Abstract: Operation of a multi-variable process involves multidimensional representation of the value (p1-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: Control of a multi-variable process involves multi-dimensional representation of the values (Qa-Qh) of the process variables according to individual coordinate axes (Xa-Xh), and response based on sets of values for the process-variables accumulated from multiple, earlier operations of the process. An acceptable range (UL-LL) for each process variable due to the current values of the other variables is defined from the accumulated values, and the existence of an alarm condition in which the current value (Qg) of a variable lies outside the range defined for it, is detected and displayed (UC) on the relevant axis (Xg). The change of the values (Qa,Qb) of one or more of the manipulatable variables (a-c) required to rectify the alarm condition is determined iteratively, and implemented by operator or automated response.

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.

Abstract: Control and output-quality variables of a process plant (1) are plotted against parallel axes in a display unit (7). Convex hulls between pairs of variables are calculated from sets of the variable-values accumulated historically in stores (7, 9) during successive runs of the process, and hulls (HH; TC, BC) between successive axis-pairs are displayed. New variable-values for process optimization are fixed for the variables taken in turn, each selection being made within displayed ranges (Rn—Rn) derived from the hulls effective between the respective variable and the variables already fixed. A display unit (13) provides on-line parallel-axis display of variable-values from the plant (1), showing alarm carets (DC, UC) where values violate limits (UL, LL) determined by the convex hulls, and allowing variation in the displayed-value for observing the resultant effect in avoiding alarm situation and towards optimization.