Consider the assembly of three components shown in Figure 9-19. The tolerances for these three components are given in Table 9-7. 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?

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Component Mean Length (cm) Tolerance (cm) 10±0.5 4±0.2 5±0.1 10