Sampling Schemes by Variables Inspection for the First-Order Autoregressive Model between Linear Profiles

We present four new sampling schemes by variables inspection to deal with the first-order autoregressive model between linear profiles. The first plan is based on exponentially weighted moving average (EWMA) and the rest of three plans are using the resubmitted sampling, repetitive group sampling (RGS), and multiple dependent state (MDS) sampling schemes. The nonlinear optimization problem is developed to find the number of profiles and the corresponding acceptance criteria, such that the producer's and consumer's risk are satisfied simultaneously. The efficiency of the proposed plans is compared with the conventional single sampling plan in terms of average sample number and the probability of acceptance. The result implies that all of the proposed sampling plans are superior to the single acceptance sampling plan by variables. In addition, the EWMA method appeared to be better than the others. The applications of proposed plans are shown with the help of industrial examples taken from calibration of an optical imaging system, and tire cornering stiffness test.