This paper assumes that an arrival order lot may contain some defective items, and the number of defective items is a random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity, the reorder point and the lead time are decision variables. In our studies, we first assume that the lead time demand follows a normal distribution, and then relax the assumption about the form of the distribution function of the lead time demand and apply the minimax distribution-free procedure to solve the problem. We develop an algorithm procedure to obtain the optimal ordering strategy. Furthermore, the effects of parameters are also included.