A Logarithmic Reliability-Growth Model for Single-Mission Systems

A logarithmic growth model for the reliability of single-mission systems is proposed, and estimators for its two parameters are analyzed. Reliability growth produced by a `test, analyze, and fix' (TAAF) program has a discrete measure of size, viz, the number of tests. The proposed growth model is similar to the popular nonhomogeneous Poisson process (Duane) growth models, and uses the discrete test-number variable in place of test time. Analysis of simulation results shows that the continuous analog estimators are superior to the least squares estimators. Both sets of estimators are s-consistent for a large number of tests, have acceptably small variability, and are easy to calculate. The continuous analog estimators have less variability than the least squares estimators and underestimate reliability, while the least squares estimators overestimate reliability. The application of the model, with the continuous analog estimators, to planning and monitoring the reliability development test program for a single-mission system is described.