Incorporation of Variance Calculation Differences in Reliability Predictions

Öz

This paper investigates the possible incorporation of the variability of a failure durations observation series into reliability estimates considering failure time series {3, 3, 5, 6, 6.2657} and {2.5097, 4.0678, 4.9942, 5.6460, 6.1684} with very similar mean and variance. The first series of failures of a device would yield the feeling of having a failure in the duration of the third period. Later on, it would have a user experience of failing anytime. The aim of the paper is to investigate how variant conditions can be incorporated into a reliability estimate. For this purpose, distinct schemes were chosen. Initial consideration was the averaging of estimated reliability functions predicted for different deviations. Later considerations involved estimating a single standard deviation figure by averaging possible deviations. Thirdly, is the normalized version of the preceding method. The conclusions drawn from the observations indicate consideration of variability into reliability calculations impacting the estimates, which would be dependent on operational conditions, such as reset costs and safety needs.

Anahtar Kelimeler

• Mean time between failures
• Reliability functions
• Reliability estimates

Varyans hesaplama farklarının güvenilirlik tahminlerine işlenmesi

Öz

Makale, arızalar arası süre gözlem serisi varyansının güvenilirlik tahminlerine olası dâhil edilmesini araştırmaktadır. Çok benzer ortalama ve varyansa sahip {3, 3, 5, 6, 6.265} ve {2.5097, 4.0678, 4.9942, 5.6460, 6.1684}hatalar arası süre serileri göz önüne alındığında. Birinci serinin geldiği cihazın arızaları sanki üçüncü periyotta arıza varmış gibi bir his uyandıracaktır. İkinci serinin geldiği cihaz ise sanki her an arıza olacakmış gibi bir kullanıcı deneyimi yaşayacaktır. Bu makale, değişken koşulların bir güvenirlik tahminine nasıl dâhil edildiğini araştırmaktır. Bu amaçla farklı yöntemler seçilmiştir. İlki, farklı sapma değerleri için tahmin edilen güvenilirlik fonksiyonlarının ortalamasının alınmasıdır. Daha sonraki yöntem ise, tek bir standart sapmanın farklı değerlerin ortalaması ile hesaplanılmasıdır. Üçüncü olarak ise, ikinci metot sonucunun normalize edilmesini içermektedir. Sonuç değişkenliğin güvenilirlik hesaplamalarına dâhil edilmesinin, her iş için oluşacak koşullara, sıfırlama maliyetlerine ve güvenlik ihtiyaçlarına göre değerlendirilmesi gereğini ortaya koymaktadır.

Anahtar Kelimeler

• Arızalar arasındaki ortalama süre
• Güvenirlik fonksiyonları

Kaynakça

1. [1] O. Yucesan , A. Ozkil ve E. Ozbek , “A Reliability Assessment of an Industrial Communication Protocol on a Windows OS Embedded PC for an Oil Rig Control Application” in Journal of Science, Technology and Engineering Research, c. 2, volume.2, pages. 22-30, Dec. 2021, doi:10.53525/jster.971534
2. [2] O. Yucesan , A. ̈Ozkil ve M. E. ̈Ozbek , “Validity of Exponential Distribution for Modelling Inter-failure Arrival Times of Windows based Industrial Process Control Data Exchange” inJournal of Science, Technology and Engineering Research, c. 3,Volum. 1, pages. 1-8, june. 2022, doi:10.53525/jster.1017004
3. [3] L. Wang, O. Thakkar and R. Mathews, "Unintended Memorization in Large ASR Models, and How to Mitigate It," ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Seoul, Korea, Republic of, 2024, pp. 4655-4659, doi: 10.1109/ICASSP48485.2024.10446083.
4. [4] A. Rai, R. Valenzuela, B. Tuffin, G. Rubino, P. Dersin ”Approximate Zero-Variance Importance Sampling for static network reliability estimation with node failures and ap- plication to rail systems.” Conference: 2016 Winter Simulation Conference (WSC) December 2016, 3201-3212.10.1109/WSC.2016.7822352.
5. [5] Y. Jiang, J. Lin, B. Cukic and T. Menzies, ”Variance Analysis in Software Fault Prediction Models,” 2009 20th International Symposium on Software Reliability Engineering, Mysuru, India,2009, pp. 99-108, doi: 10.1109/ISSRE.2009.13
6. [6] StathisChadjiconstantinidis, ”Some bounds for the renewalfunction and the variance of the renewal process,” in Applied Mathematics and Computation, Volume 436, 2023, 127497, ISSN 0096-3003, https://doi.org/10.1016/j.amc.2022.127497
7. [7] V. Khieovongphachanh, S. Kanthavong, K. Hamamoto and M. Chanthavong, "Image quality criterion of ultrasonic echo image using Standard Deviation," The 4th Joint International Conference on Information and Communication Technology, Electronic and Electrical Engineering (JICTEE), Chiang Rai, Thailand, 2014, pp. 1-3, doi: 10.1109/JICTEE.2014.6804082.
8. [8] S. Xin, Y. Wang and W. Lv, "Standard deviation control chart based on weighted standard deviation method," Proceedings of the 33rd Chinese Control Conference, Nanjing, China, 2014, pp. 3574-3579, doi: 10.1109/ChiCC.2014.6895533.

9. [9] Abu-Shawiesh, Moustafa. A control chart based on robust estimators for monitoring the process mean of a quality characteristic. International Journal of Quality & Reliability Management.(2009) 26. 480-496. 10.1108/02656710910956201.
10. [10]P. Joglekar, T. Katale, A. Katale, S. Deshpande, A. Nirgude and A. Chotrani, "A Novel approach for formation of Dense Clusters by Outlier Elimination and Standard Deviation," 2024 Fourth International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), Bhilai, India, 2024, pp. 1-6, doi: 10.1109/ICAECT60202.2024.10468952
11. [11] F. Ding and T. Cao, "Application of Daubechies Wavelet Transform in the Estimation of Standard Deviation of White Noise," 2011 Second International Conference on Digital Manufacturing & Automation, Zhangjiajie, China, 2011, pp. 212-215, doi: 10.1109/ICDMA.2011.59.
12. [12] Y. Wang, C. Zheng and H. Peng, "Covariance Mean-to-Standard-Deviation Factor for Ultrasound Imaging," 2020 IEEE International Ultrasonics Symposium (IUS), Las Vegas, NV, USA, 2020, pp. 1-4, doi: 10.1109/IUS46767.2020.9251390.
13. [13] A. Yousefpour, R. Ibrahim, H. N. Abdul Hamed, U. H. Hair Zaki and K. A. Mohamed Khaidzir, "Feature subset selection using mutual standard deviation in sentiment mining," 2017 IEEE Conference on Big Data and Analytics (ICBDA), Kuching, Malaysia, 2017, pp. 13-18, doi: 10.1109/ICBDAA.2017.8284100.
14. [14] L. Zhao, L. Wang and D. Liu, "Hyperspectral Imagery Band Selection Based on Maximal Standard Deviation," 2015 8th International Symposium on Computational Intelligence and Design (ISCID), Hangzhou, China, 2015, pp. 59-62, doi: 10.1109/ISCID.2015.141.
15. [15] K. Pengsen and Y. Zhenming, "Image blurred region detection based on RGB color space information and local standard deviation," 2017 IEEE 2nd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), Chongqing, China, 2017, pp. 2177-2181, doi: 10.1109/IAEAC.2017.8054403.
16. [16] B. S. Prakoso, I. K. Timotius and I. Setyawan, "Palmprint identification for user verification based on line detection and local standard deviation," 2014 The 1st International Conference on Information Technology, Computer, and Electrical Engineering, Semarang, Indonesia, 2014, pp. 155-159, doi: 10.1109/ICITACEE.2014.7065733.
17. [17] Yang and Zheng Zhou, "Research and implementation of image enhancement algorithm based on local mean and standard deviation," 2012 IEEE Symposium on Electrical & Electronics Engineering (EEESYM), Kuala Lumpur, 2012, pp. 375-378, doi: 10.1109/EEESym.2012.6258668.
18. [18] J. Zhang, "Study on Software Project Significant Deviation Standard," in Computer Science and Software Engineering, International Conference on, null, 2008, pp. 15-18, doi: 10.1109/CSSE.2008.721.
19. [19] W. Luo, "A comment on "Estimating the standard deviation from extreme Gaussian values"," in IEEE Signal Processing Letters, vol. 12, no. 2, pp. 109-111, Feb. 2005, doi: 10.1109/LSP.2004.840840.
20. [20] Matevska, Jasminka &Noack, Enrico & Reinhold, Manuel &Diekmann, Eike. (2020). Decentralised Avionics and Software Architecture for Sounding Rocket Missions. 10.18420/SE2020\_66
21. [21] K.S. Trivedi Probability & Statistics With Reliability, Queuing And Computer Science Applications, 2Nd Ed Wiley India Pvt.Limited, 2008, isbn 9788126518531 Conference Proceedings