Show that for two subsystems " \(\mathrm{a}\) " and " \(\mathrm{b}\) " (with reliability \(R_{\mathrm{a}}\) and \(R_{\mathrm{b}}\) ) operating (ex. two pumps supplying fluid flow) in parallel mode sharing the load, show that (i) the expression for reliability of the combined system is \(R_{\mathrm{cs}}=1-\left(1-R_{\mathrm{a}}ight) \times\left(1-R_{\mathrm{b}}ight)\). (ii) If \(\beta\) were to denote the conditional failure probability of one system, given the failure of another [i.e., probability of failure of the system, \(P(\mathrm{a} \mathrm{b})=P(\mathrm{a}) P(\mathrm{~b} / \mathrm{a})=\beta P(\mathrm{a})\) ], show that system reliability with common cause failure, ccf, \(R_{\mathrm{sccf}}\) is less than \(R_{\mathrm{s}}\), if \(\beta>P(\mathrm{~b})\).