<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">cheb</journal-id><journal-title-group><journal-title xml:lang="ru">Чебышевский сборник</journal-title><trans-title-group xml:lang="en"><trans-title>Chebyshevskii Sbornik</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-8383</issn><publisher><publisher-name>Tula State Lev Tolstoy  Pedagogical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22405/2226-8383-2021-22-1-92-104</article-id><article-id custom-type="elpub" pub-id-type="custom">cheb-934</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Стохастический анализ механической системы на предмет ее надежности с различными услугами по ремонту</article-title><trans-title-group xml:lang="en"><trans-title>Stochastic analysis to mechanical system to its reliability with varrying repairing services</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бхатти</surname><given-names>Джасдев</given-names></name><name name-style="western" xml:lang="en"><surname>Bhatti</surname><given-names>Jasdev</given-names></name></name-alternatives><bio xml:lang="ru"><p>доцент</p></bio><bio xml:lang="en"><p>Associate Professor</p></bio><email xlink:type="simple">jasdev.bhatti@chitkara.edu.in</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кумар Каккар</surname><given-names>Мохит</given-names></name><name name-style="western" xml:lang="en"><surname>Kumar Kakkar</surname><given-names>Mohit</given-names></name></name-alternatives><bio xml:lang="ru"><p>профессор</p></bio><bio xml:lang="en"><p>Professor</p></bio><email xlink:type="simple">mohit.kakkar@chitkara.edu.in</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Каур</surname><given-names>Манприт</given-names></name><name name-style="western" xml:lang="en"><surname>Kaur</surname><given-names>Manpreet</given-names></name></name-alternatives><bio xml:lang="ru"><p>доцент</p></bio><bio xml:lang="en"><p>Assistant Professor</p></bio><email xlink:type="simple">manpreet.kaur@chitkara.edu.in</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>.</surname><given-names>Дипика</given-names></name><name name-style="western" xml:lang="en"><surname>.</surname><given-names>Deepika</given-names></name></name-alternatives><bio xml:lang="ru"><p>доцент</p></bio><bio xml:lang="en"><p>Assistant Professor</p></bio><email xlink:type="simple">deepika.goyal@chitkara.edu.in</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кханна</surname><given-names>Панкадж</given-names></name><name name-style="western" xml:lang="en"><surname>Khanna</surname><given-names>Pankaj</given-names></name></name-alternatives><email xlink:type="simple">pankaj.khanna@chitkara.edu.in</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт инженерии и технологий Университета Читкары, &#13;
Университет Читкары</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Chitkara University Institute of Engineering and Technology,&#13;
Chitkara University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт инженерии и технологий Университета Читкары, Университет Читкары</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Chitkara University Institute of Engineering and Technology,&#13;
Chitkara University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>06</day><month>04</month><year>2021</year></pub-date><volume>22</volume><issue>1</issue><fpage>92</fpage><lpage>104</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Бхатти Д., Кумар Каккар М., Каур М., . Д., Кханна П., 2021</copyright-statement><copyright-year>2021</copyright-year><copyright-holder xml:lang="ru">Бхатти Д., Кумар Каккар М., Каур М., . Д., Кханна П.</copyright-holder><copyright-holder xml:lang="en">Bhatti J., Kumar Kakkar M., Kaur M., . D., Khanna P.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.chebsbornik.ru/jour/article/view/934">https://www.chebsbornik.ru/jour/article/view/934</self-uri><abstract><p>Надежность увеличивает свою ценность в развитии механического и промышленного мира за счет включения механизма ремонта, доступности и возможности изготовления машин с различной рабочей мощностью в любых условиях. Настоящая статья представляет собой инициативу, предпринятую с механической системой, работающей с единым сервером ремонта для различного характера отказов и услуг. Стратегия пассивной резервной машины используется для поддержания надежности системы на удовлетворительном уровне. Процесс проверки включен для фильтрации машин в зависимости от их неисправности или уровня ремонтных услуг. Вычисленные числовые и графические данные оказались полезными для выяснения поведения прибыли и надежности при увеличении / уменьшении скорости механизма ремонта и интенсивности отказов. Политика предпочтений была инициирована для регулярных сбоев или сбоев, требующих обычных затрат наобслуживание и периода времени, чем основные, чтобы избежать времени ожидания для обычного клиента</p></abstract><trans-abstract xml:lang="en"><p>Reliability is enhancing its value in the advancement of echanical and industrial world by incorporating the repair mechanism, availability and manufacturing possibility of machines with varying working capacity in all conditions. The present paper is an initiative taken with a mechanical system operating with single repair server facility for varying nature of failures and services. Passive standby machine strategy is adopted for maintaining reliability at a gratified level in the system. The inspection process is included for filtering the machines according to its failure or to the level of repair services. The computed numerical and raphical data is proved to be beneficial for clarifying the profit and reliability behaviour with increasing/decreasing rate of repair mechanism and failure rate. The preference policy has been initiated for regular failure or to the failure requiring normal servicing charges and time period than major ones to avoidthe waiting time for normal customer</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Моделирование надежности</kwd><kwd>геометрическое распределение</kwd><kwd>доступ- ность системы</kwd><kwd>отказ</kwd><kwd>проверка</kwd><kwd>стоимость обслуживания и функция прибыли</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Reliability modelling</kwd><kwd>geometric distribution</kwd><kwd>system availability</kwd><kwd>failure</kwd><kwd>inspection</kwd><kwd>maintenance cost and profit function</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Bhardwaj N., Kumar A. &amp; Kumar S. Stochastic analysis of a single unit redundant system with two kinds of failure and repairs // Reflections des. ERA-JMS. 2008. Vol. 3, No. 2. P. 115–134.</mixed-citation><mixed-citation xml:lang="en">Bhardwaj, N., Kumar, A. &amp; Kumar, S. 2008, “Stochastic analysis of a single unit redundant system with two kinds of failure and repairs“, Reflections des. ERA-JMS, vol. 3, no. 2, pp. 115–134.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Bhardwaj N. Analysis of two-unit redundant system with imperfect switching and connectiontime // International Transactions in Mathematical Sciences and Computer. 2009. Vol. 2, No. 2. P. 195–202.</mixed-citation><mixed-citation xml:lang="en">Bhardwaj, N. 2009, “Analysis of two-unit redundant system with imperfect switching and connection time“, International Transactions in Mathematical Sciences and Computer, nol. 2,</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Haggag M. Y. Cost analysis of a system iInvolving common cause failures and preventive maintenance // J. Math and Stat. 2009. Vol. 5, No. 4. P. 305-310.</mixed-citation><mixed-citation xml:lang="en">no. 2, pp. 195–202.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Haggag M. Y. Cost analysis of two-dissimilar unit cold standby system with three states and preventive maintenance using linear first order differential equations // J. Math and Stat. 2009.</mixed-citation><mixed-citation xml:lang="en">Haggag, M. Y. 2009, “Cost analysis of a system iInvolving common cause failures and preventive maintenance“, J. Math and Stat., vol. 5, no. 4, pp. 305-310.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Vol. 5, No. 4. P. 395-400.</mixed-citation><mixed-citation xml:lang="en">Haggag, M. Y. 2009, “Cost analysis of two-dissimilar unit cold standby system with three states and preventive maintenance using linear first order differential equations“, J. Math and Stat.,</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Rizwan S. M., Khurana V. &amp; Taneja G. Reliability analysis of a hot standby industrial system // International Journal of Modelling and Simulation. 2010. Vol. 30, No. 3. P. 315-322.</mixed-citation><mixed-citation xml:lang="en">vol. 5, no. 4, pp. 395-400.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Kumar A. &amp; Malik S. C. Reliability modeling of a computer system with priority to S/w replacement over H/w replacement subject to MOT and MRT // International Journal of Pure and Applied Mathematics. 2012. Vol. 80, No. 5. P. 693-709.</mixed-citation><mixed-citation xml:lang="en">Rizwan, S. M., Khurana, V. &amp; Taneja, G. 2010, “Reliability analysis of a hot standby industrial system“, International Journal of Modelling and Simulation, vol. 30, no. 3, pp. 315-322.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Singh D. &amp; 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. 2014. Vol. 10, No. 4. P. 436-442.</mixed-citation><mixed-citation xml:lang="en">Kumar, A. &amp; Malik, S. C. 2012, “Reliability modeling of a computer system with priority to S/w replacement over H/w replacement subject to MOT and MRT“, International Journal of</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Malhotra R. &amp; Taneja G. Stochastic analysis of a two-unit cold standby system wherein both units may become operative depending upon the demand // Journal of Quality and Reliability</mixed-citation><mixed-citation xml:lang="en">Pure and Applied Mathematics, vol. 80, no. 5, pp. 693-709.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Engineering. 2014. P. 1-13.</mixed-citation><mixed-citation xml:lang="en">Singh, D. &amp; Taneja, G. 2014, “Reliability and economic analysis of a power generating system comprising one gas and one steam turbine with random inspection“, Journal of Mathematics and Statistics, vol. 10, no. 4, pp. 436-442.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Malhotra R. &amp; Taneja G. Comparative study between a single unit system and a two unit cold standby system with varying demand // SpringerPlus. 2015. Vol. 4, P. 1-17.</mixed-citation><mixed-citation xml:lang="en">Malhotra, R. &amp; Taneja, G. 2014, “Stochastic analysis of a two-unit cold standby system wherein both units may become operative depending upon the demand“, Journal of Quality</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Bhatti J., Chitkara A. &amp; Kakkar M. Stochastic analysis of parallel system with two discrete failures // Model Assisted Statistics and Applications. 2014. Vol. 9, P. 257-265.</mixed-citation><mixed-citation xml:lang="en">and Reliability Engineering, pp. 1-13.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Kakkar M. K. &amp; Bhatti J. Reliability and profit analysis of standby unit system with correlated life time in an industry // Advance Study in Contemporary Mathematics. 2015. Vol. 25, No. 3. P. 333-340.</mixed-citation><mixed-citation xml:lang="en">Malhotra, R. &amp; Taneja, G. 2015, “Comparative study between a single unit system and a two unit cold standby system with varying demand“, SpringerPlus, vol. 4, pp. 1-17.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Kakkar M. K., Chitkara A. K. &amp; Bhatti J. Reliability analysis of two-unit parallel repairable industrial system // Decision Science Letters. 2015. Vol. 4, P. 525-536.</mixed-citation><mixed-citation xml:lang="en">Bhatti, J., Chitkara, A. &amp; Kakkar, M. 2014, “Stochastic analysis of parallel system with two discrete failures“, Model Assisted Statistics and Applications, vol. 9, pp. 257-265.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Kakkar M. K., Chitkara A. K. &amp; Bhatti J Reliability analysis of two dissimilar parallel unit repairable system with failure during preventive maintenance // Management Science Letters,</mixed-citation><mixed-citation xml:lang="en">Kakkar, M. K. &amp; Bhatti, J. 2015, “Reliability and profit analysis of standby unit system with correlated life time in an industry“, Advance Study in Contemporary Mathematics, vol. 25, no.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">vol. 6, pp. 285-296.</mixed-citation><mixed-citation xml:lang="en">, pp. 333-340.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Bhatti J., Chitkara A. &amp; Kakkar M. Stochastic analysis of dis-similar standby system with discrete failure, inspection and replacement policy // Demonstratio Mathematica. 2016. Vol.</mixed-citation><mixed-citation xml:lang="en">Kakkar, M. K., Chitkara, A. K. &amp; Bhatti, J. 2015, “Reliability analysis of two-unit parallel repairable industrial system“, Decision Science Letters, vol. 4, pp. 525-536.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">, No. 2. P. 224-235.</mixed-citation><mixed-citation xml:lang="en">Kakkar, M. K., Chitkara, A.K. &amp; Bhatti, J. 2016, “Reliability analysis of two dissimilar parallel unit repairable system with failure during preventive maintenance“, Management Science</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Hua D. G. &amp; Elsayed E. Reliability estimation of k-out-of-npairs: G balanced systems with spatially distributed units // IEEE Trans. Reliab. 2016. Vol. 65, P. 886—900.</mixed-citation><mixed-citation xml:lang="en">Letters, vol. 6, pp. 285-296.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Hua D. G. &amp; Elsayed E. Degradation analysis of k-out-of-n pairs: G balanced systems with spatially distributed units // IEEE Trans Reliab. 2016. Vol. 65, P. 941–956.</mixed-citation><mixed-citation xml:lang="en">Bhatti, J., Chitkara, A. &amp; Kakkar, M. 2016, “Stochastic analysis of dis-similar standby system with discrete failure, inspection and replacement policy“, Demonstratio Mathematica, vol. 49, no. 2, pp. 224-235.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Iqbal P. &amp; Uduman P. S. S. Reliability analysis of paper plant using boolean function with fuzzy logic technique // International Journal of Applied Engineering Research. 2016. Vol. 11, No. 1.</mixed-citation><mixed-citation xml:lang="en">Hua, D. G. &amp; Elsayed, E. 2016, “Reliability estimation of k-out-of-npairs: G balanced systems with spatially distributed units“, IEEE Trans. Reliab., vol. 65, pp. 886—900.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">P. 573-577.</mixed-citation><mixed-citation xml:lang="en">Hua, D. G. &amp; Elsayed, E. 2016, “Degradation analysis of k-out-of-n pairs: G balanced systems with spatially distributed units“, IEEE Trans Reliab., vol. 65, pp. 941–956.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Taj S. Z., Rizwan S. M., Alkali B. M., Harrison D. K. &amp; Taneja G. Probabilistic modeling and analysis of a cable plant subsystem with priority to repair over preventive maintenance //</mixed-citation><mixed-citation xml:lang="en">Iqbal, P. &amp; Uduman, P. S. S. 2016, “Reliability analysis of paper plant using boolean function with fuzzy logic technique“, International Journal of Applied Engineering Research, vol. 11, no. 1, pp. 573-577.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">I-Managers Journal on Mathematics. 2017. Vol. 6, No. 3. P. 12-21.</mixed-citation><mixed-citation xml:lang="en">Taj, S. Z., Rizwan, S. M., Alkali, B. M., Harrison, D. K. &amp; Taneja, G. 2017, “Probabilistic modeling and analysis of a cable plant subsystem with priority to repair over preventive maintenance“, I-Managers Journal on Mathematics, vol. 6, no. 3, pp. 12-21.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Adlakha N., Taneja G. &amp; 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. 2017. Vol. 12, No. 20. P. 9697-9702.</mixed-citation><mixed-citation xml:lang="en">Adlakha, N., Taneja, G. &amp; Shilpi. 2017, “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, vol. 12, no. 20, pp. 9697-9702.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Cui L. R., Gao H. D. &amp; Mo Y. C. Reliabilities for k-out-of-n: F balanced systems with m sectors // IISE Trans. 2017. Vol. 50, No. 5. P. 381–393.</mixed-citation><mixed-citation xml:lang="en">Cui, L. R., Gao, H. D. &amp; Mo Y. C. 2017, “Reliabilities for k-out-of-n: F balanced systems with m sectors“, IISE Trans., vol. 50, no. 5, pp. 381–393.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Cui L. R., Chen J. H. &amp; Li X. C. Balanced reliability systems under Markov processes // IISE Trans.. 2018. Vol. 51, No. 9. P. 1025-1035.</mixed-citation><mixed-citation xml:lang="en">Cui, L. R., Chen, J. H. &amp; Li, X. C. 2018, “Balanced reliability systems under Markov processes“, IISE Trans., vol. 51, no. 9, pp. 1025-1035.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Endharta A. J., Yun W. Y. &amp; Ko Y. M. Reliability evaluation of circular k-out-of-n:G balanced systems through minimal path sets // Reliability Engineering and System Safety. 2018. Vol.</mixed-citation><mixed-citation xml:lang="en">Endharta, A. J., Yun, W. Y. &amp; Ko, Y. M. 2018, “Reliability evaluation of circular k-out-of-n:G balanced systems through minimal path sets“, Reliability Engineering and System Safety, vol. 180, pp. 220-236.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">, P. 220-236.</mixed-citation><mixed-citation xml:lang="en">Chen, W. L. 2018, “System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy“, System Engineering, vol. 21, pp. 59–69.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">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. 2018. Vol. 21, P. 59–69.</mixed-citation><mixed-citation xml:lang="en">Bhardwaj, S., Bhardwaj, N., Kumar V. &amp; Parashar, B. 2019, “Estimation of lifespan of diesel locomotive engine“, Journal of Information and Optimization Sciences, vol. 40, no. 5, pp. 1097-</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Bhardwaj S., Bhardwaj N., Kumar V. &amp; Parashar B. Estimation of lifespan of diesel locomotive engine // Journal of Information and Optimization Sciences. 2019. Vol. 40, No. 5. P. 1097-1108.</mixed-citation><mixed-citation xml:lang="en">Bhardwaj S., Bhardwaj N., Kumar V. &amp; Parashar B. Estimation of lifespan of diesel locomotive engine // Journal of Information and Optimization Sciences. 2019. Vol. 40, No. 5. P. 1097-1108.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Dong Q. L., Cui L. R. &amp; Si S. B. Reliability and availability analysis of stochastic degradation systems based on bivariate wiener processes // Appl. Math. Model. 2019. Vol. 79, P. 414–433.</mixed-citation><mixed-citation xml:lang="en">Dong, Q. L., Cui, L. R. &amp; Si, S. B. 2019, “Reliability and availability analysis of stochastic degradation systems based on bivariate wiener processes“, Appl. Math. Model, vol. 79, pp.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Wu H., Li Y. F. &amp; B´erenguer C. Optimal inspection and maintenance for a repairable k -outofn: G warm standby system // Reliability Engineering and System Safety. 2019. Vol. 193, P.</mixed-citation><mixed-citation xml:lang="en">–433.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">-11.</mixed-citation><mixed-citation xml:lang="en">Wu, H., Li, Y. F. &amp; B´erenguer, C. 2019, “Optimal inspection and maintenance for a repairable k -out-of-n: G warm standby system“, Reliability Engineering and System Safety, vol. 193, pp.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Jia H.P., Ding Y., Peng R., Liu H. L. &amp; Song Y. H. Reliability assessment and activation sequence optimization of non-repairable multi-state generation systems considering warm</mixed-citation><mixed-citation xml:lang="en">-11.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">standby // Reliability Engineering and System Safety. 2019. Vol. 195, P. 1-11.</mixed-citation><mixed-citation xml:lang="en">Jia, H.P., Ding, Y., Peng, R., Liu, H. L. &amp; Song, Y. H. 2019, “Reliability assessment and activation sequence optimization of non-repairable multi-state generation systems considering</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Fang C. &amp; Cui L. Reliability analysis for balanced engine systems with m sectors by considering start-up probability // Reliability Engi-neering and System Safety. 2019. Vol. 197, P. 1-10.</mixed-citation><mixed-citation xml:lang="en">warm standby“, Reliability Engineering and System Safety, vol. 195, pp. 1-11.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Kakkar M. K, Bhatti J, Malhotra R., Kaur M. &amp; Goyal D. Availability analysis of an industrial system under the provision of replacement of a unit using genetic algorithm // International</mixed-citation><mixed-citation xml:lang="en">Fang, C. &amp; Cui, L. 2019, “Reliability analysis for balanced engine systems with m sectors by considering start-up probability“, Reliability Engi-neering and System Safety, vol. 197, pp. 1-10.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Journal of Innovative Technology and Exploring En-gineering (IJITEE). 2019. Vol. 9, P. 1236–1241.</mixed-citation><mixed-citation xml:lang="en">Kakkar, M. K, Bhatti, J, Malhotra, R., Kaur, M. &amp; Goyal, D. 2019, “Availability analysis of an industrial system under the provision of replacement of a unit using genetic algorithm“,</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Bhatti J. &amp; 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. 2020. Vol. 13, P. 1-7.</mixed-citation><mixed-citation xml:lang="en">International Journal of Innovative Technology and Exploring En-gineering (IJITEE), vol. 9, pp. 1236–1241.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Bhatti, J. &amp; Kakkar, M. K. 2020, “Reliability analysis of cold standby parallel system possessing failure and repair rate under geometric distribution“, Recent Advances in Computer Science and Communications, vol. 13, pp. 1-7.</mixed-citation><mixed-citation xml:lang="en">Bhatti, J. &amp; Kakkar, M. K. 2020, “Reliability analysis of cold standby parallel system possessing failure and repair rate under geometric distribution“, Recent Advances in Computer Science and Communications, vol. 13, pp. 1-7.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
