Small sample reliability growth modeling using a grey systems model

ABSTRACT

When 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.

KEYWORDS:

• AMSAA
• grey systems
• reliability
• reliability estimation
• reliability growth

About the authors

Thomas P. Talafuse is an Associate Professor in the Department of Operational Sciences at the Air Force Institute of Technology. He received his B.S. in Operations Research and in Mathematics from the United States Air Force Academy in 2007, a M.S. in Operations Research from the Air Force Institute of Technology in 2011, and a Ph.D. in Industrial Engineering from the University of Arkansas in 2016. His research interests are in reliability, applied statistics, risk analysis, and engineering optimization. He is a member of IISE and INFORMS.

Edward A. Pohl is a Professor and Head of the Department of Industrial Engineering, University of Arkansas, Fayetteville, AR, USA. He received his B.S. degree in Electrical Engineering from Boston University, a M.S. in Engineering Management from the University of Dayton, a M.S. in Reliability Engineering from the University of Arizona, a M.S. in Systems Engineering from the Air Force Institute of Technology, and a Ph.D. in Systems and Industrial Engineering from the University of Arizona. He currently serves as Director of the Center for Innovation in Healthcare Logistics (CIHL) and has previously served as the Director of the Operations Management Program at the University of Arkansas. His primary research interests are in risk, reliability, engineering optimization, healthcare and supply chain risk analysis, decision making, and quality. He is a Fellow of IISE, a Fellow of SRE, a Senior Member of IEEE, Senior Member of ASQ, a Diplomate in the Society of Health Systems, a Certified Materials and Resource Professional, a member of INCOSE, INFORMS, ASEM, and AHRMM.