1.1 Introduction to Sequential Procedures

Sequential procedures differ from other statistical procedures in that the sample size is not fixed in advance. The experimenter has the option of looking at a sequence of observations one (or a fixed number) at a time and decide whether to: stop sampling and take a decision; or to continue sampling and make a decision some time later. The order of the sequence of observations which the experimenter will take is specified in advance. Decision problems in which the experimenter may sequentially vary the treatments is of a higher order of difficulty and is called the sequential design problem. For example, consider the following problem.

Thus, an essential feature of a sequential procedure is that the number of observations required to terminate the experiment is a random variable since it depends on the outcome of the observations. Sequential procedures are of interest because they are economical in the sense that we may reach a decision earlier via a sequential procedure than via a fixed-sample size procedure. In sequential experiments we need to specify:

1. the initial sample size

2. a rule for termination of the experiment

3. the additional number of observations to take if the experiment is to...