We consider coherent and mixed reliability systems composed of elements with independent and identically distributed lifetimes. We present upper bounds on variances of system lifetimes, expressed in terms of variances of single components. We also discuss attainability conditions and some special cases and examples.

We consider coherent and mixed reliability systems composed of elements with independent and identically distributed lifetimes. We present upper bounds on variances of system lifetimes, expressed in terms of variances of single components. We also discuss attainability conditions and some special cases and examples.

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We consider the drawing with and without replacement models from numerical populations. For order statistics based on the above drawing schemes, we provide sharp upper bounds for their variances, expressed in the single observation variance units. We also characterize the populations for which the bounds are attained.