Page 15 - SUBHARADEV SEN AND AHMED

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For parallel system, when θ > 0 and p > 1, the failure rate function is
monotonically increasing (IFR) for all α and t (see Figure 2(d)). On the other
hand, when p < 1, it exhibits increasing as well as decreasing trends
depending on the values of α and t, for all θ > 0 (see Figures 2(a)-2(c) for
different failure rate plots when p < 1). Figure 2 shows some plots of failure
rate function of parallel system for different values of p, α and t, fixing θ at
5.0.

6. CONCLUDING REMARKS

The BVFR distribution considered in this article has identical component
distributions. It will be, however, more pragmatic to assume different
parameters for component lives. We have seen that dependent series system
is less reliable as compared to the hot redundant and cold redundant systems,
but its distribution preserves IFR property for a particular range of the shape
parameter. Different bounds for system reliability of independent finite
range cases should be examined and those to be reconsidered for checking
validity in dependent systems with newer possible bounds, if necessary for
the purpose. A multivariate extension will be an interesting generalization.

7. ACKNOWLEDGEMENT

The authors would like to thank the referee for a very careful reading of the
manuscript and making a number of nice suggestions which improved the
earlier version of the manuscript.

8. REFERENCES

1. Eryilmaz, S. (2011): Estimation in coherent reliability systems through
copulas, Reliability Engineering & System Safety, 96(5), 564-568.
2. Hutchinson, T. P. and Lai, C. D. (1990): Continuous bivariate distributions,
Emphasizing applications. Adelaide Rums by Scientific Publishing.
3. Lai, C.D. and Mukherjee, S. P. (1986): A Note on “A finite range
distribution of failure times”, Microelectronics Reliability, 26(1), 183-189.
4. Mukherjee, S. P. and Islam, A. (1983): A finite-range distribution of failure
times, Naval Research Logistics Quarterly, 30(3), 487-491.

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