{'fraction_non_alphanumeric': 0.03134996801023673, 'fraction_numerical': 0.0025591810620601407, 'mean_word_length': 5.59915611814346, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Reliability Growth Management Metrics and Statistical Methods for Discrete-Use Systems

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 goodness-of-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.