Abstract: A method of operating a multi-variable process comprises deriving a multi-dimensional representation of the process variables according to individual co-ordinate axes, defining a feasible region of the process variables by selecting from an accumulation of historical sets of values of all the variables, obtained from multiple operations of the process, to define an operational envelope containing a set of data points for which the product qualities are within predetermined limits, calculating the convex hull of this set of data points, determining an interior hypercube inside the convex hull, the interior hypercube having sides that are parallel to each axis, and then operating the process with the process variables as defined within the interior hypercube.

Abstract: Operation of a multi-variable process involves multidimensional representation of the value (pl-p12) of the process variables (P1-P12) according to individual coordinate axes, and an operational envelope (UB,LB) derived from a group of sets of values for the process and quality variables (P1-P12,Q1-Q2) accumulated from multiple, earlier operations of the process, defines an operating zone for the process and quality variables of the process. If the current value (p7) of any process variable (P7) goes outside the envelope, an envelope (UO,LB) for a different, wider grouping of the stored data-sets is displayed at least for the quality variables (Q1-Q2). A series of nested envelopes to provide stepwise enlargement of the operating zone may be provided, but non-nested envelopes can be used where there is clustering of acceptable values of process variables of the stored data-sets. The changes to control variables to bring the values of dependent variables within a best operating range can be determined.

Abstract: Operation of a multi-variable drilling-rig is carried out within an envelope defined by convex hulls (TC,BC) that are derived from sets of historical values for the variables accumulated in a store (3) from previous operations. A display unit (5) shows the real-time values (Q01-Q10) of the variables on parallel axes (X01-X10) together with upper and lower limits (Up01-Up10, Lp01-Lp10) of the viable ranges for each variable to remain within the envelope, taking into account the current value of each other variable. The adjustment of the value of a variable (Q03) required to correct for a variable (Q08) found to be outside its viable range, is determined tentatively before implementation, by adjusting that value in the display to bring about re-calculation and display of the changes in viable ranges that would result from such adjustment.