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This research effort in the field of software reliability is primarily based on probability: as applied to error detection rates; as applied to the generation of input tests data; and as applied to the economics of random versus constructed test cases. The background description of the flow of computations is made by means of a directed graph representation and a connection matrix depicting possible links between program segments. Random numbers selected from a given domain by several distributions are employed as input to programs instrumented to detect the use of the proram's segments. An algorithm is employed to estimate the total number of execution sequences which are likely to be eventually driven by random number inputs, and, by implication, the point in testing where the change to constructed cases should be made. Models for determining the count of these execution sequences are described and tables which facilitate estimation of the number of logical paths and related parameters are provided for convenience. (Author)

Two failure rate models for the so-called 'burn in' phase have been developed. One model based on a constant-step decrease implicitly assumed a pure state (zero residual error) could be achieved. The other, based on a geometric progression in the failure rates, has an asymptotical zero failure rate. In the new model, presented here, the system error rate is composed of a combination of a rate which is constant (mid-phase) and the geometric model. Maximum likelihood equations are developed and some of the conditions for the existence of solutions are established., Presented at the Joint National Meeting, ORSA/TIMS, 31 Mar-2 Apr 76, Philadelphia, Pa.

Two models which were developed to describe the software error detection process have applicability to the burn-in phase of hardware failure; the failure rate for the 'next' error is either proportional to the current number of remnant errors (de-eutrophication model) or decreases to a value which stands in a fixed ratio to its prior value (geometric de-eutrophication model). Estimates of the mean time to failure and the degree of completeness of testing are made on the observed time separations by maximum likelihood. The results of a study on the variances and efficiencies and robustness of the two models are presented., Proceedings presented by Joint National Meeting ORSA/TIMS, at Las Vegas, on 17-19 November 1975.