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The educational testing problem is reviewed; it concerns a reliability coefficient which measures how reliable are the student’s total scores in an examination consisting of a number of subtests. A lower bound on this coefficient is obtained by solving a certain nonlinear programming problem. Expressions for both first and second derivatives are given, and a scaling feature is described which enables the search for a solution to take place along feasible arcs on the boundary of the feasible region. The SOLVER method is used to generate the directions of search and numerical results are described. While an improvement over previous methods is obtained, some difficulties over slow convergence are observed in some cases and a possible explanation is given.
R. Fletcher (Tue,) studied this question.