A Reliability Growth Process Model with Time-Varying Covariates and Its Application

The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models.

Small sample discrete reliability growth modeling using a grey systems model

PurposeWhen performing system-level developmental testing, time and expenses generally warrant a small sample size for failure data. Upon failure discovery, redesigns and/or corrective actions can be implemented to improve system reliability. Current methods for estimating discrete (one-shot) reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. The purpose of this paper is to present an application of a modified GM(1,1) model for handling system-level testing constrained by small sample sizes.Design/methodology/approachThe paper presents a methodology for incorporating failure data into a modified GM(1,1) model for systems with failures following a poly-Weibull distribution. Notional failure data are generated for complex systems and characterization of reliability growth parameters is performed via both the traditional AMSAA model and the GM(1,1) model for purposes of comparing and assessing performance.FindingsThe modified GM(1,1) model requires less complex computational effort and provides a more accurate prediction of reliability growth model parameters for small sample sizes and multiple failure modes when compared to the AMSAA model. It is especially superior to the AMSAA model in later stages of testing.Originality/valueThis research identifies cost-effective methods for developing more accurate reliability growth parameter estimates than those currently used.

Reliability Analysis Based on Improved Bayes Method of AMSAA Model

Aiming at the defects that failure samples of five-axis NC machine tools is small, traditional reliability analysis is not accurate, this paper presents reliability analysis mode based on improved Bayesian method for AMSAA model. Firstly, we obtain the failure model of NC machine tools meets the AMSAA model according to goodness-of-fit test, and in order to meet the requirements of simplifying engineering calculations, this paper adpots a method of Coefficient equivalent which converts failure Data into index-life data; then using Bayesian methods to estimate reliability parameters for the Index-life data; for the last we proceed point estimation and interval estimation for the MTBF of the machine. Take High-speed five-axis NC machine tools t of VMC650m for example, the result proved that the method can take advantage of a small sample of the equipment to proceed point estimation and interval estimation for MTBF failure data, and provide a reference for the optimization of maintenance strategies and Diagnostic work of the NC machine tools.