Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-18T22:30:43.910Z Has data issue: false hasContentIssue false
  • English
  • Français

On the change points of mean residual life and failure rate functions for some generalized gamma type distributions

Published online by Cambridge University Press:  22 September 2014

M. Parsa ,
G.R. Motashami Borzadaran  and
A.H. Rezaei Roknabadi
Get access

Abstract

Mean residual life and failure rate functions are ubiquitously employed in reliability analysis. The term of useful period of lifetime distributions of bathtub-shaped failure rate functions is referred to the flat rigion of this function and has attracted authors and researchers in reliability, actuary, and survival analysis. In recent years, considering the change points of mean residual life and failure rate functions has been extensively utelized in determining the optimum burn-in time. In this paper we investigate the difference between the change points of failure rate and mean residual life functions of some generalized gamma type distributions due to the capability of these distributions in modeling various bathtub-shaped failure rate functions.

Keywords

Change pointfailure rate functionmean residual life functiongeneralized gammauseful period
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 5 , Issue 1 , 2014 , 102
Copyright
© EDP Sciences 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

G.M. Cordeiro, E.M.M. Ortega, G.O Silva, The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. iFirst, 1–16 (2010)
Stacy, E.W., A Generalization of the Gamma distribution, Ann. Math. Stat. 33, 1187–1192 (1962) CrossRefGoogle Scholar
Mudholkar, G.S., Srivastava, D.K., Friemer, M., The exponentiated Weibull family: A reanalysis of the bus-Motor-Failure data, Technometrics 37, 436–445 (1995) CrossRefGoogle Scholar
Mudholkar, G.S., Srivastava, D.K., Kollia, G.D., A generalization of the Weibull distribution with the application to the analysis of survival data, J. Am. Statist. Assoc. 91, 1575–1583 (1996) CrossRefGoogle Scholar
Gupta, R.D., Kundu, D., Generalized exponential distributions, Aust. N.Z. J. Stat. 41, 173–188 (1999) CrossRefGoogle Scholar
Gupta, R.D., Kundu, D., Exponential exponentiated distribution: An alternative to Gamma and Weibull distributions, Biometrika J. 43, 117–130 (2001) 3.0.CO;2-R>CrossRefGoogle Scholar
Kundu, D., Raqab, M.Z., Generalized Rayleigh distribution: Different methods of estimation, Comput. Stat. Data Anal. 49, 187–200 (2005) CrossRefGoogle Scholar
Kumaraswamy, P., A generalized probability density function for double-bounded random-process, J. Hydrol. 462, 79–88 (1980) CrossRefGoogle Scholar
Jones, M.C., Kumaraswamy’s distribution: A beta-type distribution with some tractibility advantages, Staist. Met. 6, 70–81 (2009) CrossRefGoogle Scholar
Cordeiro, G.M., de Castro, M., A new family of generalized distributions, J. Statist. Comput. Simul. , 1–17 (2009) Google Scholar
Pascoa, M.A.R., Ortega, E.M.M., Cordeiro, G.M.C., Paranaiba, P.F., The Kumaraswamy-generalized gamma distribution with application in survival analysis, Stat. Met. 8, 411–433 (2011) CrossRefGoogle Scholar
Gupta, R.C., Akman, H.O., Mean residual life functions for certain types of non-monotonic ageing, Comm. Statist. Stochastic Models 11, 219–225 (1995) Google Scholar
Mi, J., Bathtub failure rate and upside-down bathtub mean residual life, IEEE Trans. Rel. 44, 388–391 (1995) Google Scholar
Lim, J.H., Park, D.H., Trend change in mean residual life, IEEE Trans. Rel. 44, 291–296 (1995) Google Scholar
Mitra, M., Basu, S.K., Change point estimation in non-monotonic ageing models, Ann. Inst. Stat. Math. 47, 483–491 (1995) Google Scholar
Salvia, A.A., Some results on discrete mean residual life, IEEE Trans. Rel. 45, 359–361 (1996) CrossRefGoogle Scholar
F. Guess, F. Proschan, Mean Residual Life: Theory and Applications (Handbook of Statistics 7: Quality Control and Reliability, North-Holland, 1988), pp. 215–224
Ghai, G.L., Mi, J., Mean residual life and its association with failure rate, IEEE Trans. Rel. 48, 262–266 (1999) CrossRefGoogle Scholar
Tang, L.C., Lu, Y., Chew, E.P., Mean residual life of lifetime distributions, IEEE Trans. Rel. 48, 73–78 (1999) CrossRefGoogle Scholar
Chen, Z.M., Ferger, D., Mi, J., Estimation of the change point of a distribution based on the number of failed test items, Metrika 53, 31–38 (2001) CrossRefGoogle Scholar
Bekker, L., Mi, J., Shape and crossing properties of mean residual life functions, Statist. Probab. Lett. 64, 225–234 (2003) CrossRefGoogle Scholar
Mi, J., A General approach to the shape of failure rate and MRL functions, Naval Res. Logist. 51, 543–556 (2004) CrossRefGoogle Scholar
Bebbington, M., Lai, C.D., Zitikis, R., Estimating the turning point of a bathtub shaped failure distribution, J. Statist. Plann. Inference 138, 1157–1166 (2008) CrossRefGoogle Scholar
Shen, Y., Xie, M., Tang, C.D., On the change point of the mean residual life of series and parallel systems, Aust. N. Z. J. Stat. 52, 109–121 (2010) CrossRefGoogle Scholar
Shafaei Noughabi, M., Mohtashami Borzadran, G.R., Rezaei Roknabadi, A.H., On the reliability properties of some weighted models of bathtub shaped hazard rate distribution, Probab. Eng. Inform. Sci. 27, 125–140 (2013) CrossRefGoogle Scholar
Xie, M., Goh, T.N., Tang, Y., On the changing point of mean residual life and failure rate function for generalized Weibull distributions, Reliab. Eng. Syst. Safe. 84, 293–299 (2004) CrossRefGoogle Scholar
Bebbington, M., Lai, C.D., Zitikis, R., Useful period for lifetime distributions with bathtub shaped hazard rate functions, IEEE Trans. Rel. 55, 245–251 (2006) CrossRefGoogle Scholar
Bebbington, M., Lai, C.D., Zitikis, R., Optimum burn-in time for a bathtub shaped failure rate distribution, Methodol. Comput. Appl. Probab. 55, 245–251 (2007) Google Scholar
E.J. Muth, The Theory and Applications of Reliability, Reliability Models with Positive Memory Derived from the Mean Residual Life Function (Academic Press, London, 1977), Vol. 2, pp. 401–435
Calabria, R., Pulcini, G., On the maximum likelihood and least squares estimation in the inverse Weibull estimation, Statist. Appl. 2, 53–66 (1990) Google Scholar
J.F. Lawless, Statistical Models and Methods for Lifetime Data (Wiley, New York, 2003)
Cox, C., The generalized F distribution: an umberella for parametric survival analysis, Stat. Med. 27, 4301–4312 (2008) CrossRefGoogle ScholarPubMed
C.D. Lai, M. Xie, Stochastic Ageing and Dependence for Reliability (Springer, New York, 2006)
Guess, F., Nam, K.H., Park, D.H., Failure rate and mean residual life with trend changes, Asia Pac. J. Oper. Res. 15, 239–244 (1998) Google Scholar
Weiss, G.H., Dishon, M., Some economic problems related to burn-in programs, IEEE Trans. Rel. 20, 190–195 (1971) CrossRefGoogle Scholar
Yun, W.Y., Lee, Y.W., Ferreira, L., Optimal burn-in time under cumulative free replacement warranty, Reliab. Eng. Syst. Safety 78, 93–100 (2002) CrossRefGoogle Scholar