Preservation properties of stochastic orderings by transformation to Harris family with different tilt parameters
نویسندگان
چکیده
Harris family of distributions models lifetime of a series system when the number of components is a positive random variable. In this paper, we reveal several stochastic comparisons in the Harris family with different tilt parameters and different baseline distributions with respect to the usual stochastic, shifted stochastic, proportional stochastic and shifted proportional stochastic orderings. Such comparisons are particularly useful in lifetime optimization of reliability systems. We shall also present two bounds for a Harris family survival function conditioned on its tilt parameter which are useful when aging properties are considered. Our results generalize several previous findings in this connection.
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