Consider a binary system with \(n\) components. Let \(X=(X_ 1,\dots,X_ n)\) be the state vector of the system. Let \(\phi(X)\) denote the structure function of the system. Let \(p=(p_ 1,p_ 2,\dots,p_ n)\), where \(0\leq p_ i\leq 1\) is the random reliability of the component \(i\). The reliability function of the system is defined by \(h(p)=E[\phi(X)\mid p]\). The problem considered in this paper is to obtain a new upper bound for the \(m\)th moment of the reliability function \(h(p)\). Under certain conditions, it is shown that \(E[h(p)]^ m\leq\{h(E p^ m)^{1/m}\}^ m\).