This paper assumes that an arrival order lot may contain some defective items, and considers that the number of defective items in the sub-lot sampled to be a random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity, reorder point and lead time are decision variables. In our studies, we first assume that 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 for each case. Furthermore, the effects of parameters are also included.