Self-Checked Metamorphic Testing of Monte Carlo Simulation

Abstract

Photon propagation in biological tissues can be modeled with Monte Carlo simulations numerically. However, testing a such program is difficult due to the unknown character of the test oracles. Although approaches based on Beer-Lambert law, van de Hulst's table or Radiative Transfer Equation (RTE) can be used for testing the Monte Carlo modeling programs, these approaches are only applied to the programs that are designed for homogeneous media. A rigorous way for testing the Monte Carlo modeling programs for heterogeneous media is needed. Metamorphic testing, as an effective approach for testing systems that do not have test oracles, is one of possible supplementary approaches to test a Monte Carlo modeling program for heterogeneous media. In metamorphic testing, instead of verifying the correctness of a test output, the satisfaction of a metamorphic relation of the test outputs is checked. If a violation of the metamorphic relation is found, the system implementation must have some faults. However, checking only the metamorphic relations is not good enough to ensure the testing quality. Randomly or accidently generated incorrect outputs may satisfy a metamorphic relation as well. Therefore, it is necessary to provide a systematic approach to measure the test effectiveness of a metamorphic testing, to choose metamorphic relations, and to generate test input data. In this thesis, we propose a new approach called self-checked metamorphic testing. In our new approach, the original metamorphic testing is extended with the evaluation of the adequacy of testing coverage criteria to measure the quality of a metamorphic testing, to guide the creation of metamorphic relations, to generate testing inputs, and to investigate the found exceptions. The effectiveness of this approach has been demonstrated through testing a parallel Monte Carlo modeling program we developed for simulating photon propagation in human skins. This thesis contains three parts of work. In first part, the enhanced Monte Carlo modeling program was used to preliminarily study the relationship between the height of the collection lens and the contrast values of the reflectance image of the system. In second part, the homogenous part of the Monte Carlo program was validated with van de Hulst's table method, which compares the simulation results with the calculated values on van de Hulst's table. The third and the main part of the thesis is applying the self-checked metamorphic testing approach to test the Monte Carlo modeling program.