Standard acceptance sampling plans models the production process as a sequence of independent identically distributed Beruoulli random variables. However, the quality of items sampled sequentially from an ongoing production process often exhibits statistical dependency that is not accounted for in standard acceptance sampling plans. In this paper, a dependent production process is modelled as an ARMA process and as a two-state Markov chain. A simulation study of each is performed. A comparison of the probability of acceptance is done for the simulation method and for the approximation method.