Suppose that a machine consists of n components with the lifetimes X1, X2,

. . . , Xn, respectively, where Xi’s are independent and identically distributed. Suppose that the machine remains operative unless k or more of its components fail. Then X(k), the kth order statistic of {X1,X2, . . . ,Xn}, is the time when the machine fails. Also, X(1) is the failure time of the first component.