Evaluating the lifespan of a Stirling cooler system, considering different failure modes

Document Type : Original Article

Author
Aerospace Research institute
10.22034/jssta.2026.513896.1238
Abstract
The expected lifespan is a primary concern for engineers involved in the design and construction of equipment. Accurately calculating the lifespan of complex systems necessitates the use of specific techniques and methodologies. This paper presents an experimental investigation of a Stirling cooler, as a heat engine that generates cryogenic temperatures through the cyclic compression and expansion of helium gas at different temperature levels. The data obtained from lifespan testing have been thoroughly analyzed. Four samples of this cooler were utilized for the test, and control parameters, including temperature and current intensity, were closely monitored. A system failure or an increase in its parameters beyond specified levels is considered as a failure event. This study explores the differentiation of failure modes and their impact on reliability calculations, as well as recommendations for inspection and maintenance intervals. Due to the limited number of samples, various nonparametric methods, including Nelson-Allen, Kaplan-Meier and Crow, were employed to analyze and estimate the parameters. The research findings indicate that the results obtained from the Kaplan-Meier method are less accurate compared to the other two methods. Furthermore, for repairable systems, isolating failure modes enhances the reliability calculation process and reduces maintenance costs.
Keywords
Subjects

[1] M. R. Azmoodeh, A. Keshavarz, A. Batooei, H. Saberinejad, M. Payandehdoost, and H. Keshtkar, “Experimental study and thermal analysis of a gamma-type Stirling engine for multi-objective optimization,” Int. J. Automot. Res., vol. 10, no. 3, pp. 3281–3294, 2020.
[2] E. Hassanzadeh, M. Aliehyaei, S. Jafari Mehrabadi, A. Mohammadi, and H. Mazaheri, “Experimental investigation on the gamma-model Stirling engine for cooling production using various gases,” J. Engine Res., vol. 59, pp. 17–28, 2020. (in Persian).
[3] N. Pundak, Z. Porat, M. Barak, Y. Zur, and G. Pasternak, “Field reliability of Ricor microcoolers,” in Proc. SPIE, Infrared Technol. Appl. XXXV, vol. 7298, Art. no. 72983I, Orlando, FL, USA, 2009.
[4] A. Katz, V. Segal, A. Filis, Z. B. Haim, I. Nachman, E. Krimnuz, and D. Gover, “Ricor's cryocoolers development and optimization for hot IR detectors,” in Proc. SPIE, vol. 9070, Baltimore, MD, USA, 2014.
[5] A. Filis, N. Pundak, Y. Zur, et al., “Cryocoolers for infrared missile warning systems,” in Proc. SPIE, Infrared Technol. Appl. XXXVI, vol. 7660, Art. no. 76602L, Orlando, FL, USA, 2010.
[6] J. M. Cauquil, C. Seguineau, J.-Y. Martin, and T. Benschop, “Reliability improvements on Thales RM2 rotary Stirling coolers: Analysis and methodology,” in Proc. SPIE, vol. 9821, Baltimore, MD, USA, 2016.
[7] University of Oxford, “Cryocoolers for space application.” Accessed: May 10, 2025. [Online]. Available: https://eng.ox.ac.uk/cryogenics/research/cryocoolers-for-space-application
[8] M. A. Farsi, Test Stand Design and Failure Analysis of Stirling Coolers. ARI Research Report, 2023. (in Persian).
[9] J. S. Reed and G. D. Peskett, “Development of a low-power Stirling cycle cryocooler for space applications,” in Cryocoolers, R. G. Ross, Ed. Boston, MA, USA: Springer, 2003, ch. 12. doi: 10.1007/0-306-47919-2_4.
[10] T. A. Arslan and T. Kocakulak, “A comprehensive review on Stirling engines,” Eng. Perspect., vol. 3, no. 3, pp. 42–56, 2023.
[11] R. G. Ross Jr., Cryocooler Reliability and Redundancy Considerations for Long-Life Space Missions. Boston, MA, USA: Kluwer Academic/Plenum Publishers, 2001.
[12] G. Hu and F. Huffer, “Modified Kaplan–Meier estimator and Nelson–Aalen estimator with geographical weighting for survival data,” Geogr. Anal., vol. 52, no. 1, pp. 28–48, 2020.
[13] E. Colosimo, F. Ferreira, M. Oliveira, and C. Sousa, “Empirical comparisons between Kaplan–Meier and Nelson–Aalen survival function estimators,” J. Stat. Comput. Simul., vol. 72, no. 4, pp. 299–308, 2002.
[14] A. Erdmann, J. Beyersmann, and E. Bluhmki, “Comparison of nonparametric estimators of the expected number of recurrent events,” Pharm. Stat., vol. 23, no. 3, pp. 339–369, 2024.
[15] M. Zarourati, M. Mirshams, and M. Tayefi, “Active under-actuation fault-tolerant backstepping attitude tracking control of a satellite with interval error constraints,” Adv. Control Appl. Eng. Ind. Syst., vol. 215, 2024, doi: 10.1002/adc2.215.
[16] M. Moaveni-Tajoddin, M. A. Farsi, and I. Bahman Jahromi, “Optimal sensors positioning by using value of information method,” Int. J. Reliab. Risk Saf. Theory Appl., vol. 6, no. 1, pp. 87–96, 2023, doi: 10.22034/IJRRS.2023.6.1.10.
[17] M. A. Farsi, Principles of Reliability Engineering, 2nd ed. Tehran, Iran: Symayeh Danesh, 2022. (in Persian).
[18] M. Modarres, M. P. Kaminskiy, and V. Krivtsov, Reliability Engineering and Risk Analysis: A Practical Guide, 3rd ed. Boca Raton, FL, USA: CRC Press, 2016.
[19] W. B. Nelson, Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications. Philadelphia, PA, USA: SIAM, 2003.
[20] D. Trindade and N. S. Nathan, “Analysis of repairable systems with severe left censoring or truncation,” Qual. Eng., vol. 30, no. 2, pp. 329–338, 2018.
[21] W. Si, Q. Yang, L. Monplaisir, and Y. Chen, “Reliability analysis of repairable systems with incomplete failure time data,” IEEE Trans. Reliab., vol. 67, no. 3, pp. 1043–1059, 2018.
[22] P. Chen and Z.-S. Ye, “Random effects models for aggregate lifetime data,” IEEE Trans. Reliab., vol. 66, no. 1, pp. 76–83, 2017.
[23] M. Kijima, “Some results for repairable systems with general repair,” J. Appl. Probab., vol. 26, no. 1, pp. 89–102, 1989.
[24] M. Luz Gámiz, K. B. Kulasekera, N. Limnios, and B. H. Lindqvist, Applied Nonparametric Statistics in Reliability. New York, NY, USA: Springer, 2011.
[25] L. H. Crow, “Methods for reducing the cost to maintain a fleet of repairable systems,” in Proc. Annu. Reliab. Maintainab. Symp. (RAMS), USA, 2003, pp. 392–399.
[26] S. Shuhei, K. Tanaka, Y. Sato, K. Shinozaki, and S. Mitani, “Evaluation method for effect of active vibration control on cooling performance of Stirling cooler,” Cryogenics, vol. 117, Art. no. 103308, 2021.
 
Volume 5, Issue 2
March 2026
Pages 144-155

  • Receive Date 15 April 2025
  • Revise Date 18 May 2025
  • Accept Date 28 June 2026