Statistical analysis of failures

• Autorzy: Knopik L.
• Języki publikacji: EN

Abstrakty

EN

The lifetime distribution is important in reliability studies. There are many situations in lifetime testing, where an item (technical object) fails instantaneously and hence the observed lifetime is reported as a small real positive number. The investigation in this article was motivated by an extended and generalized Weibull distribution. We suggest a mixture of a singular distribution and Weibull distribution. We apply the maximum likelihood method to estimate the parameters of the mixture. The method is illustrated by a numerical example for the time between the failures of bus engines.

Słowa kluczowe

EN

Weibull distribution; mixture of distributions; maximum likelihood method; confidence interval; early failures

• Wydawca: Faculty of Ocean Engineering and Ship Technology, Gdańsk University of Technology
• Czasopismo: Journal of Polish CIMAC
• Rocznik: 2012
• Tom: Vol. 7, no 2
• Strony: 91--95
• Opis fizyczny: Bibliogr. 10 poz., rys., tab.

Twórcy

autor

Knopik L.

• University of Technology and Life Science in Bydgoszcz Faculty of Management Science Fordonska 424 st, 85-789 Bydgoszcz, Poland,

Bibliografia

• 1. Aitchison I.: (1955) On the distribution of a positive random variable having a discrete probability mass at origin, Journal of the American Statistical Associations, vol. 50, pp. 901-908.
• 2. Jayade V. P. and Parasad M. S.: (1996) Estimations of parameters of mixed failure time distribution. Communications Statistics, Theory and Method, vol19, pp. 4667-4677.
• 3. Kale B. K. and Muralidharan K.: (2000) Optimal estimating equations in mixture distributions accommodating instantaneous or early failures, Journal Indian Statistical Associations, vol. 38, pp.317-329.
• 4. Kleyle R.M. and Dahiya R.L.: (1975) Estimation of parameters of mixed failure time distribution from censored data, Communications Statistics, Theory and Method, vol.4, pp. 873-882.
• 5. Muralidharan K.: (1999) Test for mixing proportion in mixture of a degenerate and exponential distributions, Journal Indian Statistical Associations, vol. 37, pp. 105-119.
• 6. Muralidharan K.: (2000) The UMVUE and Bayes estimate of reliability of mixed failure time distribution, Communications Statistics, Simulation Computer, vol. 29, No 2, pp. 603-158.
• 7. Muralidharan K. and Kale B.K.: (2002) Modified gamma distribution with singularity at zero, Communications Statistics, Simulation Computer, vol. 31, No1, pp.143-158.
• 8. Muralidharan K. and Lathika P.: (2006) Analysis of instantaneous and early failures in Wiebull distribution, Metrika vol. 64, pp.305-316.
• 9. Knopik L.: (2010) Mixture of distributions as a lifetime distribution of a technical object, Scientific Problems of Machines Operation and Maintenance, 2010, vol.45, 2(165), pp. 53-60.
• 10. Wdzięczny A., Woropay M. and Muslewski Ł.: Division and investigation of damages to technical object and their influence on the reliability of operation and maintenance systems Scientific Problems of Machines Operation and Maintenance, 2008, vol.44, 2(154), 2008, pp. 31-43.