The Weibull lifetime model with randomised failure-free time

• Authors: Piotr Sulewski , Magdalena Szymkowiak

Abstracts

EN

The paper shows that treating failure-free time in the three-parameter Weibull distribution not a constant, but as a random variable makes the resulting distribution much more flexible at the expense of only one additional parameter.

Keywords

EN

Weibull lifetime model; randomised failure-free time; compound Weibull distributions

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2022
• Volume: 23
• Issue: 4
• Pages: 59-76

Dates

published

2022

Contributors

author

Piotr Sulewski

• Pomeranian University, Institute of Exact and Technical Sciences, Poland

author

Magdalena Szymkowiak

• Poznan University of Technology, Institute of Automatic Control and Robotics, Poland

References

• Ahrens, J. H., Dieter, U. (1982). Generating gamma variates by a modified rejection technique. Communications of the ACM, 25, pp. 47–54.
• Ahrens, J. H., Dieter, U. (1974). Computer methods for sampling from gamma, beta, poisson and binomial distributions. Computing, 12, pp. 223–246.
• Alamlki, S. J.,Nadarajah, S., (2014). ,Modifications of the Weibull distribution: a review. Reliability Engineering and System Safety, 124, pp. 32–55.
• Balakrishnan, N., Ristic, M. M., (2016). Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal, Journal of Multivariate Analysis, 143, pp. 194–207.
• Drapella, A., (1993). Complementary Weibull distribution: Unknown or just forgotten. Quality and Reliability Engineering International, 9, pp. 383–385.
• Drapella, A., (1999). An improved failure-free time estimation method. Quality and Reliability Engineering International, 15, pp. 235–238.
• Dubey, S. D. (1968). A compound Weibull distribution. Naval Research Logistics Quarterly, 15, pp. 179–188.
• Gertsbakh, I. B., Kordonskiy, K. H. B., (1969). Models of failure, Verlag: Springer.
• Kao, J. H. K. (1966). Lifetime models with applications, In: Reliability Handbook. W.G. Ireson Editor-in-chief. McGraw-Hill Company.
• Kao, J. H. K. (1960). A summary of some new techniques on failure analysis, Proc. Sixth Natl. Symp. on Reliability and Quality Control.
• Kececioglu, D. (1991). Reliability Engineering Handbook, New York: Prentice Hall, Eaglewood Cliffs.
• Kendall, M. G., Stuart, A. (1961). The advanced theory of statistics, Vol. 2, Charles Griffin and Company.
• Lai, C. D. (2014). Generalized Weibull Distributions, New York: Springer.
• Lai, C. D., Xie, M. (2006). Stochastic ageing and dependence for reliability, Springer Science and Business Media.
• Lam, S. W., Halim, T., Muthusamy, K. (2010). Models with failure-free life-Applied review and extensions, IEEE Transactions on Device and Materials Reliability, 10(2), pp. 263–270.
• Mahmood, S. W., Algamal, Z. Y. (2021). Reliability Estimation of Three Parameters Gamma Distribution via Particle Swarm Optimization, Thailand Statisticia, 19(2), pp. 308–316.
• Mudholkar, G. S., Srivastava, D. K., (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data IEEE Transactions on Reliability, 42, pp. 299–302.
• Murthy, D. N. P., Xie, M., Jiang, R., (2004). Weibull models, Hoboken: Wiley. O’Connor, P. D. T. (1985). Practical reliability engineering, New York: Wiley.
• Park, C. (2018). A Note on the Existence of the Location Parameter Estimate of the Three- Parameter Weibull Model Using the Weibull Plot, Mathematical Problems in Engineering, 10(2), pp. 1–6.
• Qutb, N., Rajhi, E., (2016). Estimation of the Parameters of Compound Weibull Distribution, IOSR Journal of Mathematics, 12, pp. 11–18.
• Ramakrishnan, M., Viswanathan, N., (2017). Comparing the methods of estimation of three-parameterWeibull distribution, IOSR Journal of Mathematics, 13(1), pp. 42–45.
• Rossberg, H. J., Jesiak, B., Siegel, G., (1985). Analytic Methods of Probability Theory, Berlin: Academie Verlag.
• Saffawy, S. Y., Algmal, Z. Y (2006). The Use of Maximum Likelihood and Kaplan-Meir method to Estimate the Reliability Function An Application on Babylon Tires Factory, Tanmiyat Al-Rafidain, 82(28), pp. 9–20.
• Seidel, W. (2010). Mixture model, In Lovric, M., International Encyclopedia of Statistical Science, Heidelberg: Springer.
• Stacy, E.W., (1962). A generalization of the gamma distribution, The Annals of Mathematical Statistics, pp. 1187–1192.
• Szymkowiak, M. (2018a). Characterizations of distributions through aging intensity, IEEE Transactions on Reliability, 67(2), pp. 446–296.
• Szymkowiak, M. (2018b). Generalized aging intensity functions, Reliability Engineering and System Safety, 178, pp. 198–208.
• Szymkowiak, M., (2020). Lifetime analysis by aging intensity functions, Cham: Springer. Weber, M. D., Leemis, L. M., Kincaid, R. (2006). Minimum Kolmogorov–Smirnov test statistic parameter estimates, Journal of Statistical Computation and Simulation, 76(3), pp. 195–206.
• Weibull, W. (1951). A statistical distribution function of wide applicability, Journal of Applied Mechanics, 18, pp. 29–296.
• Wichura, M. J., (1988). Algorithm AS 241: The percentage points of the normal distribution, Applied Statistics, 37, pp. 477–484.

Identifiers

DOI

10.2478/stattrans-2022-0042

Biblioteka Nauki

2156948