This paper investigates and analyzes that an arrival order lot may contain some defective items, and the defective rate is a random variable. It also considers a mixture inventory model with backorders and lost sales in which the lead time, order quantity and reorder point are viewed as decision variables. In this study, 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 lead time demand and only assume that the mean and variance are known. For each case, we develop an algorithm to find the optimal ordering policy. Furthermore, the sensitivity analysis is performed.