On the Theory of Runs with some Applications to Quality Control

Recent developnIents in the theory of runs. The increasing number and importance of recent advances in the theory and statistical applications of runs may make a brief paper on the subject of some interest. The large volume of material and its wide dispersal, together with the limitations of space, will of necessity make these remarks far from exhaustive and complete. I shall not define a run because new advances and applications of new criteria to new problems would probably soon render most definitions obsolete. Runs as used in statistics are best characterized by a philosophy and a technique rather than by the employment of any one specific device. What is always involved is the ordering of observations according to some characteristic and the resultant effect of this ordering on the ordering according to some other characteristic. For example, if the seats at a meeting of statisticians and engineers are numbered and occupied by m engineers and n statisticians, then if we list the numbers of the occupied seats in ascending order and replace each number by E or S according as the seat is occupied by an engineer or statistician, we shall have a sequence of m + n elements, m E's and n S's. Thus, if m = 7 and n = 6, such a sequence might be