Control charts have been in use for a number of years, more particularly in engineering and allied industries where there is only a single factor involved in each measurement. With more recent developments covering wider fields, there is a serious danger that instead of measuring the effect of a single component in a process, we are measuring a combination of confounded effects. This could lead to false decisions on the necessity for corrective action, in cases where the component which one assumes is being measured is not the one at fault. Such practices can not only be seriously misleading, but may rapidly undermine confidence in the use of statistical methods generally. A perfect example of this occurs in the pottery industry, where the effects of the raw material and its processing could easily be confounded. The clay body from which whiteware products are made changes from day to day due to variations in the fresh material being added to storage tanks or to a planned formula change, and a reasonable control must be maintained. One way in which this can be achieved is by examining the fired whiteware, measuring such quantities as shrinkage or water absorption. Any measurement on the fired ware, however, will be a combination of body and kiln effects and a random component, plus other factors which may or may not be taken into account. In the usual course of events, no evaluation of the separate effects can be made, because only one body is fired each day. Unsatisfactory pieces may equally well be due to an undetected fault in the kiln or lack of control in the body. Similarly the effect of a formula change might be masked by excessive kiln variation and only detectable by a special experiment. However, it will be shown in this paper, by means of a very simple overlapping arrangement, i.e. testing each body on more than one day and more than one body each day, as in fig. 1, or by simple modifications of this basic scheme, that:(1) unbiased measures of body and firing differences can be simply obtained, and these are exactly the least squares solutions when a series of any length is considered; (2) unbiased estimates of the error variance are easily calculated, under certain simplifying assumptions, without the need for a least squares solution and analysis of variance; (3) other factors which it is desired to investigate can be superimposed on the