Measuring the Process Yield for Circular Profiles

Abstract

Two indices C p (circular) and C pk (circular) based on the functional method have been proposed to measure the process capability of circular profiles. However, these two indices only provide potential capability and a lower bound on the process yield, respectively. In this paper, we develop a new yield index S pk (circular) for circular profiles. This index provides an exact measure of process yield. The asymptotic normal distribution of the estimated index is derived. The statistical inferences such as hypothesis testing, confidence interval, and lower confidence interval can be easily constructed. A simulation study is conducted to assess the performance of the proposed method. The simulation results confirm that the estimates are close to the true value and the coverage rates of the confidence intervals are greater than the 95% lower limit of the stated nominal in most cases. One real data set is used to illustrate the applicability of the proposed method.

Optimal Scheme for Process Quality and Cost Control by Integrating a Continuous Sampling Plan and the Process Yield Index

“…The accuracy of the natural estimator has been investigated with a simulation technique [28]. The process yields for some specified cases, such as the imprecise sample data, circular profiles, autocorrelation between linear profiles, and multiple stream processes, have been analyzed in some literature [29][30][31][32]. In the above researches, the index was used to only reflect the process capability.…”

Process Capability Indices for Logistic Regression Profile

“…Simulation results showed that the simultaneous application of these three methods could provide comprehensive information about the process capability of multivariate linear profiles. Wang proposed a method for precise measurement of PCI of circular profiles. Wang also proposed a method for measuring the exact value of PCI for simple linear profiles.…”

Implementing the Ratio Test Statistic to Compare Two Suppliers for Linear Profiles

“…However, those indices only provide an approximate measure rather than an exact measure of the process yield. A process yield index S pkA for simple linear, nonlinear, and circular profiles have been proposed to evaluate the process yield …”

“…A process yield index S pkA for simple linear, nonlinear, and circular profiles have been proposed to evaluate the process yield. [13][14][15][16] Comparing the process yield for linear profiles is an essential task in managing supply chains. Two methods such as the difference test statistic and the ratio test statistic can be used to solve this comparison problem.…”