Stress-Strength Weibull Analysis Applied to Estimate Reliability Index in Industry 4.0

Document Type : Original Research Article


1 . Industrial and Technology Department, Instituto Tecnológico Superior de Nuevo Casas Grandes, Casas Grandes, México

2 Industrial and Manufacturing Department, Institute of Engineering and Technology, Autonomous University of Ciudad Juarez; Ciudad Juarez, Mexico


With technological advances, companies are allowed to integrate digital data, physical supplies, and human resources, and all this integration capability can be done thanks to Industry 4.0. This concept, also called the fourth industrial revolution, refers to smart companies that work with intelligent cyber-physical systems. Industry 4.0enables automation, data interchange, and big data processing, among others. Then, the process decision-making, efficiency, and productivity improvement for companies will become faster and more accurate, thanks to real-time data processes and all supply chain integration allowed by Industry 4.0. However, the implementation of Industry 4.0 carries several challenges for companies to have success in the transformation of a normal industry into an Industry 4.0, like the necessity of adding new hardware, software, and other technologic devices. Because of this, the implementation and control of Industry 4.0 come with new issues to handle and new failure modes for both hardware and electronic devices. These problems can be faced using reliability engineering tools. Then the object of this research is the use of reliability engineering methodology stress-strength Weibull analysis, highlighting that the behavior of frequency emitted by electronics devices follows a Weibull distribution most of the time. Also, a stress-strength Weibull with a different shape parameter close solution is presented to increase the efficiency and productivity in Industry 4.0 electronic devices.


Main Subjects

  1. -G. Ciobanu and D. M. Neamţu, “The impact and importance of new technologies in business development in context of economic diversity,” Proc. Int. Conf. Bus. Excell., vol. 11, no. 1, pp. 698–710, 2017, doi: 10.1515/picbe-2017-0074.
  2. F. Cascio and R. Montealegre, “How Technology Is Changing Work and Organizations,” Annu. Rev. Organ. Psychol. Organ. Behav., vol. 3, no. 1, pp. 349–375, 2016, doi: 10.1146/annurev-orgpsych-041015-062352.
  3. D. Gowda, S. B. Sridhara, K. B. Naveen, M. Ramesha, and G. N. Pai, “Internet of things: Internet revolution, impact, technology road map and features,” Adv. Math. Sci. J., vol. 9, no. 7, pp. 4405–4414, 2020, doi: 10.37418/amsj.9.7.11.
  4. Wielki, “THE IMPACT OF THE INTERNET OF THINGS CONCEPT DEVELOPMENT ON CHANGES IN THE OPERATIONS OF MODERN ENTERPRISES,” Polish J. Manag. Stud., vol. 15, no. 1, pp. 262–275, 2017, doi: 10.17512/pjms.2017.15.1.25.
  5. Kumar, P. Tiwari, and M. Zymbler, “Internet of Things is a revolutionary approach for future technology enhancement: a review,” J. Big Data, vol. 6, no. 1, 2019, doi: 10.1186/s40537-019-0268-2.
  6. Yaqoob et al., “Internet of Things Architecture: Recent Advances, Taxonomy, Requirements, and Open Challenges,” IEEE Wirel. Commun., vol. 24, no. 3, pp. 10–16, 2017, doi: 10.1109/MWC.2017.1600421. I. Yaqoob et al., “Internet of Things Architecture: Recent Advances, Taxonomy, Requirements, and Open Challenges,” IEEE Wirel. Commun., vol. 24, no. 3, pp. 10–16, 2017, doi: 10.1109/MWC.2017.1600421.
  7. Lampropoulos, K. Siakas, and T. Anastasiadis, “Internet of Things in the Context of Industry 4.0: An Overview,” Int. J. Entrep. Knowl., vol. 7, no. 1, pp. 4–19, 2019, doi: 10.2478/ijek-2019-0001.
  8. M. Müller, D. Kiel, and K. I. Voigt, “What drives the implementation of Industry 4.0? The role of opportunities and challenges in the context of sustainability,” Sustain., vol. 10, no. 1, 2018, doi: 10.3390/su10010247.
  9. C. Ng, S. Y. Lau, M. Ghobakhloo, M. Fathi, and M. S. Liang, “The Application of Industry 4.0 Technological Constituents for Sustainable Manufacturing: A Content-Centric Review,” Sustain., vol. 14, no. 7, 2022, doi: 10.3390/su14074327.
  10. M. Katz, Structural reforms, productivity and technological change in Latin America. 2001.
  11. Zhang, Y. Yang, and G. Yang, “Smart supply chain management in Industry 4.0: the review, research agenda and strategies in North America,” Ann. Oper. Res., 2022, doi: 10.1007/s10479-022-04689-1.
  12. Alcácer and V. Cruz-Machado, “Scanning the Industry 4.0: A Literature Review on Technologies for Manufacturing Systems,” Eng. Sci. Technol. an Int. J., vol. 22, no. 3, pp. 899–919, 2019, doi: 10.1016/j.jestch.2019.01.006.
  13. Nagy, J. Oláh, E. Erdei, D. Máté, and J. Popp, “The role and impact of industry 4.0 and the internet of things on the business strategy of the value chain-the case of hungary,” Sustain., vol. 10, no. 10, 2018, doi: 10.3390/su10103491.
  14. A. Farsi and E. Zio, “Industry 4.0: Some Challenges and Opportunities for Reliability Engineering,” Int. J. Reliab. Risk Saf. Theory Appl., vol. 2, no. 1, pp. 23–34, 2019, doi: 10.30699/ijrrs.2.1.4.
  15. OECD, “The Next Production Revolution: A Report for the G20,” 2017. [Online]. Available:
  16. Bennis, M. Debbah, and H. V. Poor, “Journal of Industrial Information Integration,” Proc. IEEE, vol. 106, no. 10, pp. 1834–1853, 2018, doi: 10.1109/JPROC.2018.2867029.
  17. Pokorni, “Reliability and availability of the Internet of things,” Vojnoteh. Glas., vol. 67, no. 3, pp. 588–600, 2019, doi: 10.5937/vojtehg67-21363.
  18. R. Piña-Monarrez, M. L. Ramos-Lopez, A. Alvarado-Iniesta, and R. D. Molina-Arredondo, “Robust sample size for Weibull demonstration test plan,” DYNA Colomb., vol. 83, no. 197, p. In press, 2016.
  19. R. Piña-Monarrez, “Weibull stress distribution for static mechanical stress and its stress/strength analysis,” Qual. Reliab. Eng. Int., vol. 34, no. 2, pp. 229–244, 2018, doi: 10.1002/qre.2251.
  20. Baro and M. P. Monarrez, “Reliability Engineering in Industry 4.0,” in Critical Factor in Industry 4.0, vol. 1, no. 4, Ciudad Juárez: El Colegio de Chihuahua, 2021, pp. 37–72.
  21. de la Cruz, H. S. Salinas, and C. Meza, “Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution,” Symmetry (Basel)., vol. 14, no. 4, pp. 1–17, 2022, doi: 10.3390/sym14040837.
  22. R. Piña-Monarrez, J. F. Ortiz-Yañez, and M. I. Rodríguez-Borbón, “Non-normal Capability Indices for the Weibull and Lognormal Distributions,” Qual. Reliab. Eng. Int., p. n/a-n/a, 2015, doi: 10.1002/qre.1832.
  23. C. Méndez-González, L. A. Rodríguez-Picón, D. J. Valles-Rosales, A. Alvarado Iniesta, and A. E. Q. Carreón, “Reliability analysis using exponentiated Weibull distribution and inverse power law,” Qual. Reliab. Eng. Int., vol. 35, no. 4, pp. 1219–1230, 2019, doi: 10.1002/qre.2455.
  24. Z. Hosseinifard and B. Abbasi, “Process Capability Analysis in Non Normal Linear Regression Profiles,” Commun. Stat. - Simul. Comput., vol. 41, no. 10, pp. 1761–1784, 2012, doi: 10.1080/03610918.2011.611313.
  25. Lu, “Industry 4.0: A survey on technologies, applications and open research issues,” J. Ind. Inf. Integr., vol. 6, pp. 1–10, 2017, doi:
  26. Kormut’ák et al., “Introgressive hybridization between Scots pine and mountain dwarf pine at two localities of northern Slovakia,” Folia Oecologica, vol. 40, no. 2, pp. 201–205, 2013.
  27. LAWSON and D. SAMSON, “Developing Innovation Capability in Organisations: a Dynamic Capabilities Approach,” Int. J. Innov. Manag., vol. 05, no. 03, pp. 377–400, 2001, doi: 10.1142/s1363919601000427.
  28. Tjahjono, C. Esplugues, E. Ares, and G. Pelaez, “What does Industry 4.0 mean to Supply Chain?,” Procedia Manuf., vol. 13, pp. 1175–1182, 2017, doi: 10.1016/j.promfg.2017.09.191.
  29. M. R. Tortora, A. Maria, D. P. Valentina, R. Iannone, and C. Pianese, “A survey study on Industry 4.0 readiness level of Italian small and medium enterprises,” Procedia Comput. Sci., vol. 180, pp. 744–753, 2021, doi: 10.1016/j.procs.2021.01.321.
  30. -S. Chen and H.-T. Tsou, “Performance effects of IT capability, service process innovation, and the mediating role of customer service,” J. Eng. Technol. Manag., vol. 29, no. 1, pp. 71–94, Jan. 2012, doi: 10.1016/j.jengtecman.2011.09.007.
  31. Breeding and W. Smith, “Welcome to Software Industry 4.0,” Digit. Evol., vol. 248, no. 5, pp. 70–75, 2013.
  32. Koch and S. Kuge, Industry 4.0 in Practice. 2015.
  33. Biggs, The State of Broadband 2015, no. September. 2019. doi: 10.1017/CBO9781107415324.004.
  34. Govindan, K. Zeng, and P. Mohapatra, “Probability density of the received power in mobile networks,” IEEE Trans. Wirel. Commun., vol. 10, no. 11, pp. 3613–3619, 2011, doi: 10.1109/TWC.2011.080611.102250.
  35. P. Raptis, A. Passarella, and M. Conti, “Data management in industry 4.0: State of the art and open challenges,” IEEE Access, vol. 7, pp. 97052–97093, 2019, doi: 10.1109/ACCESS.2019.2929296.
  36. Liu, R. W. White, and S. Dumais, “Understanding web browsing behaviors through weibull analysis of dwell time,” SIGIR 2010 Proc. - 33rd Annu. Int. ACM SIGIR Conf. Res. Dev. Inf. Retr., pp. 379–386, 2010, doi: 10.1145/1835449.1835513.
  37. Andrzej, “Uncertainty in the Sphere of the Industry 4.0 – Potential Areas To Research,” Business, Manag. Educ., vol. 14, no. 2, pp. 275–291, 2016, doi: 10.3846/bme.2016.332.
  38. Phister, “Reliability , Availability , and Maintainability,” in Reliability, Availability, and Maintainability >, SEBok, Ed. 2019.
  39. V Varde, “Physics-of-Failure Based Approach for Predicting Life and Reliability of Electronics Components,” Barc Newsl., no. 313, pp. 38–46, 2010.
  40. Rinne, Distribution The Weibull Distribution A Handbook. Giessen, Germany, 2009. doi: 10.1201/9781420087444.
  41. Sorenson, “Accelerated Life Testing,” Syst. Reliab. Theory Model. Stat. …, pp. 1–26, 2011, doi: 10.1002/9780470316900.ch12.
  42. K. Mohajan, “Two Criteria for Good Measurements in Research: Validity and Reliability,” Ann. Spiru Haret Univ. Econ. Ser., vol. 17, no. 4, pp. 59–82, 2017, doi: 10.26458/1746.
  43. Kihl, P. Ödling, C. Lagerstedt, and A. Aurelius, “Traffic analysis and characterization of internet user behavior,” 2010 Int. Congr. Ultra Mod. Telecommun. Control Syst. Work. ICUMT 2010, pp. 224–231, 2010, doi: 10.1109/ICUMT.2010.5676633.
  44. Weibull, “A Statistical Theory of the Strength of Materials,” Ingeniørs Vetenskaps Akad. Handl., vol. 151, pp. 1–45, 1939.
  45. R. Mischke, “A Distribution-Independent Plotting Rule for Ordered Failures,” J. Mech. Des., vol. 104, no. 3, p. 593, 1979, doi: 10.1115/1.3256391.
  46. A. Guimaraes, Digital Transmission: A Simulation-Aided Introduction with VisSim/Comm. 2009. doi: 10.1007/978-3-642-01359-1.
  47. C. Ugweje, Radio Frequency and Wireless Communications, no. April 2004. 2004. doi: 10.1002/047148296x.tie151.
  48. K. Aggarwal, TOPICS IN SAFETY, RELIABILITY AND QUALITY, vol. 53, no. 9. 2013. doi: 10.1017/CBO9781107415324.004.
  49. Roblek, M. Meško, and A. Krapež, “A Complex View of Industry 4.0,” SAGE Open, vol. 6, no. 2, pp. 0–11, 2016, doi: 10.1177/2158244016653987.
  50. S. Wang, F. S. Hsu, and P. P. Liu, “Modeling the bathtub shape hazard rate function in terms of reliability,” Reliab. Eng. Syst. Saf., vol. 75, no. 3, pp. 397–406, 2002, doi: 10.1016/S0951-8320(01)00124-7.
  51. Hasan, W. Ahmed, S. Tahar, and M. S. Hamdi, “Reliability block diagrams based analysis: A survey,” AIP Conf. Proc., vol. 1648, no. March, 2015, doi: 10.1063/1.4913184.
  52. A. Arfeen, K. Pawlikowski, D. McNickle, and A. Willig, “The role of the Weibull distribution in Internet traffic modeling,” Proc. 2013 25th Int. Teletraffic Congr. ITC 2013, 2013, doi: 10.1109/ITC.2013.6662948.
  53. W. Veile, D. Kiel, J. M. Müller, and K. I. Voigt, “Lessons learned from Industry 4.0 implementation in the German manufacturing industry,” J. Manuf. Technol. Manag., vol. 31, no. 5, pp. 977–997, 2019, doi: 10.1108/JMTM-08-2018-0270.
  54. H. Collins and R. L. Warr, “Failure time distributions for complex equipment,” Qual. Reliab. Eng. Int., vol. 35, no. 1, pp. 146–154, 2019, doi: 10.1002/qre.2387.
  55. Hilber, Component reliability importance indices for maintenance optimization of electrical networks (RCM). 2005.
  56. Horváth and R. Z. Szabó, “Driving forces and barriers of Industry 4.0: Do multinational and small and medium-sized companies have equal opportunities?,” Technol. Forecast. Soc. Change, vol. 146, no. October 2018, pp. 119–132, 2019, doi: 10.1016/j.techfore.2019.05.021.
  57. H. M. Zaidin, M. N. M. Diah, and S. Sorooshian, “Quality management in industry 4.0 era,” J. Manag. Sci., vol. 1, no. 2, pp. 182–191, 2018, doi: 10.26524/jms.2018.17.
  58. Baro-Tijerina, M. R. Piña-Monárrez, and B. Villa-Covarrubias, “Stress-strength weibull analysis with different shape parameter β and probabilistic safety factor,” DYNA, vol. 87, no. 215, pp. 28–33, 2020, doi: 10.15446/dyna.v87n215.84909.