On Stationarity of Variance Calculation Series

Year 2023, Volume: 7 Issue: 2, 161 - 164, 25.07.2023

Ongun Yucesan

https://doi.org/10.30518/jav.1168121

Abstract

While making reliability observations, more samples mean one can make a statistically representative prediction. It is possible to model the failure arrival characteristics statistically using this knowledge. As a natural product of many experiments, a mean and variance figure can be identified for modelling the different occurrences. Even though the different situations can be modelled with such parameters, it may not wholly outline the condition of the product being developed and under test. The variance calculation series derived from the original reliability observation series, which is normally used for simple variance calculation, can be an important consideration. This consideration is rarely encountered. With a mean and a variance figure, a statistical prediction can be made. However, with the very same parameters, another reliability characteristic possessing product or a subcomponent may exist. For this instance, identifying whether the variance calculation series has stationarity and incorporating it in calculations can yield a possible prediction of a more accurate statistical model. In this study, the variance calculation series is considered for their stationary character at hand and is shown to possess such character yielding further modelling possibilities and emphasizing the importance of this consideration.

Keywords

Stationarity, Heteroscedasticity, Variance, Mean, Mean Time Between Failure (MTBF), Reliability

References

• Dickey, D. A., and W. A. Fuller. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. Vol. 74, pp. 427-431.
• Engle, R. (1988). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica. Vol. 96, pp. 893-920.
• Kipiński, L., König, R., Sielużycki, C., & Kordecki, W. (2011). Application of modern tests for stationarity to single-trial MEG data: transferring powerful statistical tools from econometrics to neuroscience. Biological cybernetics, 105(3-4), 183–195.
• Kwiatkowski, D., P. C. B. Phillips, P. Schmidt and Y. Shin. (1992) Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of Econometrics. Vol. 54, pp. 159-178.
• Machiwal, D., & Sharma, A (2008). Testing homogeneity, stationarity and trend in climatic series at Udaipur – a case study. Journal of Agrometeorology, 10(2), 127–135.
• Marcus J Chambers, (1996). Fractional integration, trend stationarity and difference stationarity Evidence from some U.K. macroeconomic time series, Economics Letters, Volume 50, Issue 1, Pages 19-24.
• Parey, S., Hoang, T.T.H. & Dacunha-Castelle, D. (2019). Future high-temperature extremes and stationarity. Nat Hazards 98, 1115–1134.
• Ulrich K. Müller, (2005). Size and power of tests of stationarity in highly autocorrelated time series, Journal of Econometrics, Volume 128, Issue 2, Pages 195-213.
• Yucesan, O., Özkil, A. & Özbek, 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, 2 (2), 22-30.
• Yucesan, O., Özkil, A. & Özbek, 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, 3 (1), 1-8.
• Zeybekoğlu, U. & Aktürk, G. (2022). Homogeneity and Trend Analysis of Temperature Series in Hirfanli Dam Basin. Türk Doğa ve Fen Dergisi, 11 (1), 49-58.