Methodology for Evaluating Reliability Growth Programs of Discrete Systems

Abstract

The term Reliability Growth (RG) refers to the elimination of design weaknesses inherent to intermediate prototypes of complex systems via failure mode discovery, analysis, and effective correction. A wealth of models have been developed over the years to plan, track, and project reliability improvements of developmental items whose test durations are continuous, as well as discrete. This research reveals capability gaps, and contributes new methods to the area of discrete RG projection. The purpose of this area of research is to quantify the reliability that could be achieved if failure modes observed during testing are corrected via a specified level of fix effectiveness. Fix effectiveness factors reduce initial probabilities (or rates) of occurrence of individual failure modes by a fractional amount, thereby increasing system reliability. The contributions of this research are as follows. New RG management metrics are prescribed for one-shot systems under two corrective action strategies. The first is when corrective actions are delayed until the end of the current test phase. The second is when they are applied to prototypes after associated failure modes are first discovered. These management metrics estimate: initial system reliability, projected reliability (i.e., reliability after failure mode mitigation), RG potential, the expected number of failure modes observed during test, the probability of discovering new failure modes, and the portion of system unreliability associated with repeat failure modes. These management metrics give practitioners the means to address model goodness-of-fit concerns, quantify programmatic risk, assess reliability maturity, and estimate the initial, projected, and upper achievable reliability of discrete systems throughout their development programs. Statistical procedures (i.e., classical and Bayesian) for point-estimation, confidence interval construction, and model goodness-of-fit testing are also developed. In particular, a new likelihood function and maximum likelihood procedure are derived to estimate model parameters. Limiting approximations of these parameters, as well as the management metrics, are also derived. The features of these new methods are illustrated by simple numerical example. Monte Carlo simulation is utilized to characterize model accuracy. This research is useful to program managers and practitioners working to assess the RG program and development effort of discrete systems.