STATISTICAL TESTING OF MODEL HYPOTHESIS IN BINOMIAL REGRESSION

NUMEROUS MILITARILY SIGNIFICANT PROBLEMS, SUCH AS THE EVALUATION OF WEAPONS SYSTEM EFFECTIVENESS, THE SENSITIVITY AND RELIABILITY OF MUNITIONS, AND THE VULNERABILITY OF COMPLEX STRUCTURES TO SEVERE LOADING CONDITIONS, OFTEN INVOLVE THE REGRESSION OF A BINOMIAL PROPORTION (NUMBER OF SUCCESSES/NUMBER OF TRIALS) ON SOME LOADING FUNCTIONS OR QUANTITY THAT IS ASSUMED TO CHARACTERISE THE SEVERITY OF THE TRAIL ENVIRONMENT. THE PROBABILITY OF SUCCESS ESTIMATED IN THIS MANNER (AS THE MEAN OF THE BINOMIAL PROPORTION) AS WELL AS FURTHER INFERENCE, IS DEPENDENT UPON THE ASSUMED MODEL HYPOTHESIS, I.E., THE LOADING FUNCTION (OR CLASS OF FUNCTIONS) EMPLOYED AND THE CLASS OF DISTRIBUTIONS USED TO RELATE PROBABILITY OF SUCCESS TO LOADING LEVEL. THE CREDIBILITY OF ANY PREDICTION MODEL DEVELOPED IN THIS MANNER DEPENDS ON A STATISTICAL TEST OF THE MODEL HYPOTHESIS AND THE POWER OF THE TEST AGAINST ALTERNATIVE MODEL HYPOTHESES. IN PHASE I, A CHI-SQUARED-BASED GOODNESS-OF-FIT TEST FOR MODELS OF BINOMIAL FAILURE DATA WILL BE STUDIED BY SIMULATION, AND CORRESPONDING POWER AND SAMPLE-SIZE RESULTS WILL BE TABULATED AND MODELED. A NOVEL GOODNESS-OF-FIT TEST BASED ON BINARY STORAGE TREE STRUCTURES WILL BE EXPLORED. THIS TEST HAS PROMISE TO SUPERCEDE THE KOLMOGOROV-SMIRNOV TEST IN SOME CIRCUMSTANCES. IN PHASE II, THIS AND OTHER GOODNESS-OF-FIT TESTS WILL BE FURTHER DEVELOPED.