On a measure of reliability based on point processes with random fuzzy marks

This paper considers the problem faced by a reliability analyst who has detected faults in a system, which were caused by a combination of random and systematic factors. Such faults usually occur at random points in space or time. The analyst's challenge is to accurately gauge the scale of the problem, accepting the fact that an appropriate reliability estimate must also take into consideration the subjective nature of her assessment. In this paper, we introduce a reliability measure, which we called a gauge measure, which incorporates the randomness due to the locations of the faults as well as the imprecision caused by the subjective nature of the assessment. The randomness of the locations will be modeled by a point process and the subjective assessment of each fault by a random fuzzy mark. The mean and variance of a gauge measure will be obtained. Finally, through a generic example and several real world applications, we show how this measure can be applied to measure the reliability of many occurring working systems, especially software systems.