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

Abstract

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.

Process Yield Index and Variable Sampling Plans for Autocorrelation Between Nonlinear Profiles

“…This section looks at the circumstance where the supplier is permitted to ask for resampling when a lot is not accepted. For linear profiles [11] and auto-correlated linear profiles [15] proposed resubmitted sampling plans based on the yield index. Both authors found the resubmitted sampling plan has a better-operating characteristics curve (OC) compared to a single sampling plan.…”

“…If the test is costly and destructive the RGS plan takes a sequence of small samples from the lot and allows the number of repetitions (rp) to be determined entirely by the results of the sampling process. For the first-order autoregressive between linear profiles [15] proposed RGS plan. The RGS plan for AR(1) nonlinear profiles based on S pkA:P is given as follows:…”

“…In addition, resubmitted [11], repetitive group [13], and multiple dependent state repetitive [14] sampling plans become proven resources to provide sample size reduction for linear profiles. Tamirat et al [15] provided EWMA, resubmitted, repetitive group, and multiple dependent state repetitive sampling plans by variables inspection to deal with the first-order autoregressive model between linear profiles.…”

“…All aforementioned studies including [11]- [15] were done based on the assumption of linear regression models. Nevertheless, in many real-world applications, the linear models are unsatisfactory.…”