If the tubes were arranged in the furnace in two crossed orientations, for instance, some having  their tops facing the electrical furnace resistive heating elements, and the remaining perpendicular to the first, you may well have a bimodal length (or diameter) size distribution. Therefore, two somewhat distinct shrinkage percentages, may possibly apply to each kind of spatial arrangement. Such shrinkage differences may occur due to differences in the heat transfer patterns, and consequently, of the temperature profile of the green bodies being fired. By red heat temperatures (800─900ºC) differences at the spatial arrangement in the furnace can be particularly important, as they may significantly influence the local contribution of radiative heat transfer. Relying in statistical analysis, it may be possible to discriminate the tubes in two groups, with two distinct mean shrinkages. By revising the firing schedule and the spatial arrangement of the green bodies to be fired, a single representative shrinkage value may possibly be achieved, what is generally considered advantageous.

Here is the orientation of the nozzles in the furnace. The nozzles are like a frustum shaped figure with varying diameters on both sides. The thing is we want to control the shrinkage of the smaller diameter. In consideration with this info, can you provide some more light into the issue. We are heating the furnace at 1660 deg C and then cooling it.

From the picture inserted above, I can see that the arrangement given to the tubes in the furnace is very different than that I was thinking about. Moreover, the furnace seems not electrical, as I was supposing. If the furnace is gas-fired, the flame is possibly located in the head-space above the green bodies. With the depicted arrangement, the tubes being fired in the top row may possibly show increased shrinkage than those at the beneath rows, since their firing is favoured by the radiative heat transfer pattern of the furnace. Gas furnaces often proportionate steepest and poorly controlled heating rates by red heat temperatures and below, what may enhance shrinkage differences, which might otherwise be less significant with the slower heating rates that can be usually achieved with electrical furnaces.

Put some two or three tubes in center of the furnace and repeat the heating process. Probably you'll have not troubles if your tubes were uniformly produced. Unequal heat distribution inside the furnace may do it! Don't put a lot tubes in the same time and don't put a stacked tubes on the other. To verify the shrinkage rate of the material, carry out some measurements in pieces of material in a dilatometer.

You need to make measurements whith dilatometry,  if you do not have the dilatometer, measure a sample in green and then sintered and measure the % shrinkage

The furnace is coil based electric