Properties of Control Chart Zone Tests

1.1 General In using an X control chart to maintain control of a process average, we periodically measure n units of the product and plot the average measurement X,, on the control chart in its chronological position. T h e control chart presents a pictorial summary of production history t h a t is useful in: (a) detecting changes in the process average, and (b) providing clues to the causes of such changes. Various run tests have proved useful in application (b). 1 Most of the literature on run theory pertains to this application. There are tests for runs up and for runs up and down; there are tests for the number of runs and for the lengths of runs. T h e control chart is particularly suitable for run tests. We shall consider the use of a particular type of run test in application (a). In application (a), as each point is plotted we decide whether or not to look for trouble (to take action to eliminate the cause of the change in the process average). Using the standard control chart t e s t , 2 , 3 we look for trouble if a point falls in a zone outside of two control limits symmetrically placed on either side of a line representing the nominal process average. The control limits, called the 3a (3-sigma) limits, are placed at AY ± 3 ( a ' / y / n ) , where AY and a' are the nominal process average and standard deviation, respectively, and n is the sample size, or number of units of product measured for each point. We shall assume t h a t AY and a' are known, and that a' remains fixed.