If we have historical data of similar manufacturing operations, we can estimate standard deviation by measuring existing part dimensions of similar nature. There may be a bias present where the mean has shifted from the nominal dimension. We use the nominal dimension as mean, although this needs to be verified that the mean of the samples are the same as well. We could do a test run of x parts to determine the standard deviation of the dimension. Standard deviation (sigma) is governed by whatever process, equipment, etc. Let's use an example for both of these situations where we assume the dimension in question follows a normal distribution. To do this, we either need to have a batch of parts and measure dimensions or we need to have knowledge of the manufacturing process to specify parameters. We will discuss two methods: Root sum squared (RSS) and Monte Carlo simulation.īoth of these methods require that we fully specify the probability distribution and the parameters of the distribution. Statistical methods also allow for the possibility that some parts are above their nominal dimension and others are below their nominal dimension, therefore cancelling out each one's variation to some degree. This is less conservative, but we also take into account that most of the time parts are not at their maximum or minimum material conditions. These methods allow for more relaxed tolerances (or tighter fits) while allowing for a certain percentage of assemblies to not fit together. Statistical analysis makes assumptions that the dimensional variation follows a probability distribution. In worst-case analysis we assumed nothing about dimensional variation other than it is in the tolerance range. Within the statistical methods category there are various methods that can be employed. Tolerance analysis methods generally fall into two categories: This process is repeated until a balance of performance and cost is achieved. Then a tolerance analysis is conducted to verify that a large percentage of assemblies will not have assembly problems. For example, a loose fitting joint may not work properly or give an impression of poor quality. This can be an iterative process where tolerances are allocated to each part partly on restrictions in the manufacturing of each component and partly on performance and quality requirements. Tolerance analysis entails determining an acceptable rejection rate based on the tolerances for each part.
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