Minimum Number Of Tests Research Articles

The Connectedness Game and thec-Complexity of Certain Graphs

When $\mathcal{Z}$ is a finite family of finite sets such that $ \cup \mathcal{Z} \in \mathcal{Z}$, there is an associated game $D( \mathcal{Z} )$ that a certain player can always win by making enough tests, where a test is a special sort of move in the game. The complexity of $\mathcal{Z}$ is defined as the minimum number of tests that suffices to win the game. As a specialization of this notion, there is associated with each connected graph $G = ( {V,E} )$ a game $C( G )$ that involves detecting, in a dynamic setting, the connectedness of a subgraph of G. The number of tests required to win $C( G )$ is called the c-complexity of G. Both the c-complexity and a closely related computational notion are shown to be $O| V |$ when G belongs to a class of graphs that includes all paths and circuits.

Derivation of Minimal Test Sets for Monotonic Logic Circuits

It is shown that the number of maximal false vertices and minimal true vertices is the minimum number of tests required to detect all s-a-1 and s-a-0 faults in any irredundant two-level realization of a 2-monotonic function.

Tool-Life Testing by Response Surface Methodology—Part 2

This paper is a continuation of a previous paper in which the basic philosophy of response surface methodology has been explained and a first-order tool-life-predicting equation has been developed. This part of the paper illustrates the development of a second-order tool-life-predicting equation in 18 and 24 tests. It was found that the second-order effect did not show statistical significance within the cutting ranges of this project; however, the second-order effect of cutting speed has been found important by the study of residuals. If only one independent variable is investigated, a minimal number of tests can be used to find a second-order equation. Examples of designs in three, five, and six tests are illustrated.