Impact of Operations on a Series per Reliability Perspective

Year 2025, Volume: 9 Issue: 1, 1 - 4, 26.02.2025

Ongun Yucesan

https://doi.org/10.30518/jav.1475257

Abstract

The Mean Time Between Failure (MTBF) figures are the average of test durations between failure observations formed into a series. They can be seen to suit classical statistical distributions. An equally possible condition is that they are not stationary as a contradiction to the previous statement. In such worse conditions accepting availability of a concealed statistical property, this paper tries to identify the impact of Bi-sample Differencing and Bi-sample mean manipulations. In other words, operating on reliability observations series to reveal concealed statistical knowledge. Experimentation based on observation over a stationary series as a controlled experiment. As an outcome of experiments, the differencing seems to be alleviating the trend and seasonality to a degree. The bi-sample averaging is observed to be hiding variant conditions.

Keywords

Differencing , Stationary , Heteroscasdicity , MTBF , AutoRegression Moving Average (ARMA)

References

• Basu, P. Rudoy, D. and Wolfe, P. J. (2009). A nonparametric test for stationarity based on local Fourier analysis, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009, first and last page 3005-3008.
• Chambers, M.J., (1996). Fractional integration, trend stationarity and difference stationarity Evidence from some U.K. macroeconomic time series, Economics Letters, Volume and Issue 50(1), first and last page 19-24,
• Chowdhury, S.K., Nimbarte, A.D. (2017). Effect of fatigue on the stationarity of surface electromyography signals, International Journal of Industrial Ergonomics, Volume 61, first and last page 120-125,
• Franklin, W.W. and White, K.P. (2008). Stationarity tests and MSER-5: Exploring the intuition behind mean- squared-error-reduction in detecting and correcting initialization bias, 2008 Winter Simulation Conference, 2008, first and last page 541-546.
• Gimeno, R., Manchado, B., Minguez, R., (1999). Stationarity
• tests for financial time series, Physica A: Statistical Mechanics and its Applications, Volume and Issue 269(1), first and last page 72-78
• HyunWook, L., Granata, K. (2008). Process stationarity and reliability of trunk postural stability, Clinical Biomechanics, Volume and Issue 23(6), first and last page 735-742
• James, C., and Murthy, H. A., (2011). Time series models and its relevance to modeling TCP SYN based DoS attacks, 2011 7th EURO-NGI Conference on Next Generation Internet Networks, 2011, first and last page 1-8.
• Kipinski, L., Konig, R., Sieluzycki, C. (2011). Application of modern tests for stationarity to single-trial MEG data. Biol Cybern Volume 105, first and last page 183–195.
• Lee H. L., Granata K. P. (2008). Process stationarity and reliability of trunk postural stability, Clinical Biomechanics, Volume 23, Issue 6, 2008,
• first and last page 735-742
• Li, M., Chen, WS. and Han, L. (2010). Correlation matching method for the weak stationarity test of LRD traffic. Telecommun Syst. Volume 43, first and last page 181–195.
• Machiwal, D., and Sharma, A. (2008). Testing homogeneity, stationarity and trend in climatic series at Udaipur - a case study. Journalf Agrometeorology. Volume 10, first and last page 127-135.
• Marti-Cardona, B., Lopez-Martinez, C. and Dolz-Ripolles, J. (2012). Local texture stationarity indicator for filtering Do ̃Nana wetlands SAR images, IEEE International Geoscience and Remote Sensing Symposium, 2012, first and last page 4903-4906.
• Maystrenko, A.V. & Svetlakov, A.A. & Gandsha, Taras & Dmitriev, V.M. & Aksenova, Natalia.(2017) ”Application of numerical signal differentiation methods to determine stationarity of A process”. Petroleum and Coal. Volume 59, first and last page 311-318.
• Muheialdin, O. Van Swearingen, J., Karim, H., Huppert, T., Sparto, P.J., Erickson, K.I., Sejdi ́c, E. (2014). An investigation of fMRI time series stationarity during motor sequence learning foot tapping tasks. J Neurosci Methods. Apr 30; Volume 227, first and last page 75-82.
• Muller, U.K. (2005). Size and power of tests of stationarity in highly autocorrelated time series, Journal of Econometrics, Volume and Issue 128(2), first and last page 195-213
• Parey, S., Hoang, T.T.H. and Dacunha-Castelle, D. (2019). Future high temperature extremes and stationarity. Nat Hazards 98, first and last page 1115–1134.
• Presno, M.J., Lopez, A.J. (2003). Testing for stationarity in series with a shift in the mean. A fredholm approach. Test Volume 12, first and last page 195–213.
• Rasoulzadeh, V., Erkus, E.C., Yogurt, T.A. (2017). A comparative stationarity analysis of EEG signals. Ann Oper Res., Volume 258, first and last page 133–157.
• Sadhukhan, B., Mukherjee, S., Agarwal, S. (2019). Investigation of Fractality and Stationarity Behaviour on Earthquake In: Thampi S.,
• Marques O., Krishnan S., Li KC, Ciuonzo D., Kolekar M. Advances in Signal Processing and Intelligent Recognition Systems. SIRS 2018. Communications in Computer and Information Science, Volume 968. Springer, Singapore.
• Sun, X and Chen, Z. (2021). A Comparison of Mean Reverting Forex Trading Strategies Based on Stationarity Testing Methods, 2021 5th International Conference on E-Business and Internet (ICEBI 2021). Association for Computing Machinery, New York, NY, USA, first and last page 147–150.
• Taylor R, A. (2003). Robust Stationarity Tests in Seasonal Time Series Processes. Journal of Business & Economic Statistics, Volume and Issue 21(1), first and last page 156–163
• Worden, K., Iakovidis, I., Cross, E.J. (2019). On Stationarity and the Interpretation of the ADF Statistic. In: Dynamics of Civil Structures, Conference Proceedings of the Society for Experimental Mechanics Series. Volume 2. Springer, Cham.
• Yucesan, O., Ozkil, A. and Ozbek, M. E. (2021). A Reliability Assessment of an Industrial Communication Protocol on a Windows OS Embedded PC for an Oil Rig Control Application, Journal of Science, Technology and Engineering Research, c. 2, volume. 2, first and last page 22-30.
• Yucesan, O., Ozkil, A. ve Ozbek, M. E. (2022). Validity of Exponential Distribution for Modelling Inter-failure Arrival Times of Windows based Industrial Process Control Data Exchange, Journal of Science, Technology and Engineering Research, c. 3, Volume 1, first and last page 1-8.