Sequential and non-sequential acceptance sampling plans for autocorrelated processes using ARMA(p,q) models

Abstract

This paper presents variable acceptance sampling plans based on the assumption that consecutive observations on a quality characteristic(X) are autocorrelated and are governed by a stationary autoregressive moving average (ARMA) process. The sampling plans are obtained under the assumption that an adequate ARMA model can be identified based on historical data from the process. Two types of acceptance sampling plans are presented: (1) Non-sequential acceptance sampling: In this case historical data is available based on which an ARMA model is identified. Parameter estimates are used to determine the action limit (k) and the sample size(n). A decision regarding acceptance of a process is made after a complete sample of size n is selected. (2) Sequential acceptance sampling: Here too historical data is available based on which an ARMA model is identified. A decision regarding whether or not to accept a process is made after each individual sample observation becomes available. The concept of Sequential Probability Ratio Test (SPRT) is used to derive the sampling plans. Simulation studies are used to assess the effect of uncertainties in parameter estimates and the effect of model misidentification (based on historical data) on sample size for the sampling plans. Macros for computing the required sample size using both methods based on several ARMA models can be found on the author's web page http://pages.towson.edu/aminza/papers.html .