Testing and evaluating one-dimensional latent ability

• A new approach to evaluation of engineering ability test results is proposed.
• Levels of difficulty of non-destructive test items are unknown beforehand.
• Item response function is considered to be self-similar and scale invariant.
• The main assumptions of the proposed approach are strictly formulated.
• An algorithm for solving the problem and numerical example are provided.

A new approach to evaluation of binary test results when checking a one-dimensional ability is proposed. We consider the case where a qualitatively homogeneous population of objects is tested by a set of non-destructive test items having different, but unknown beforehand levels of difficulty, and we need to evaluate/compare both the intrinsic abilities of these objects and the level of difficulty of the test items. We assume that the responses to different test items, applied to the same part, do not affect one another and the same scale invariant item response model applies to all members of the tested population of objects under test (OUTs). OUT can mean an electronic component, examinee, program unit or material under test, etc. An algorithm for solving the problem, applicable for engineering testing, is proposed. It combines item response theory, maximum likelihood estimation, method of flow redistribution and other methods. Numerical example is presented.