Non-parametric analysis of maintenance data for Attitude Indicator of a commercial aircraft fleet

Year 2023, , 103 - 108, 15.08.2023

Selda Kapan Ulusoy Mahmut Sami Şaşmaztürk

https://doi.org/10.35860/iarej.1184070

Abstract

Analysis of maintenance data for a repairable system provides information about the failure behavior of the system. Such information is needed for determining preventive maintenance and retirement policy for the system. Parametric and non-parametric models can be used for analysis. Parametric models require more assumptions about the failure process of the systems under consideration compared to non-parametric models. To verify these assumptions statistical expertise needed. The purpose of this paper is to show that in practice non-parametric estimator of mean cumulative function can be utilized easily to model the failure behavior of a fleet. Mean cumulative function estimates the mean number of failures as function of operating hours. The method is exemplified on the attitude indicator units of a commercial aircraft fleet. Sampling uncertainty of the estimates is quantified by normal approximation confidence intervals.

Keywords

Aircraft, Mean cumulative function, Multiple repairable systems, Recurrence data, Recurrence rate

References

• 1. Cha, J.H. and M. Finkelstein, Point Processes for Reliability Analysis: Shocks and Repairable Systems, in Point Processes for Reliability Analysis: Shocks and Repairable Systems. 2018, Springer: New York. p. 1-419.
• 2. Lawless, J., Statistical methods in reliability. Technometrics, 1983. 25(4): p. 305-316.
• 3. Nelson, W., Graphical analysis of system repair data. Journal of Quality Technology, 1988. 20(1): p. 24-35.
• 4. Trindade, D. and S. Nathan. Simple plots for monitoring the field reliability of repairable systems. in Annual Reliability and Maintainability Symposium, 2005. Proceedings. 2005. IEEE.
• 5. Block, J., et al., Fleet-level reliability analysis of repairable units: a non-parametric approach using the mean cumulative function. International Journal of Pedagogy, Innovation and New Technologies, 2013. 9(3): p. 333-344.
• 6. Trindade, D. and S. Nathan, Analysis of repairable systems with severe left censoring or truncation. Quality Engineering, 2018. 30(2): p. 329-338.
• 7. Rausand, M. and A. Høyland, System reliability theory: models, statistical methods, and applications. Vol. 396. 2003: John Wiley & Sons.
• 8. Cook, R.J. and J.F. Lawless, The statistical analysis of recurrent events. 2007: Springer.
• 9. Ascher, H. and H. Feingold, Repairable systems reliability: modeling, inference, misconceptions and their causes. 1984: M. Dekker New York.
• 10. Garmabaki, A., et al., A reliability decision framework for multiple repairable units. Reliability Engineering & System Safety, 2016. 150: p. 78-88.
• 11. Kvaløy, J.T. and B.H. Lindqvist, TTT-based tests for trend in repairable systems data. Reliability Engineering & System Safety, 1998. 60(1): p. 13-28.
• 12. Rigdon, S.E. and A.P. Basu, Statistical methods for the reliability of repairable systems. 2000: Wiley New York.
• 13. Kvaløy, J.T. and B.H. Lindqvist, A class of tests for renewal process versus monotonic and nonmonotonic trend in repairable systems data, in Mathematical and Statistical Methods in Reliability. 2003, World Scientific. p. 401-414.
• 14. Viertävä, J. and J.K. Vaurio, Testing statistical significance of trends in learning, ageing and safety indicators. Reliability Engineering & System Safety, 2009. 94(6): p. 1128-1132.
• 15. Shen, L., B. Cassottana, and L.C. Tang, Statistical trend tests for resilience of power systems. Reliability Engineering & System Safety, 2018. 177: p. 138-147.
• 16. Kvaløy, J.T. and B.H. Lindqvist, A class of tests for trend in time censored recurrent event data. Technometrics, 2020. 62(1): p. 101-115.
• 17. Ascher, H.E. and C.K. Hansen, Spurious exponentiality observed when incorrectly fitting a distribution to nonstationary data. IEEE transactions on reliability, 1998. 47(4): p. 451-459.
• 18. Ascher, H.E., A set-of-numbers is NOT a data-set. IEEE Transactions on Reliability, 1999. 48(2): p. 135-140.
• 19. Nelson, W.B., Recurrent events data analysis for product repairs, disease recurrences, and other applications. Vol. 10. 2003: SIAM.
• 20. Zuo, J., W.Q. Meeker, and H. Wu, A simulation study on the confidence interval procedures of some mean cumulative function estimators. Journal of Statistical Computation and Simulation, 2013. 83(10): p. 1868-1889.
• 21. Chan, K.C.G. and M.-C. Wang, Semiparametric modeling and estimation of the terminal behavior of recurrent marker processes before failure events. Journal of the American Statistical Association, 2017. 112(517): p. 351-362.
• 22. Nelson, W., Confidence limits for recurrence data—applied to cost or number of product repairs. Technometrics, 1995. 37(2): p. 147-157.
• 23. Nelson, W.B., Repair Data, Sets of: How to Graph, Analyze, and Compare. Encyclopedia of Statistics in Quality and Reliability, 2008.
• 24. Zuo, J., W.Q. Meeker, and H. Wu, Analysis of window-observation recurrence data. Technometrics, 2008. 50(2): p. 128-143.
• 25. Jiang, R., et al., A robust mean cumulative function estimator and its application to overhaul time optimization for a fleet of heterogeneous repairable systems. Reliability Engineering & System Safety, 2023: p. 109265.
• 26. Nelson, W.B., Repair Data, Sets of: How to Graph, Analyze, and Compare. Encyclopedia of Statistics in Quality and Reliability, 2008. 4.
• 27. Nelson, W.B., Recurrent events data analysis for product repairs, disease recurrences, and other applications. 2003: SIAM.
• 28. William, W. and L.A. Escobar, Statistical methods for reliability data. A. Wiley Interscience Publications, 1998.