Designing an accelerated degradation test plan considering the gamma degradation process with multi-stress factors and interaction effects

ABSTRACT

The effectiveness of accelerated degradation test and subsequent reliability assessment depends on the efficient test plan. Designing an accelerated test plan requires determining the optimal values of several decision variables. The problem of designing an accelerated degradation test becomes even more challenging when multiple stress factors and their interaction effects are considered. In this work, an optimal accelerated degradation test plan is presented considering the stochastic gamma process with constant stress loading. Both gamma parameters are treated as stress-dependent variables to capture the impact of stress levels. An optimization model is formulated considering multiple stress factors and their interaction effects for offering a more realistic test plan. The optimization criteria are set to minimizing the asymptotic variance of the maximum likelihood estimator of the lifetime at normal operating conditions within the total experimental cost constraints. The decision variables comprised in the optimization model are measurement time intervals, the frequency of measurements, stress levels, and sample allocation at each stress level. The sensitivity analysis is performed to investigate the model's robustness against the budget constraints and pre-estimates of model parameters. To demonstrate the proposed methodology, a case example of carbon film-resistors’ performance data is considered for designing the degradation test plan.

KEYWORDS:

• Accelerated degradation test
• gamma process
• multi-stress factors
• interaction effects
• monotonic degradation
• asymptotic variance

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported under the Research ND program by the North Dakota Department of Commerce; under Grant number: FAR0023608; and Doosan Infracore Construction Equipment(Bobcat), under Grant/Award Number: FAR0023610;Doosan Infracore Construction Equipment (Bobcat) [FAR0023610];Research ND program by the North Dakota Department of Commerce [FAR0023608].

Notes on contributors

Shah Limon

Shah Limon is an Assistant Professor of Industrial & System Engineering at Slippery Rock University of Pennsylvania, USA. He received his M.Sc. and Ph.D. from the Department of Industrial and Manufacturing Engineering at North Dakota State University, Fargo, USA and B.Sc. degree in Industrial and Production Engineering from Bangladesh University of Engineering & Technology, Dhaka, Bangladesh. His research interest includes but not limited to reliability estimation, accelerated test design and analysis, stochastic modeling, failure analysis, process improvement, and warranty estimation. Shah’s research work has been published in Quality & Reliability Engineering International, Journal of Risk & Reliability, International Journal of Quality & Reliability Management, and International Journal of Quality Engineering and Technology. He is a member of IISE.

Esmaeil Rezaei

Esmaeil Rezaei has graduated from the Department of Industrial Engineering at the University of Science and Technology of Mazandaran, Behshahr, Iran. He also received his MS from the same school in 2015. His research interests include reliability centered maintenance, operating research, and mathematical modeling.

Om Prakash Yadav

Om Prakash Yadav a Professor and Duin Endowed Fellow in the Department of Industrial and Manufacturing Engineering at North Dakota State University, Fargo. He received his Ph.D. degree in Industrial Engineering from Wayne State University, MS in Industrial Engineering from National Institute of Industrial Engineering Mumbai (India), and BS in Mechanical Engineering from Malaviya National Institute of Technology, Jaipur (India). His research interests include reliability modeling and analysis, risk assessment, design optimization, robust design, and manufacturing systems analysis. The research work of his group has been published in high-quality journals such as reliability engineering and systems safety, journal of risk and reliability, quality and reliability engineering international, and engineering management journal.  has published over 130 papers in peered reviewed journals and conference proceedings in the area of quality, reliability, product development, and operations management.  Dr. Yadav is a recipient of the 2015 & 2018 IISE William A.J. Golomski best paper awards. He has published over 130 research papers in the area of reliability, risk assessment, design optimization, and operations management. He is currently a member of IISE, ASQ, SRE, and INFORMS.