Statistical analysis involves the application of statistical probability distributions to analyzing tolerances for assemblies. It will prevent overly conservative designs, which can increase the cost of the product without adding to quality. With statistical analysis, tolerances can be widened, readily achieving six sigma.
Statistical tolerance analysis is based on the assumption that most mechanical parts are made to normal probability distributions within their specified tolerance limits. The distributions of individual parts can be combined into a normal distribution, representing the variability of parts from their nominal dimensions. In six sigma quality, the nominal dimension of a part is set to its average，and the specified tolerance limits of that part at ±6<r.
8.3.5Tolerance Analysis Example
An example is given in this section to demonstrate some of the concepts of tolerance analysis. An assembly consisting of three parts or rectangular blocks is to be assembled together into a box cover (see Figure 8.7). Their critical dimensions (mating surfaces) and their specified tolerances are also shown in Figure 8.7. If the box cover for these three parts is be designed, what specifications should be assigned to the box for these three parts to fit? The problem will be solved using worst-case analysis and then by statistical analysis.
For the worst case analysis in Table 8.11, Case 1, the cumulative dimension of the three parts is at a maximum of 3.902 inches. It is comprised of the individual maximum dimensions of the blocks. The mini- mum dimension of the box should be set at 3.903 inches, ensuring a minimum clearance gap of 0.001. Assigning a box tolerance of ±0.005 inches, the nominal dimension for the box is 3.903 + 0.005 = 3.908 inches, and the maximum box dimension is 3.913 inches. This shows that there could be a maximum gap of 3.913 - 3.848 = 0.065 inches, and average gap of 3.908 - 3.875 = 0.033 inches. Having such a wide variation (0.055 to 0.001 inches) may not be acceptable as functional requirement for the assembly of the box and three blocks. If this assembly were part of a front panel, having a gap average of 0.033 inches might not be aesthetically pleasant and could convey the impression of poor quality.