ABSTRACT
The introductory statistics chapter covered preliminary material dealing with basic statistical concepts. This discussion provided a demonstration of the relatively uncomplicated nature of the mathematical calculations and concepts that can be employed to provide an objective description of a manufacturing operation. Characteristics such as the mean, variance, standard deviation, and probability density functions were presented in light of the manner in which these statistical entities could be used to describe populations of measurements. The subsequent chapter described deterministic manufacturing methods in a somewhat general fashion. This presentation described a manufacturing philosophy that depends heavily on what is essentially common sense, which is bolstered by the use of statistics, to control the quality of a manufacturing operation. However, no explicit information was presented on how particular statistical techniques were used to achieve a higher level of quality control. The present chapter shows some statistical methods that can be employed beneficially to obtain an accurate model that describes the condition of a process. Once this analysis has been accomplished, the quality of the operation can be estimated accurately and therefore controlled. (Assuming it is permissible to perform process parameter adjustments as a means of achieving improved system performance.)
One set of circumstances that is often a concern with certification programs is the question about the occurrence of multiple defects in the output of a manufacturing process. This situation involves a subject called conditional probability. It deals with instances in which one event is known to have occurred and the problem is to determine the likelihood that another event also has happened. If the events of concern are independent events, then the probability of the second event occurring, given the fact that the first event has already occurred, is the same as the probability for the second event occurring by itself. The probability of both events occurring is the product of the probabilities of the individual events. On the other hand, if the events in question are not independent of each other, then the occurrence of one event influences the likelihood of the occurrence of the other event. Interest in these topics leads to an area of statistics called acceptance sampling, where it is assumed that a certain percentage of defects exist and information that defines the probability of locating these defects via a sampling plan is required.
