In general, the software-testing time may be measured by two kinds of time scales: calendar time (day) and test-execution time (CPU time). In this paper, we develop bivariate software fault-detection models with two time measures and incorporate both of them to assess the quantitative software reliability with higher accuracy. The resulting stochastic models are characterized by a simple binomial process and the bivariate order statistics of software fault-detection times with different time scales. We investigate the dependence of test-execution time as a testing effort on the software reliability assessment and validate quantitatively the software fault-detection models with two time scales.
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