Small sample reliability growth modeling using a grey systems model

Abstract

ABSTRACTWhen 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 reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. For purposes of handling limited failure data, we propose the use of a modified GM(1,1) model to predict system reliability growth parameters and investigate how parameter estimates are affected by systems whose failures follow a poly-Weibull distribution. Monte-Carlo simulation is used to map the response surface of system reliability, and results are used to compare the accuracy of the modified GM(1,1) model to that of the AMSAA growth model. It is shown that with small sample sizes and multiple failure modes, the modified GM(1,1) model is more accurate than the AMSAA model for prediction of growth model parameters.