In given Exercise, suppose that the specifications for the gap are 1.05± 0.15 cm. An assembly with a gap exceeding the upper specification limit is scrapped, whereas that with a gap less than the lower specification limit can be reworked to increase the gap dimension. The unit cost of rework is $0.15 and that for scrap is $0.40. If the daily production rate is 2000, calculate the daily total cost of scrap and rework. How can this cost be reduced?
Exercise
Consider the assembly of three components shown in Figure. The tolerances for these three components are given in Table. Assume that the tolerances on the components are independent of each other and that the lengths of the components are normally distributed with a capability ratio of 1.
What is the tolerance of the gap?
Assuming normality, if specifications for the gap are 0.9± 0.201 cm, what proportion of the assemblies will not meet specifications? How could the proportion of nonconforming assemblies be reduced?
| Component |
Mean Length (cm) |
Tolerance (cm) |
| A |
10 |
10 ± 0.5 |
| B |
4 |
4 ± 0.2 |
| C |
5 |
5 ± 0.1 |