A material performance index is a combination of properties derived from a design objective and constraint. It ranks materials for that specific structural function.

Consider a tie rod of length $L$ carrying tensile force $F$. Minimize mass

$$m=\rho AL$$

subject to a maximum elastic extension $\delta$:

$$\delta=\frac{FL}{AE}\le\delta_{\max}.$$

At minimum mass the constraint is active, so

$$A=\frac{FL}{E\delta_{\max}}.$$

Substitute into mass:

$$m=\frac{FL^2}{\delta_{\max}}\frac{\rho}{E}.$$

All quantities except $\rho/E$ are fixed by the design. Minimum mass therefore requires maximizing

$$M=\frac{E}{\rho}.$$

That result was derived, not guessed.

A different component geometry, loading mode, failure criterion or objective can produce a different combination of material properties. The procedure remains the same:

1. write the objective, such as mass or cost;
2. write the governing constraint;
3. eliminate the free geometric variable;
4. separate fixed design quantities from material properties;
5. rank materials by the resulting property combination.

A performance index is therefore meaningful only together with the assumptions from which it was derived. Changing what the design is allowed to vary can change the index and the resulting material ranking.