, we can set the target dimensions as per the type (quality) of the output as:

1) Defects within std deviation from the mean => Targets will be (1000 - 1*1, 1000 + 1*1) = (999 mm, 1001 mm)

2) Defects within 2 std deviations from the mean => Targets will be (1000 - 2*1, 1000 + 2*1) = (998 mm, 1002 mm)

3) Defects within 2 std deviations from the mean => Targets will be (1000 - 3*1, 1000 + 3*1) = (997 mm, 10 mm)

Obviously, given the lower error tolerance in Case 1, it will be of a superior quality compared to the other 2. Hence, the product/service 1 will be rated/priced high compared to the others given higher accuracy and adherence to the mean specifications.