References
- Free , E. W. 1986 . Warranty analysis and renewal function estimation . Nav. Res. Logist. Quart. , 33 : 361 – 372 . (doi:10.1002/nav.3800330302)
- Murphy , D. N.P. and Blishke , W. R. 1992 . Product warranty management-III: A review of mathematical models . Eur. J. Oper. Res. , 62 : 1 – 34 . (doi:10.1016/0377-2217(92)90052-B)
- Liao , H. , Wang , P. and Jin , T. 2008 . Spare parts management considering new sales . Annual Reliability and Maintainability Symposium . January 2008 , Las Vegas , NV . pp. 28 – 31 .
- Moors , J. J.A. and Strijbosch , L. W.G. 2002 . Exact fill rates for (R, s, S) inventory control with gamma distributed demand . J. Oper. Res. Soc. , 53 : 1268 – 1274 . (doi:10.1057/palgrave.jors.2601441)
- Girish , M. K. and Hu , J. Q. 2001 . Approximations for the departure process of the G/G/1 queue with Markov-modulated arrivals . Eur. J. Oper. Res. , 134 : 540 – 556 . (doi:10.1016/S0377-2217(00)00276-9)
- Kumar , U. D. and Knezevic , J. 1998 . Availability based spare optimization using renewal process . Reliab. Eng. Syst. Safety , 59 : 217 – 223 . (doi:10.1016/S0951-8320(97)00155-5)
- Cox , D. R. and Isham , V. 1981 . Point Processes , London : Chapman and Hall .
- Cui , L. and Xie , M. 2003 . Some normal approximations for renewal function of large Weibull shape parameters . Comm. Stat. Simul. Comput. , 32 : 1 – 16 . (doi:10.1081/SAC-120013107)
- Ayhan , H. , Limon-Robles , J. and Wortman , M. A. 1999 . An approach for computing tight numerical bounds on renewal functions . IEEE Trans. Reliab. , 48 : 182 – 188 . (doi:10.1109/24.784278)
- Xie , M. 1989 . On the solution of renewal-type integral equations . Comm. Stat. Simul. Comput. , 18 : 281 – 293 . (doi:10.1080/03610918908812760)
- Brown , M. , Solomon , H. and Stephens , M. A. 1981 . Monte Carlo simulation of the renewal function . J. Appl. Probab. , 18 : 426 – 434 . (doi:10.2307/3213288)
- McConalogue , D. J. 1981 . Numerical treatment of convolution integrals involving distributions with densities having singularities at the origin . Comm. Stat. Simul. Comput. , 10 : 265 – 280 . (doi:10.1080/03610919808812206)
- Jiang , R. 2008 . A gamma-normal series truncation approximation for computing the Weibull renewal function . Reliab. Eng. Syst. Safety , 93 : 616 – 626 . (doi:10.1016/j.ress.2007.03.026)
- Smeitink , E. and Dekker , R. 1990 . A simple approximation to the renewal function . IEEE Trans. Reliab. , 39 : 71 – 75 . (doi:10.1109/24.52614)
- From , S. G. 2001 . Some new approximations for the renewal function . Comm. Stat. Simul. Comput. , 30 : 113 – 128 . (doi:10.1081/SAC-100001862)
- Garg , A. and Kalagnanam , K. 1998 . Approximations for the renewal functions . IEEE Trans. Reliab. , 47 : 66 – 72 . (doi:10.1109/24.690909)
- Jin , T. and Gonigunta , L. 2010 . Exponential approximation to Weibull renewal with decreasing failure rate . J. Statist. Comput. Simul. , 80 : 273 – 285 . (doi:10.1080/00949650802623922)
- Jin , T. and Gonigunta , L. 2009 . Weibull and Gamma renewal approximation using generalized exponential functions . Comm. Stat. Simul. Comput. , 38 : 154 – 171 . (doi:10.1080/03610910802440327)
- Constantine , A. G. and Robinson , N. I. 1997 . The Weibull renewal function for moderate to large arguments . Comput. Stat. Data Anal. , 24 : 9 – 27 . (doi:10.1016/S0167-9473(96)00052-7)
- Mudholkar , G. S. and Srivastava , D. K. 1993 . Exponentiated Weibull family for analyzing bathtub failure-rate data . IEEE Trans. Reliab. , 42 : 299 – 302 . (doi:10.1109/24.229504)
- Gupta , R. D. and Kundu , D. 1999 . Generalized exponential distribution . Aust. N.Z. J. Stat. , 41 : 901 – 916 . (doi:10.1111/1467-842X.00072)
- Gupta , R. D. and Kundu , D. 2001 . Exponentiated exponential family: An alternative to gamma and Weibull . Biom. J. , 43 : 117 – 130 . (doi:10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R)
- Gupta , R. D. and Kundu , D. 2003 . Closeness of gamma and generalized exponential distribution . Comm. Statist. Theory Methods , 32 : 705 – 721 . (doi:10.1081/STA-120018824)
- Gupta , R. D. and Kundu , D. 2004 . Discriminating between gamma and generalized exponential distributions . J. Statist. Comput. Simul. , 74 : 107 – 121 . (doi:10.1080/0094965031000114359)
- From , S. G. and Tortorella , M. 2005 . Parametric confidence intervals for the renewal function using coupled integral equations . Comm. Stat. Simul. Comput. , 34 : 663 – 672 . (doi:10.1081/SAC-200068472)