Hostname: page-component-89b8bd64d-4ws75 Total loading time: 0 Render date: 2026-05-07T11:39:46.454Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE RELIABILITY PROPERTIES OF SOME WEIGHTED MODELS OF BATHTUB SHAPED HAZARD RATE DISTRIBUTIONS

Published online by Cambridge University Press:  18 December 2012

M. Shafaei Noughabi ,
G.R. Mohtashami Borzadaran  and
A.H. Rezaei Roknabadi
M. Shafaei Noughabi
Affiliation:
Ferdowsi University of Mashhad, Mashhad, Iran E-mail: mohamad.shafaee@gmail.com; grmohtashami@um.ac.ir; rezaei@um.ac.ir
G.R. Mohtashami Borzadaran
Affiliation:
Ferdowsi University of Mashhad, Mashhad, Iran E-mail: mohamad.shafaee@gmail.com; grmohtashami@um.ac.ir; rezaei@um.ac.ir
A.H. Rezaei Roknabadi
Affiliation:
Ferdowsi University of Mashhad, Mashhad, Iran E-mail: mohamad.shafaee@gmail.com; grmohtashami@um.ac.ir; rezaei@um.ac.ir
Get access Rights & Permissions [Opens in a new window]

Abstract

Let F be a bathtub-shaped (BT) hazard rate distribution function. It has been shown that the hazard rate function of the order statistics may be BT, increasing, etc. Then, we have carried out a graphical study for some useful lifetime models.

Moreover, we are interested to compare the time that maximizes the mean residual life (MRL) function of F with the one related to a general weighted model in terms of their locations. Also, the times maximizing the conditional reliability proposed by Mi [13] of F have been compared with the corresponding times of a general weighted model. As special cases, we consider order statistics and the proportional hazard rate model.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 125 - 140
Copyright
Copyright © Cambridge University Press 2013

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.)

Article purchase

Temporarily unavailable

References

1.Block, H.W. & Savits, T.H. (1997). Burn-in. Statistical Science 12: 1–19.CrossRefGoogle Scholar
2.Block, H.W., Savits, T.H. & Singh, H. (2002). A criteria for burn-in that balances mean residual life and residual variance. Operations Research 50(2): 290–296.CrossRefGoogle Scholar
3.Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics and Probability Letters 49: 155–161.CrossRefGoogle Scholar
4.Franco-Pereira, A.M., Lillo, R.E. & Romo, J. (2010). Characterization of bathtub distributions via percentile residual life functions. Working paper 10-26. Universidad Carlos III de Madrid.Google Scholar
5.Glaser, R.E. (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Association 75: 667–672.CrossRefGoogle Scholar
6.Kao, J.H.K. (1959). A graphical estimation of mixed Weibull parameters in life testing of electronic tubes, Technometrics 1: 389–407.CrossRefGoogle Scholar
7.Karlin, S. (1968). Total positivity. CA: Stanford University Press.Google Scholar
8.Kundu, C., Nanda, A.K. & Hu, T.Z. (2009). A note on reversed hazard rate of order statistics and record values. Journal of Statistical Planning and Inference 139(4): 1257–1265.CrossRefGoogle Scholar
9.Lai, C.D., Xie, M. & Murthy, D.N.P. (2001). Bathtub-shaped failure rate life distributions. Balakrishnan, N. and Rao, C.R. (eds.), Handbook of Statistics 20: 69–104.Google Scholar
10.Lai, C.D., Xie, M. & Murthy, D.N.P. (2003). A modified Weibull distribution. IEEE Transactions on Reliability 25(1): 33–37.CrossRefGoogle Scholar
11.Leemis, L.M. & Beneke, M. (1990). Burn-in models and methods: A review. IIE Transactions 22(2): 172–180.CrossRefGoogle Scholar
12.Lieberman, G.J. (1969). The status and impact of reliability methodology. Naval Research Logistic Quarterly 14: 17–35.CrossRefGoogle Scholar
13.Mi, J. (1994a). Maximization of a survival probability and its application. Journal of Applied Probability 31(4): 1026–1033.CrossRefGoogle Scholar
14.Mi, J. (1994b). Burn-in and maintenance policy. Advances in Applied Probability 26: 207–221.CrossRefGoogle Scholar
15.Mi, J. (1995). Bathtub failure rate and upside-down bathtub mean residual life. IEEE Transactions on Reliability 44(3): 388–396.Google Scholar
16.Misra, N., Manoharan, M. & Singh, H. (1993). Preservation of some aging properties by order statistics. Probability in the Engineering and Informational Sciences 7: 437–440.CrossRefGoogle Scholar
17.Mitra, M. & Basu, S.K. (1996). On some properties of the bathtub failure rate family of life distributions. Microelectronics Reliability 36(5): 679–684.CrossRefGoogle Scholar
18.Mudholkar, G.S. & Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 42: 299–302.CrossRefGoogle Scholar
19.Murthy, D.N.P. & Jiang, R. (1997). Parametric study of sectional models involving two Weibull distributions. Reliability Engineering and System Safety 56: 151–159.CrossRefGoogle Scholar
20.Nagaraja, H.N. (1990). Some reliability properties of order satistics. Communications in Statistics-Theory and Methods 19: 307–316.CrossRefGoogle Scholar
21.Navarro, J. & Hernandez, P.J. (2004). How to obtain bathtub-shaped failure rate models from normal mixtures. Probability in the Engineering and Informational Sciences 18: 511–531.CrossRefGoogle Scholar
22.Rajarshi, S. & Rajarshi, M.B. (1988). Bathtub distributions: a review. Communications in Statistics-Theory and Methods 17(8): 2597–2621.CrossRefGoogle Scholar
23.Schabe, H. (1994). Constructing lifetime distributions with bathtub shaped failure rate from DFR distributions. Microelectronics Reliability 34: 1501–1508.CrossRefGoogle Scholar
24.Shen, Y., Xie, M. & Tang, L.C. (2010). On the change point of the mean residual life of series and parallel systems. Australian and New Zealand Journal of Statistics 52(1): 109–121.CrossRefGoogle Scholar
25.Takahasi, K. (1988). A note on hazard rates of order statistics. Communications in Statistics-Theory and Methods 17: 4133–4136.CrossRefGoogle Scholar
26.Wang, F.K. (2000). A new model with bathtub-shaped failure rate using an additive Burr XII distribution. Reliability Engineering and System Safety 70: 305–312.CrossRefGoogle Scholar
27.Xie, M., Tang, Y. & Goh, T.N. (2002). A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering and System Safety 76: 279–285.CrossRefGoogle Scholar