Investigation of System Readiness When Some Defect Types Unknown

Abstract

Abstract : A system consists of subsystems and performs satisfactorily when defects in subsystems do not cause its failure. For each subsystem, defect types are identified by their nature and by their level of probabilistic influence on system failure (finite number of levels). The subsystems and possible defect types are so defined that, for satisfactory system performance, a defect type can occur at most once in a subsystem. Also, for this conditional case, probabilities for a defect type are not influenced by occurrence of other defect types. Moreover, the defect types are independent and have small probabilities with respect to occurrence. System ability is represented by the Readiness Index (RI), which is the probability of no defect that causes system failure. Statistical investigation of the RI is complicated by possible existence of defect types which have not yet been identified. Suitable data are available for each combination of subsystem and level of probabilistic influence on system failure. For every combination, the number of defect types occurring is observed over some repetitions. Unbiased estimation, also approximate tests and confidence intervals, are developed (some results are conservative and/or apply to at least moderately large RI values).