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

[[abstract]]In this paper, a process yield-index for autocorrelation between nonlinear profiles is proposed. Applying a one-dimensional Taylor series expansion, the mean and variance of the estimator of the yield index are derived. To evaluate the performance of the proposed yield index a simulation study is conducted. The new index is employed to design three acceptance sampling plans for quality characteristics described by auto-correlated nonlinear profiles. The first sampling plan is based on resubmission. The remaining two follow the repetitive group and multiple dependent repetitive sampling schemes respectively. For all sampling plans, the operating characteristic function is developed. A non-linear optimization approach with search algorithm is employed to determine the number of profiles required for inspection and to decide critical values for acceptance, rejection, and resubmission criteria. The performance of the new methods is investigated and compared with traditional single sampling plan. The comparison confirms all of the three proposed methods possess higher efficiency than a single sampling plan in terms of sample size. For practical applications tables are provided. Two numerical examples from the automobile engine testing and particleboard manufacturing process are used to demonstrate the applicability of the proposed methods

Multiple Comparisons With the Best and Difference Test Statistic for Supplier Selection for Nonlinear Profiles

[[abstract]]It is vital to choose the right supplier to reduce cost and provide high-quality products. However, a gap remains because the supplier’s process is mainly measured using qualitative and intangible criteria. Further, with technological advances, the measurement of quality characteristics is transforming through smart data sensors. With a specific time or space measurements can be done at high frequency. The functional relationships between the measures or profiles can be established. The profiles indicate the pattern in the data. The literature focused on the case when quality characteristics are described by linear profile and consider symmetric tolerance. However, in a real-world application, nonlinear profiles and asymmetric tolerance is frequently found. This study proposed multiple comparisons with the best and the difference test statistic methods to select the best suppliers when the quality characteristics are described by nonlinear profile with asymmetric tolerances. A Monte Carlo simulation study is conducted, computer programs are written in the R programming language. The result indicated in terms of rejecting inferior suppliers, the multiple comparisons with the best method perform better than the difference test statistics. With the proposed methods, managers can make decisions using a single, easy-to-understand index. Also, these methods can handle any number of suppliers. For the convenience of a decision-maker, critical values, and profile size requirements are provided. An illustrative example is included to give a better insight into the proposed methods

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