Mechanical Equipment Reliability Analysis: Case Study

Document Type : Case study

Authors

1 Mining Engineering, Faculty of Technical & Engineering, Imam Khomeini International University, Qazvin, Iran

2 Faculty of Mining, Petroleum & Geophysics Engineering, Shahrood University of technology, Shahrood, Iran

Abstract

In civil and mining industries, Wheel loaders are an important component and their cost capability at effective operation. The environmental and operational factors dramatically affect the performance of loaders. In many cases, failure data are often collected from multiple and distributed units in different operational conditions, which can introduce heterogeneity into the data. Part of such heterogeneity can be explained and isolated by the observable covariates, whose values and the way they can affect the item's reliability are known. However, some factors that may affect the item's reliability are typically unknown and lead to unobserved heterogeneity. These factors are categorized as unobserved covariates. In most reliability studies, the effect of unobserved covariates is neglected. This may lead to erroneous model selection for the time to failure of the item, as well as wrong conclusions and decisions. There is a lack of sufficient knowledge, theoretical background, and a systematic approach to model the unobserved covariate in reliability analysis. This paper aims to present a framework for reliability analysis in the presence of unobserved and observed covariates. The unobserved covariates will be analyzed using frailty models (Such as Mixed Proportional Hazard).A case will illustrate the application of the framework.

Keywords

Main Subjects


  1. Kikuchi, M. Tochizawa, S. Takeda, S. Kamada, and K. Hirosawa, “Automatic excavator,” 1991, pp. 277–284.
  2. Topal and S. Ramazan, “A new MIP model for mine equipment scheduling by minimizing maintenance cost,” Eur. J. Oper. Res., vol. 207, no. 2, pp. 1065–1071, 2010.
  3. M. Louit, R. Pascual, and A. K. Jardine, “A practical procedure for the selection of time-to-failure models based on the assessment of trends in maintenance data,” Reliab. Eng. Syst. Saf., vol. 94, no. 10, pp. 1618–1628, 2009.
  4. Liu, “Survival models on unobserved heterogeneity and their applications in analyzing large-scale survey data,” J. Biom. Biostat., vol. 5, 2014.
  5. F. Lawless, Statistical Models and Methods for Lifetime Data. John Wiley & Sons, 2011.
  6. Finkelstein, “Imperfect repair and lifesaving in heterogeneous populations,” Reliab. Eng. Syst. Saf., vol. 92, no. 12, pp. 1671–1676, Dec. 2007, doi: 10.1016/j.ress.2006.09.018.
  7. G. Thompson and S. J. Sharp, “Explaining heterogeneity in meta‐analysis: a comparison of methods,” Stat. Med., vol. 18, no. 20, pp. 2693–2708, 1999.
  8. P. Higgins and S. G. Thompson, “Quantifying heterogeneity in a meta‐analysis,” Stat. Med., vol. 21, no. 11, pp. 1539–1558, 2002.
  9. Garmabaki, A. Ahmadi, J. Block, H. Pham, and U. Kumar, “A reliability decision framework for multiple repairable units,” Reliab. Eng. Syst. Saf., vol. 150, pp. 78–88, 2016, doi: 10.1016/j.ress.2016.01.020.
  10. Guida and M. Giorgio, “Reliability analysis of accelerated life-test data from a repairable system,” IEEE Trans. Reliab., vol. 44, no. 2, pp. 337–346, 1995.
  11. Giorgio, M. Guida, and G. Pulcini, “Repairable system analysis in presence of covariates and random effects,” Reliab. Eng. Syst. Saf., vol. 131, pp. 271–281, Nov. 2014, doi: 10.1016/j.ress.2014.04.009.
  12. F. Lawless, “Regression methods for Poisson process data,” J. Am. Stat. Assoc., vol. 82, no. 399, pp. 808–815, 1987.
  13. Kumar and B. Klefsjö, “Proportional hazards model: a review,” Reliab. Eng. Syst. Saf., vol. 44, no. 2, pp. 177–188, 1994.
  14. G. Gutierrez, “Parametric frailty and shared frailty survival models,” Stata J., vol. 2, no. 1, pp. 22–44, 2002.
  15. Hougaard, “Frailty models for survival data,” Lifetime Data Anal., vol. 1, no. 3, pp. 255–273, Sep. 1995, doi: 10.1007/BF00985760.
  16. W. Vaupel, K. G. Manton, and E. Stallard, “The impact of heterogeneity in individual frailty on the dynamics of mortality,” Demography, vol. 16, no. 3, pp. 439–454, 1979.
  17. Barabadi, J. Barabady, and T. Markeset, “Maintainability analysis considering time-dependent and time-independent covariates,” Reliab. Eng. Syst. Saf., vol. 96, no. 1, pp. 210–217, 2011.
  18. H. Abbring and G. J. Van Den Berg, “The unobserved heterogeneity distribution in duration analysis,” Biometrika, vol. 94, no. 1, pp. 87–99, 2007.
  19. T. P. Leszczyc and F. M. Bass, “Determining the effects of observed and unobserved heterogeneity on consumer brand choice,” Appl. Stoch. Models Data Anal., vol. 14, no. 2, pp. 95–115, 1998.
  20. Barabadi, O. T. Gudmestad, and J. Barabady, “RAMS data collection under Arctic conditions,” Reliab. Eng. Syst. Saf., vol. 135, pp. 92–99, 2015, doi: 10.1016/j.ress.2014.11.008.
  21. Gao, J. Barabady, and T. Markeset, “An approach for prediction of petroleum production facility performance considering Arctic influence factors,” Reliab. Eng. Syst. Saf., vol. 95, no. 8, pp. 837–846, 2010.
  22. H. S. Garmabaki, A. Ahmadi, Y. A. Mahmood, and A. Barabadi, “Reliability Modelling of Multiple Repairable Units,” Qual. Reliab. Eng. Int., vol. 32, no. 7, pp. 2329–2343, Nov. 2016, doi: 10.1002/qre.1938.
  23. G. Asfaw and B. H. Lindqvist, “Unobserved heterogeneity in the power law nonhomogeneous Poisson process,” Reliab. Eng. Syst. Saf., vol. 134, pp. 59–65, 2015.
  24. [24]M. Li and J. Liu, “Bayesian hazard modeling based on lifetime data with latent heterogeneity,” Reliab. Eng. Syst. Saf., vol. 145, pp. 183–189, 2016.
  25. G. Clayton, “A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence,” Biometrika, vol. 65, no. 1, pp. 141–151, 1978.
  26. Asadzadeh, A. Aghaie, H. Shahriari, and S. T. A. Niaki, “The application of proportional hazards and frailty models to multistage processes surveillance,” Int. J. Adv. Manuf. Technol., vol. 74, no. 1, pp. 461–470, Sep. 2014, doi: 10.1007/s00170-014-5914-4.
  27. Slimacek and B. H. Lindqvist, “Nonhomogeneous Poisson process with nonparametric frailty,” Reliab. Eng. Syst. Saf., vol. 149, pp. 14–23, May 2016, doi: 10.1016/j.ress.2015.12.005.
  28. Asha, A. V. Raja, and N. Ravishanker, “Reliability modelling incorporating load share and frailty,” Appl. Stoch. Models Bus. Ind., vol. 34, no. 2, pp. 206–223, 2018, doi: 10.1002/asmb.2294.
  29. Xu and X. Li, “Negative dependence in frailty models,” J. Stat. Plan. Inference, vol. 138, no. 5, pp. 1433–1441, 2008.
  30. Misra, N. Gupta, and R. D. Gupta, “Stochastic comparisons of multivariate frailty models,” J. Stat. Plan. Inference, vol. 139, no. 6, pp. 2084–2090, Jun. 2009, doi: 10.1016/j.jspi.2008.09.006.
  31. Finkelstein, “Shocks in homogeneous and heterogeneous populations,” Reliab. Eng. Syst. Saf., vol. 92, no. 5, pp. 569–574, 2007.
  32. Slimacek and B. H. Lindqvist, “Reliability of wind turbines modeled by a Poisson process with covariates, unobserved heterogeneity and seasonality,” Wind Energy, vol. 19, no. 11, pp. 1991–2002, 2016, doi: 10.1002/we.1964.
  33. Lancaster, “Econometric methods for the duration of unemployment,” Econom. J. Econom. Soc., pp. 939–956, 1979.
  34. Ghomghaleh et al., “Prediction of remaining useful life (RUL) of Komatsu excavator under reliability analysis in the Weibull-frailty model,” Plos One, vol. 15, no. 7, p. e0236128, 2020.
  35. Ghomghale, M. Ataei, R. Khalokakaie, A. Barabadi, and A. Nouri Qarahasanlou, “The Application of Frailty Model in Remaining Useful Life Estimation (Case Study: Sungun Copper Mine’s Loading System),” J. Model. Eng., vol. 18, no. 62, Oct. 2020, doi: 10.22075/jme.2020.19249.1817.
  36. Barabadi, M. Ataei, R. Khalokakaie, and A. Nouri Qarahasanlou, “Observed and Un-Observed Covariate Effects on Baseline Hazard Rate - Case study: Jajarm Bauxite Mine,” J. Model. Eng., vol. 0, Nov. 2019, doi: 10.22075/jme.2019.17837.1721.
  37. Barabadi, M. Ataei, R. Khalokakaie, A. Barabadi, and A. N. Qarahasanlou, “Spare Part Management Considering Risk Factors,” in International Congress and Workshop on Industrial AI, 2021, pp. 24–39.
  38. Barabadi, M. Ataei, R. Khalokakaie, and A. Nouri Qarahasanlou, “Spare-part management in a heterogeneous environment,” Plos One, vol. 16, no. 3, p. e0247650, 2021.
  39. Zaki, A. Barabadi, J. Barabadi, and A. Nouri Qarahasanlou, “Observed and unobserved heterogeneity in failure data analysis,” Proc. Inst. Mech. Eng. Part O J. Risk Reliab., p. 1748006X211022538, 2021.
  40. Rod, A. Barabadi, and M. Naseri, “Recoverability Modeling of Power Distribution Systems Using Accelerated Life Models: Case of Power Cut due to Extreme Weather Events in Norway,” J. Manag. Eng., vol. 36, no. 5, p. 05020012, 2020.
  41. Nouri Qarahasanlou, M. Ataei, R. Khalokakaie, S. Fatoorachi, and R. Barabady, “Operating Environment Based Reliability Analysis of Mining Equipment Case Study: Molybdenum-Copper Mine (Sungun Copper Mine),” J. Anal. Numer. Methods Min. Eng., vol. 9, no. 18, pp. 129–141, Apr. 2019.
  42. Barabadi, “Reliability model selection and validation using Weibull probability plot—A case study,” Electr. Power Syst. Res., vol. 101, pp. 96–101, Aug. 2013, doi: 10.1016/j.epsr.2013.03.010.
  43. C. Kimber, “A Weibull-based score test for heterogeneity,” Lifetime Data Anal., vol. 2, no. 1, pp. 63–71, Mar. 1996, doi: 10.1007/BF00128471.
  44. J. Gray, “Tests for Variation over Groups in Survival Data,” J. Am. Stat. Assoc., Feb. 2012, Accessed: Jan. 30, 2019. [Online]. Available: https://www.tandfonline.com/doi/abs/10.1080/01621459.1995.10476502
  45. Commenges and P. K. Andersen, “Score test of homogeneity for survival data,” Lifetime Data Anal., vol. 1, no. 2, pp. 145–156, Jun. 1995, doi: 10.1007/BF00985764.
  46. Mittlböck and H. Heinzl, “A simulation study comparing properties of heterogeneity measures in meta-analyses,” Stat. Med., vol. 25, no. 24, pp. 4321–4333, 2006, doi: 10.1002/sim.2692.
  47. P. A. Ioannidis, “Interpretation of tests of heterogeneity and bias in meta-analysis,” J. Eval. Clin. Pract., vol. 14, no. 5, pp. 951–957, 2008, doi: 10.1111/j.1365-2753.2008.00986.x.
  48. B. Huedo-Medina, J. Sánchez-Meca, F. Marín-Martínez, and J. Botella, “Assessing heterogeneity in meta-analysis: Q statistic or I2 index?,” Psychol. Methods, vol. 11, no. 2, p. 193, 2006.
  49. J. Brewer, A. Butler, and S. L. Cooksley, “The relative performance of AIC, AICC and BIC in the presence of unobserved heterogeneity,” Methods Ecol. Evol., vol. 7, no. 6, pp. 679–692, 2016.
  50. W. Lagakos, “The graphical evaluation of explanatory variables in proportional hazard regression models,” Biometrika, vol. 68, no. 1, pp. 93–98, Apr. 1981, doi: 10.1093/biomet/68.1.93.
  51. Arjas, “A graphical method for assessing goodness of fit in Cox’s proportional hazards model,” J. Am. Stat. Assoc., vol. 83, no. 401, pp. 204–212, 1988.
  52. J. Gray, “Some Diagnostic Methods for Cox Regression Models Through Hazard Smoothing,” Biometrics, vol. 46, no. 1, pp. 93–102, 1990, doi: 10.2307/2531633.
  53. R. Cox, “A note on the graphical analysis of survival data,” Biometrika, vol. 66, no. 1, pp. 188–190, Apr. 1979, doi: 10.1093/biomet/66.1.188.
  54. Schoenfeld, “Partial residuals for the proportional hazards regression model,” Biometrika, vol. 69, no. 1, pp. 239–241, Apr. 1982, doi: 10.1093/biomet/69.1.239.
  55. N. Pettitt and I. B. Daud, “Investigating Time Dependence in Cox’s Proportional Hazards Model,” J. R. Stat. Soc. Ser. C Appl. Stat., vol. 39, no. 3, pp. 313–329, 1990, doi: 10.2307/2347382.
  56. Park and D. J. Hendry, “Reassessing Schoenfeld Residual Tests of Proportional Hazards in Political Science Event History Analyses,” Am. J. Polit. Sci., vol. 59, no. 4, pp. 1072–1087, 2015, doi: 10.1111/ajps.12176.
  57. D. Kalbfleisch and R. L. Prentice, The statistical analysis of failure time data. Wiley-Interscience, 2011.
  58. Schoenfeld, “Chi-squared goodness-of-fit tests for the proportional hazards regression model,” Biometrika, vol. 67, no. 1, pp. 145–153, Jan. 1980, doi: 10.1093/biomet/67.1.145.
  59. O’Quigley and F. Pessione, “Score Tests for Homogeneity of Regression Effect in the Proportional Hazards Model,” Biometrics, vol. 45, no. 1, pp. 135–144, 1989, doi: 10.2307/2532040.
  60. W. McKeague and K. J. Utikal, “Goodness-of-Fit Tests for Additive Hazards and Proportional Hazards Models,” Scand. J. Stat., vol. 18, no. 3, pp. 177–195, 1991.
  61. Gill and M. Schumacher, “A simple test of the proportional hazards assumption,” Biometrika, vol. 74, no. 2, pp. 289–300, Jun. 1987, doi: 10.1093/biomet/74.2.289.
  62. R. Neumann, “A Generalized Moments Specification Test of the Proportional Hazards Model AU - Horowitz, Joel L.,” J. Am. Stat. Assoc., vol. 87, no. 417, pp. 234–240, Mar. 1992, doi: 10.1080/01621459.1992.10475197.