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.
Highlights
Functional profiles express the relationship between one or more explanatory variables, the controllable inputs and a response variable which is the critical-to-quality characteristics
Profile monitoring has extensive application in the calibration of an optical imaging system; in tire cornering stiffness test the relationship between force and displacement can be modeled by linear profile
The result indicates that the exponentially weighted moving average (EWMA) sampling plan is more efficient in terms of average sample number than other four schemes, multiple dependent state (MDS) is second best, and resubmitted and repetitive group sampling (RGS) are very close to each other
Summary
Functional profiles express the relationship between one or more explanatory variables, the controllable inputs and a response variable which is the critical-to-quality characteristics. For a process with linear profiles, [16] provided a single variable sampling plan based on EWMA model using the yield index SpkA. In the literature Aslam et al [15] and Wang [16] suggested that a sampling plan based on EWMA yield index for a normal process and a process with linear profiles has more flexibility and economy than the single sampling plan based on yield index while providing the same protection to both suppliers and buyers. When the data can be considered as identically, independently, and normally distributed linear profiles, [21] proposed variables sampling plan for resubmitted lots based on the yield index SpkA. With the absence of autocorrelation between linear profiles, [16] provided MDS sampling plan based on yield index SpkA. We propose four new acceptance sampling plans based on the yield index for a first-order autoregressive process. We offer a conclusion and suggestions for future studies
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