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Exact expressions for the expected number of surfaced failure modes and system failure intensity as functions of test time are presented under the assumption that the surfaced modes are mitigated through corrective actions. These exact expressions depend on a large number of parameters. Functional forms are derived to approximate these quantities that depend on only a few parameters. Such parsimonious approximations are suitable for developing reliability growth plans and portraying the associated planned growth path. Simulation results indicate that the functional form of the derived parsimonious approximations can adequately represent the expected reliability growth associated with a variety of patterns for the failure mode initial rates of occurrence. A sequence of increasing MTBF target values can be constructed from the parsimonious MTBF projection approximation based on the following:(1) planning parameters that determine the parsimonious approximation; (2) corrective action mean lag time with respect to implementation and; (3) test schedule that gives the number of planned Reliability, Availability, and Maintainability (RAM) test hours per month and specifies corrective action implementation periods.

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In this article we present new methodology for analyzing reliability growth of discrete-use systems (i.e., systems whose test duration is measured in terms of discrete trials, shots, or demands). The methodology is applicable to the case where corrective actions are applied to prototypes anytime after associated failure modes are first discovered. Thus, the system configuration need not be constant. The methodology consists of several model equations for estimating: system reliability; the expected number of failure modes observed during testing; the probability of failure due to a new failure mode, and the portion of system unreliability associated with repeat, or known, failure modes. These model equations are used to: (1) estimate the initial and projected reliability as well as the reliability growth potential; (2) address model goodnessof-fit concerns; (3) quantify programmatic risk; and (4) assess reliability maturity of discrete-use systems undergoing development. Statistical procedures for point estimation, confidence interval construction, and goodness-of-fit testing are also given. In particular, a new likelihood function (and associated maximum likelihood procedure) is derived to estimate model parameters, that is, the shape parameters of the beta distribution. An application to a missile program is given to illustrate the utility of the presented approach. Supplemental materials for this article are available on the Technometrics website.