Evaluation Of Autocorrelated Process Capability Index With Batching Method

The conventional statistical process control is based on the hypothesis that independent identically distributed data, but with a lot of modern industry automation and computer aided manufacturing, process data is no longer meet IID features. Conventional statistical control theory will uesless if the data gathered often existing autocorrelation. In the paper, some of quantitative characterization of coefficient of Process capability analysis for stable autocorrelation based on AR(1) model are analyzed firstly. Secondly, evaluating the capability analysis of autocorrelation utilizing bathing mean method. Finally,Constructing confidence interval is additional discussed. The main contents are summarized as follows:1. The simulation process of autocorrelation of AR(1) model is made by Matlab,based on the industry the most widely appeared in the process of autocorrelation sequence.Then a series of parameters that can effect the process capability of autocorrelation is analysised.Discussed the cause of difference of PPM and APPM, and prove the batching mean method can eliminate the correlation of data effectively. Researches show that using the conventional approach of process capability indexes will decrease within autocorrelation data.Build the procedure taking advantage of batching mean method applying to real data.2. Discussing the whole procedure of autocorrelation process capability indexes using batching method and test the preform of bathing method by comparing with Zhang’s method and Chou’s method. We use two kind of time series models: AR(1) and ARMA(1,1)model to simulate. The performance is compared with the coverage percentage. Batching method shows a convergence rate and it is more reliable and robust when we have large enough sample sizes.3. Constructing confidence interval of autocorrelation process capability is additional discussed, and learning the methods from previous researcher’s result. The results show that the higher auto-relationship, the bigger variance of process capability indices and more unsteadiness of process with limited samples, while the degree of correlation not impact the variance of process capability indices directly with unlimited samples. On the discussion of relationship of each parameter, we focus on the number of samples n, Cp/Cpk and autocorrelation coefficient have influence on confidence interval estimation. Simulations show that for given autocorrelation coefficient, the confidence interval is decrease with increase the value of n; for given the value of n, the confidence interval is increase with increase autocorrelation coefficient. The confidence interval of Cp/Cpk has better preform with limited samples and high autocorrelation coefficient. In regard to the value of k in Zhang’s method, simulations demonstrate that the value of k=2 is not always meet all conditions.