Research On The Selection Of Parameter Of VSI CUSUM Chart

VSI CUSUM(Variable Sampling Interval Cumulative Sum) chart is widely used in detecting the modest shifts in many fields, and also shows very excellent control performance. In practice, both the low nonconformity process and the auto-correlated process are prevalent, and it is found that the geometric CUSUM chart and VSI CCC(Variable Sampling Interval Cumulative Count of Conforming) chart are usually used in the low nonconformity process, and residual CUSUM chart is usually used in the auto-correlated process. As a result, Based on low nonconformity process and auto-correlated process as the application background, the selection of the sampling interval is the main research object of this paper, dividing the in-control area through the simulation method, to prove that the control performance of VSI CUSUM chart is promoted with the increase of the number of sampling interval.In this paper, the basic principle of FSI CUSUM(Fixed Sampling Interval Cumulative Sum) chart and VSI CUSUM chart is introduced at first, and it is also presented that the selection method of reference value k and decision value h and how to calculate the average run length by using the integral equation method. Then, the method for selecting samping interval is discussed for VSI CUSUM chart, and a method for selecting samping interval is given when the sample size equals to one, and it is given that an approximate division method for in-control area according to the dicision value h. At last, by means of the simulaton method, it is analyzed that the value of ATS of VSI CUSUM charts with different number of sampling intervals to the same set of random data, when the target fraction defective p0 takes different values and in different shift level. Employing the concept of improvement factor, the control performance of any two control scheme are compared, and the results are displayed as follows: VSI CUSUM chart with two samping intervals has much larger performace improvement than FSI CUSUM chart; VSI CUSUM chart with three samping intervals has much larger performace improvement than VSI CUSUM with two samping intervals; VSI CUSUM chart with five samping intervals has larger performace improvement than VSI CUSUM with three samping intervals, but not significant. The simulation result of the AR(1) process with a positive coefficient is displayed that the ATS of VSI CUSUM chart remains stable with the increase of coefficient when the offsets are equal, and the ATS of VSI CUSUM chart decreases with the increase of offset when the coefficients are equal, and VSI CUSUM chart with three sampling intervals superiors to VSI CUSUM chart with two sampling intervals when the offset is larger(2~3 SD).As a result, the control performance of VSI CUSUM chart is more and more improved with the increase of the number of sampling intervals in the low nonconformity process and the auto-correlated process.