Nonparametric Statistical Process Control

1Background/Review of Statistical Concepts

Chapter Overview

This chapter gives an overview of some key statistical concepts as they relate to statistical process control (SPC). This will aid in familiarizing the reader with concepts and terminology that will be helpful in reading the following chapters.

1.1 Basic Probability

The term probability indicates how likely an event is or what the chance is that the event will happen. Most events can't be predicted with total certainty; the best we can do is say how likely they are to happen, and quantify that likelihood or chance using the concept of probability. A probability is a real number between (and including) zero and one. When an event is certain to happen, its probability equals one, whereas when it is impossible for the event to happen, its probability equals zero. Otherwise, the event is likely to happen or occur with a certain probability, expressed as a fraction between zero and one. For example, when a coin is tossed, there are two possible outcomes, namely, that a head (H) or a tail (T) can be observed. Note that an outcome is the result of a single trial of an experiment and the sample space (S) constitutes all possible outcomes of an experiment (the sample space is exhaustive). In the coin tossing example, the sample space is given by S = {H,T}. If the coin is unbiased (or fair), the probability (P) of observing a head is the same as the probability of observing a tail, each of which equals . The probability of the ...