Mathematical modelling to industrial repair and maintenance policy system for its reliability

2021;
: pp. 465–473
https://doi.org/10.23939/mmc2021.03.465
Received: February 04, 2021
Revised: May 28, 2021
Accepted: June 19, 2021

Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 465–473 (2021)

1
Chitkara University Institute of Engineering and Technology, Chitkara University
2
Department of Mathematics and Statistics, Ch. Charan Singh Haryana, Agricultural University
3
Department of Applied Sciences, Panipat Institute of Engineering and Technology

The present paper is an initiative taken by emerging reliability model to a automobile repair industries for its products by dividing repair policy into two categories as (a) regular/normal service and (b) strategy for accidental or additional failure.  The concept of inspection process has been introduced for proper verification of failure and also to its repairing strategy with time and cost.  The maintenance cost for regular services are fixed but for the case of additional failures the additional cost will be decided upon the level of damage.  The stochastic analysis for system been numerically and graphically analyzed by calculating reliability variables like MTSF, availability, inspection and maintenance analysis of the system with the concept of geometric distribution, Markov process and regenerative technique.  The results been proved beneficial for fulfilling the objective of calculating profit function that increases with increasing repair and decreasing failure rate.

  1. Singh D., Taneja G.  Reliability and economic analysis of a power generating system comprising one gas and one steam turbine with random inspection.  Journal of Mathematics and Statistics. 10 (4), 436–442 (2014).
  2. Bhatti J., Chitkara A., Kakkar M.  Stochastic analysis of parallel system with two discrete failures.  Model Assisted Statistics and Applications. 9, 257–265 (2014).
  3. Bhatti J., Chitkara A., Kakkar M.  Stochastic analysis of dis-similar standby system with discrete failure, inspection and replacement policy.  Demonstratio Mathematica. 49 (2), 224–235 (2016).
  4. Hua D. G., Elsayed E.  Reliability estimation of k-out-of-npairs: G balanced systems with spatially distributed units.  IEEE Trans. Reliability. 65, 886–900 (2016).
  5. Hua D. G., Elsayed E.  Degradation analysis of k-out-of-n pairs: G balanced systems with spatially distributed units.  IEEE Trans. Reliability. 65, 941–956 (2016).
  6. Taj S. Z., Rizwan S. M., Alkali B. M., Harrison D. K., Taneja G.  Probabilistic modeling and analysis of a cable plant subsystem with priority to repair over preventive maintenance.  I-Managers Journal on Mathematics. 6 (3), 12–21 (2017).
  7. Adlakha N., Taneja G., Shilpi. Reliability and cost-benefit analysis of a two-unit cold standby system used for communication through satellite with assembling and activation time.  International Journal of Applied Engineering Research. 12 (20), 9697–9702 (2017).
  8. Cui L. R., Gao H. D., Mo Y. C.  Reliabilities for k-out-of-n: F balanced systems with m sectors.  IISE Trans. 50 (5), 381–393 (2017).
  9. Cui L. R., Chen J. H., Li X. C.  Balanced reliability systems under Markov processes.  IISE Trans. 51 (9), 1025–1035 (2018).
  10. Endharta A. J., Yun W. Y., Ko Y. M.  Reliability evaluation of circular k-out-of-n:G balanced systems through minimal path sets.  Reliability Engineering and System Safety. 180, 220–236 (2018).
  11. Chen W. L.  System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy.  System Engineering. 21, 59–69 (2018).
  12. Saini M., Kumar A.  Stochastic modeling of a single-unit system operating under different environmental conditions subject to inspection and degradation.  Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 21, 1–8 (2018).
  13. Kumar A., Saini M.  Analysis of some reliability measures of single-unit systems subject to abnormal environmental conditions and arbitrary distribution for failure and repair activities.  Journal of Information and Optimization Sciences. 39 (2), 545–559 (2018).
  14. Barak M. S., Yadav D., Barak S. K.  Stochastic analysis of two unit redundant system with priority to inspection over repair.  Life Cycle Reliability and Safety Engineering. 21, 1–9 (2018).
  15. Bhardwaj S., Bhardwaj N., Kumar V., Parashar B.  Estimation of lifespan of diesel locomotive engine.  Journal of Information and Optimization Sciences. 40 (5), 1097–1108 (2019).
  16. Dong Q. L., Cui L. R., Si S. B.  Reliability and availability analysis of stochastic degradation systems based on bivariate wiener processes.  Appl. Math. Model. 79, 414–433 (2019).
  17. Wu H., Li Y. F., Bйrenguer C.  Optimal inspection and maintenance for a repairable k-out-of-n:G warm standby system.  Reliability Engineering and System Safety. 193, 1–11 (2019).
  18. Jia H. P., Ding Y., Peng R., Liu H. L., Song Y. H.  Reliability assessment and activation sequence optimization of non-repairable multi-state generation systems considering warm standby.  Reliability Engineering and System Safety. 195, 1–10 (2019).
  19. Kakkar M. K., Bhatti J., Malhotra R., Kaur M., Goyal D.  Availability analysis of an industrial system under the provision of replacement of a unit using genetic algorithm.  International Journal of Innovative Technology and Exploring Engineering (IJITEE). 9, 1236–1241 (2019).
  20. Fang C., Cui L.  Reliability analysis for balanced engine systems with m sectors by considering start-up probability.  Reliability Engineering and System Safety. 197, 1–10 (2020).
  21. Garg R., Dube M., Krishna H.  Estimation of Parameters and Reliability Characteristics in Lindley Distribution Using Randomly Censored Data.  Statistics, Optimization and Information Computing. 8 (1), 80–97 (2020).
  22. Bhatti J., Kakkar M. K., Bhardwaj N., Kaur M., Goyal D.  Reliability analysis to industrial active standby redundant system.  Malaysian Journal of Science. 39 (3), 74–84 (2020).
  23. Bhatti J., Kakkar M. K., Kaur M.  Stochastic Analysis to an Power Supply System Through Reliability Modelling.  Transactions Issue Mathematics, Azerbaijan National Academy of Sciences. 41 (1), 35–43 (2021).
  24. Bhatti J., Kakkar M. K., Kaur M., Goyal D., Khanna P.  Stochastic analysis to mechanical system to its reliability with varrying repairing services.  Chebyshevskii Sbornik. 22 (1), 92–104 (2021).
  25. Bhatti J., Kakkar M. K.  Reliability analysis of cold standby parallel system possessing failure and repair rate under geometric distribution.  Recent Advances in Computer Science and Communications.  14 (3), 968–974 (2021).