Study On Double Sampling And Variable Sampling Interval (?) Control Chart When Process Parameters Are Estimated

Quality control chart is a kind of effective tool for the detection and monitoring the quality of the product attributes, it can make the process to be stable and efficient. Among them, the double sampling and variable sampling intervals X control chart due to its efficiency to the smaller shifts and can also reduce the sample size, it is widely used in the research. However, in the past study the DSVSI (?) control chart is usually researched under the assumption of known process parameters. In practice, the process parameters are rarely known and they must be estimated from the past in control samples of history. When process parameters are estimated, the properties of the control chart are quite different from known process parameters. So in this paper, we will study the DSVSI (?) control chart under the estimated process parameters. We will construct the model from the aspects of statistical and economical. And explore the performance of the control chart under the estimated process parameters. This article main research content is as follows:This article first introduces the research background of control chart, then gives the statistical process control and relevant principles of the structure of control chart, and then illustrates the dynamic control chart and the thought of parameter estimation, then introduce the operation of DSVSI (?) control chart in detail, at last we gives the criteria of control chart.Secondly, we study the statistical preference of the DSVSI (?) control chart under the estimated process parameters. We construct the model under the estimated process parameters, and by calculating the average time to signal to measure the performance of control chart. We solve the model through the genetic algorithm, and find that parameter estimation has a great influence on the control chart, and with the increase of estimate sample sizes the difference between them become smaller. Also we give the optimal design of the DSVSI (?) control chart under the estimated process parameters, and analyze the effect of mean shift, we find that the more smaller, the greater influence on parameter estimation.We study the economic preference of the DSVSI (?) control chart under the estimated process parameters. We construct the economic design model under the estimated process parameters and solve the model through the genetic algorithm. We compare the economic preference of the DSVSI (?) control chart with estimated and known process parameters and analyze the influence of parameters estimation on the economic preference of the DSVSI (?) control chart. We find that the parameters estimation cause the cost of the control chart increase and also change the optimization parameters design of the control chart. We calculate the optimal parameters of the control chart and the optimal estimated samples and evaluate the estimated parameters to the cost. Then we can make the control chart more realistic so that it can enhance the effectiveness of the control chart in practical application.