The figures which we have given throughout this example have been based on statistical theory, and the application of theory to real life situations is rarely straightforward. Before leaving this section, there are a few points which should be stressed, some of which have already been mentioned earlier:

• It would be impossible to take all the different variables into account when presenting such an example. Consequently, we have given a highly simplified model in which the only variable that was considered was the radius of each of the components.
  
  
• The processes which produced the shafts and bearings were initially considered to be uncontrolled, but stable. This is an inescapable paradox. If we assume that the processes are out of control, then there are assignable causes present, and it would be possible to reduce the overall variation. However, in such a situation, the process average and standard deviation would almost certainly be fluctuating, and it would be impossible to calculate probabilities in any consistent manner. Therefore, we had to use a fixed standard deviation and, assume that it would be possible to keep the processes centred on the target value.
  
  
• None of the figures given in this example should be taken as precise predictions - they are likely estimates calculated from a theoretical normal distribution. It is reasonable to expect that the figures for a real process would be somewhere in the region of those presented here, no more than that.