Unstable warpage leads to buckling of components. The contribution of each of the three shrinkage variates to the total deflection can no longer be assumed to be linear.
In this case, a so-called sensitivity analysis is used. This functionality is available for Midplane analysis technology only.
The aim of the sensitivity analysis is to determine the change in load factor for a known change in the shrinkage. The load factor indicates at what factor of the actual applied loads, in the case of Shrink analysis these being the loads internal to the part, the part warpage becomes unstable, leading to buckling. A load factor less than one indicates the actual loads are sufficient to result in buckling of the part. A load factor greater than one indicates that the warpage is stable as the onset of buckling has been determined to be at a load magnitude higher than the actual loading.
, can be regarded as a function of these components, that is, 
To solve a warpage problem, we wish to know which component to change to increase the load factor, that is to make the warpage stable. One way of doing this is to take the partial derivatives of with respect to each component. Unfortunately this cannot be done analytically as there is no known function relating to the components. Instead the partial derivatives are approximated.
. Now increase one of the shrinkage components by some amount, 
say, to give a new total shrinkage S'. For example, if we increase the differential shrinkage component, we would have: 
, the derivative of with respect to the differential shrinkage component is approximated as follows: 
as illustrated in the image below:
Load factor as a function of shrinkage
.(a) Load Factor, (b) Shrinkage
The value (1 + ) is called the sensitivity factor which is a program input.
The above holds for one element only. For a real part, each individual element has a value of 
. To cope with this, the various elemental changes are combined into a single measure of shrinkage change. The norm of these changes is used in the elemental shrinkages to obtain the single value, which is reported in the analysis log as Norm of shrinkage change.
where N is the number of elements in the model.
Similarly, the sensitivities of the load factors for differential cooling and orientation effects variates, respectively, are calculated.
The Norm of shrinkage change, then, is the sum of shrinkage change squares at each element, and is used in the sensitivity analysis of warpage buckling.