Competing Risk Models in Reliability Systems, an Exponential Distribution Model with Gamma Prior Distribution, a Bayesian Analysis Approach

  • Ismed IskandarEmail author
  • Muchamad Oktaviandri
  • Rachmawati Wangsaputra
  • Zamzuri Hamedon
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


This paper is a second paper on the use of Exponential distribution in competing risk problems. The difference is this model is developed using Gamma distribution as its prior distribution. For the cases where the failure data together with their causes of failure are simply quantitatively inadequate, time consuming and expensive to perform the life tests, especially in engineering areas, Bayesian analysis approach is used. This model is limited for independent causes of failure. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability using Bayesian analysis approach and presenting their analytic methods. Once the model has been developed through the system likelihood function and individual posterior distributions then the parameter of estimates are derived. The results are the estimations of the failure rate of individual risk, the MTTF of individual and system risks, and the reliability estimations of the individual and of the system of the model.


Reliability Competing risks Exponential distribution Bayesian 


  1. 1.
    Martz, H.F., Waller, R.A.: Bayesian Reliability Analysis. Krieger Publishing Company, Malabar (1991)zbMATHGoogle Scholar
  2. 2.
    Fu, J., Tang, Y., Guan, Q.: Objective bayesian analysis for recurrent events in presence of competing risks. Qual. Technol. Quant. Manag. 11(3), 265–279 (2014)CrossRefGoogle Scholar
  3. 3.
    Do, G., Kim, Y.J.: Analysis of interval censored competing risk data with missing causes of failure using pseudo values approach. J. Stat. Comput. Simul. 87(4), 631–639 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Liu, F., Shi, Y.: Inference for a simple step-stress model with progressively censored competing risks data from Weibull distribution. Commun. Stat.- Theory Methods 46(14), 7238–7255 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Shen, Y., Xu, A.: On the dependent competing risks using Marshall-Olkin bivariate Weibull model: parameter estimation with different methods. Commun. Stat. – Theory Methods 47(22), 5558–5572 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Liu, H.: Reliability and maintenance modeling for competing risk processes with Weibull inter-arrival shocks. Appl. Math. Model. 71, 194–207 (2019)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bhattacharjee, A.: Bayesian competing risks model: an application to breast cancer clinical trial with incomplete observations. J. Stat. Manag. Syst. 18(4), 381–404 (2015)CrossRefGoogle Scholar
  8. 8.
    Lu, T.: Bayesian nonparametric mixed-effects joint model for longitudinal-competing risks data analysis in presence of multiple data features. Stat. Methods Med. Res. 26(5), 2407–2423 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Iskandar, I., Gondokaryono, Y.S.: Competing risk models in reliability systems, a Weibull distribution model with bayesian analysis approach. In: IOP Conference Series: Materials Science and Engineering, vol. 114, no. 1, pp. 012064 (2016)CrossRefGoogle Scholar
  10. 10.
    Iskandar, I.: Competing risk models in reliability systems, a gamma distribution model with bayesian analyses approach. In: IOP Conference Series: Materials Science and Engineering, vol. 114, no. 1, pp. 012098 (2016)CrossRefGoogle Scholar
  11. 11.
    Iskandar, I.: Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach. In: IOP Conference Series: Materials Science and Engineering, vol. 319, no. 1, pp. 012069 (2018)CrossRefGoogle Scholar
  12. 12.
    Iskandar, I., Razali, N.M.: Multi-mode failure models for attribute test data in reliability systems, a bayesian analysis approach using multi-nomial distribution model. In: Advanced Material Research, vol. 903, pp. 419–424 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Ismed Iskandar
    • 1
    Email author
  • Muchamad Oktaviandri
    • 1
    • 3
  • Rachmawati Wangsaputra
    • 2
  • Zamzuri Hamedon
    • 1
  1. 1.Faculty of Mechanical and Manufacturing EngineeringUniversiti Malaysia PahangPekanMalaysia
  2. 2.Bandung Institute of TechnologyBandungIndonesia
  3. 3.Fakultas Teknologi Industri, Universitas Bung HattaPadangIndonesia

Personalised recommendations