Statistical bootstrap in the problem of availability factor estimating: example of SRs 1200 excavator reliability


It is difficult sometimes to estimate the confidence intervals for the particular statistics, because there is no so far for some of them mathematical expression for their variance. That is true for availability factor—complex characteristic of restorable items reliability. Statistical bootstrap, as one of resampling methods, has been applied to this problem. Availability of subsystems of rotary excavator has been considered using the proposed method. The data of reliability were collected in Serbia, at open coal development. The proposed model is based on statistical bootstrap method. On the basis of proposed method, the availability factor confidence intervals and histograms for excavator subsystems were built. The availability factor of the system in a whole was also evaluated. The results, as well as comparison with existing approaches, are presented. The attempt has been made to estimate the risk factor of subsystems using the data of availability.

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  1. Adler YuP, Gadolina IV, Ljandres MN (1987) Bootstrap-modeling in building of confidence intervals for censored sets. Zavodskaja laboratorija 10:90–94 (In Russian)

    Google Scholar 

  2. Baxter LA (1996) Nonparametric estimation of limiting availability. Lifetime Data Anal 2:391–402

    Article  Google Scholar 

  3. Bevrani H (2005) Statistical methods for analyzing complicated systems’ reliability based on some asymptotic statistics. Dissertation, Moscow State University (In Russian)

  4. Efron B (1979) Bootstrap method: another look at jackknife. Ann Stat 7(1):1–26

    MathSciNet  Article  Google Scholar 

  5. Efron B, Tibshirani RL (1993) An introduction of the bootstrap. Chapman and Hall/CRC, New York

    Google Scholar 

  6. Erokchin GN, Konovskii VV (2014) Characteristics of reliability monitoring for combine harvesters. Nauka v centralnoi Rossii 1:16–20

    Google Scholar 

  7. Garcia AC, Papic L (2015) Reliability modeling and prediction. DQM, Prijevor

    Google Scholar 

  8. Mannen E (1991) When does Boostrtap work? Asymptotic results and simulation. Springer, Berlin

    Google Scholar 

  9. Marks CE (2014) Applying bootstrap methods to system reliability. Am Stat 68(3):174–182

    MathSciNet  Article  Google Scholar 

  10. Ogieva FE, Ike AS, Anyaeji CA (2015) Egbin power station generator availability and unit performance studies. Int J Phys Sci 10(4):155–172

    Article  Google Scholar 

  11. Papic L, Aronov J, Pantelic M (2009) Safety based maintenance concept. Int J Reliab Qual Saf Eng 16(6):1–17

    Article  Google Scholar 

  12. Stamatis DH (2003) Failure mode and effects analysis, FMEA from theory to execution. ASQ Quality Press, Milwaukee

    Google Scholar 

  13. Zainetdinov RI (1996) Using bootstrap modeling for statistical evaluation of the reliability parameters of load-carrying welded structures in freight wagons. Weld Int 10(6):491–494 In Russian

    Article  Google Scholar 

  14. Zainetdinov RI, Plokhikh IV (2012) Refined estimation and prediction of availability function of Sapsan train on the base of imitation simulation of operational process. Transp Nauka Techn Upr 12:11–19 (In Russian)

    Google Scholar 

  15. Zaynetdinov RI, Rudnikova MA, Plokhikh I (2016) Russian experience of the availability function prediction for the “Velaro Rus” high-speed train by means of the operation process simulation. In: Proceedings of the 7th DQM international conference life cycle engineering and management ICDQM-2016, pp 32–42

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Appendix 1

Rotary excavator SRs 1200 × 24/4 × 0(400 kW) + VR, No. 5

The excavator was used in opencast coal development Field D, Open coal development Kolubara, Lazarevac, Serbia Electrical. A backhoe works on digging the earth. Digging Yalova earth runs to a depth of 120–180 m until it starts to do the digging for coal. Sometimes on the surface of the yalovoy earth digging 3 bucket wheel excavators operate at the same time, in different positions.

Were examined serially connected subsystems of the excavator SRs 1200x24/4x0(400 kW) + VR. Photo of the excavator is shown in Fig. 3.

Fig. 3

General view of the excavator

Main parameters of the excavator:

  • manufacturer: Förderanlagen und Baumaschinen GmbH, Magdeburg, Germany:

  • operating weight: 1.528 t,

  • digging height: 24 m,

  • digging depth: 4 m,

  • power reducer impeller drive: 400 kW,

  • theoretical capacity (100% filling of the bucket Yalova earth): 3.465 m3/h,

  • rotor diameter: 8.2 m,

  • number of buckets: 8,

  • bucket capacity: 800 l.

Every year the planned preventive maintenance is carried out. Nether the less the failures of the subsystems of machine take place. Subsystems are restored, repaired products, therefore, to characterize their reliability the availability factor AF is used. In the process of operation after completion of annual maintenance during the calendar year, the observation of the technical state of its subsystems is carried out.

Appendix 2

The data, which were used for statistical modeling bootstrap for estimation of availability factor variability, are shown in Table 6.

Table 6 Up-states and down-states of the system of material digging

The Table 6 gives the example of reliability list of subsystem “digging of material”, MKM. Here in the Table, R—time in up-state, min; O—down-state. The entries go consequently as they were registered during one year service.

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Gadolina, I., Papic, L. & Zaynetdinov, R. Statistical bootstrap in the problem of availability factor estimating: example of SRs 1200 excavator reliability. Int J Syst Assur Eng Manag 10, 21–28 (2019).

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  • Statistical bootstrap
  • Reliability
  • Rotor excavator
  • Availability factor
  • Confidence intervals
  • Risk evaluation