Accumulation And Method Of Selecting Control Chart Parameters

Control charts, which control the production process condition and guarantee the process quality, are the important statistics process control tools. In order to improve the sensitivity that control charts monitor the small undulation of the process, Page proposed the cumulative sum (Cusum) control charts in 1954. The Cusum control charts accumulate the small undulation of the process to achieve the magnification effect, therefore when the process has the small undulation, it can promptly find out, then enhance the monitoring efficiency of the control charts. The research of the Cusum control charts mainly concentrate on three aspects: consummating the theory of the Cusum control charts; developing the application of the Cusum control charts; researching the algorithm realization technology of the Cusum control charts. The design of the control parameter is the key of the Cusum control charts theory. This paper investigates and analyzes the design of K H which is the parameter of the Cusum control charts.In this paper, we first introduce the mathematic principle of the Cusum control charts that is the sequential likelihood ratio test and two methods of constructing the Cusum control charts: the V-mask method and the list method. And we give the relations between two groups of parameters K H and dθ, where K is the reference value, H is the determinant distance, d is the lead distance,θis the half angle of V mask. And then, we talk on how to choose parameter K and H according to the mathematic theory of the Cusum. What's more, we precisely prove the selection of parameter when the quality characterization subjects to Normal distribution Binomial distribution Exponential distribution Poisson distribution, and give their results respectively. We also look on average run length (ARL) as a criterion, to talk about parameter K and H selection, summarizing two methods of calculating ARL: the classical integral method and the Markov chain method. We give the parameter selection rules on the basis of ARL. Finally, we take into account the design of the Cusum control charts under the economical significance, introduce the LV economic model and establish the economic model of the Cusum control charts. We find the one kind of optimized search algorithm of gaining the most superior parameter K and H which is genetic algorithm, and provide the solution process of genetic algorithm.The characteristics and the innovation of this paper are as follows: firstly, using the sequential likelihood ratio test to determine the most superior parameter; secondly, establishing the economic model of the Cusum control charts; finally, using the genetic algorithm to gain the most superior parameter.