Design Of The Adaptive (?) Control Chart With Switching Rules And Its Extension And Application

With the development of economic globalization, competition among products's quality is more and more intense. Statistical process control is an effective approach for improving product quality and saving production costs, and control chart is considered as an important tool of statistical process control. Thus, achievements of the application and research of control chart are richful increasely. Traditional control chart is static in the sense three design parameters (sampling interval h, sample size n, control limit coefficient k) of control chart are fixed for the duration of operation. Recently developed control chart is adaptive, which at least one of the three parameters is allowed to change in real time based on the actual state of operation. This adaptive design can make the control chart detect the process assignable shift quickly. But in the operation of the adaptive control chart, the selection of the design parameters of the next sample is only based the information of current sample. It can cause large number of switches among different parameters, which results in inconvenient operation of the chart. In order to overcome this shortcoming, the switching rule is proposed in the design of control chart. The adaptive X control chart with application of the switching rule is the research object of this dissertation. The deep and systematic research, improvenment and extention about theory and methods of the switching rule are carried out in the aim of improving the performance of adaptive control charts.The main works and contributions are summarized as follows:(1) Design of the traditional adaptive X control chartThe adaptive X chart is modeled, and the expressions for the performance indexes are derived by using a Markov chain approach in the basis of summarized performance indexes for measuring the adaptive X charts. The performance index ANSW is added to measure the number of switches. At the same time, the cost about the switch is considered in designing economic model. Based the classic example, comparisons of statistical and economical performances of adaptive X control charts are presented, and the results show the propertity of each kind of adaptive X control charts. Further, with the application of experiment design and genetic algorithm, effects of cost and time parameters on the selection of optimal design parameters for adaptive X control charts are studied. The results show that the economical performances of adaptive X control charts are also better than the standard Shewhart X control charts with increasing the cost about switches. At the same time, the main factors of affecting adaptive X control chart's cost per time are the cost about parameter's switches and sampling cost.(2) Design of the adaptive X control chart with B&L switching ruleWith application of B&L switching rule in design of the adaptive X control chart, the shortcoming of switching frequently is overcomed, and it make the control chart use easily. First, the adaptive X control chart with B&L switching rule is proposed and analysis using a Markov chain model of three states. The first probability and transition probability are derived. Based on comparasion analysis methods, effects of various switching parameters of B&L switching rule are showed. The results show that with the application of B&L switching rule, ability of detecting assignable cause is increase and cost per time is decrease for adaptive X control chart.(3) Design of the adaptive X control chart with A&L switching ruleCompared with B&L switching rule which is a tight control scheme, A&L switching rule is a relax control scheme that also can decrease switching numbers. In the literatures, the Markov chain method is not used in the study of A&L switching rule, so it is not easily applied to the design of another control charts. And there are some unreasonable places in deriving the performance indexes of A&L switching rule. In order to solve these questions, a Markov chain model of three states is used to build the state space of an adaptive X control chart with A&L switching rule. The expressions of first probability and transition probability are derived. From statistical design and economical design viewpoint, we analyze the effect of various switching parameter on the performances of adaptive X control chart with A&L switching rule. The results show that saving costs focus on two sides:cost of detecting assignable cause and cost of parameter switch for adaptive X control chart with A&L switching rule.(4) Design of the adaptive X control chart with M&N switching ruleBased the properties of A&L switching rule and B&L switching rule, a new switching, denoted by M&L switching rule, is proposed. An advantage of the M&N switching rule is that is a simplified relax control scheme compared with A&L switching rule. We bulid the state space of the adaptive X control chart with M&N switching rule by a Markov chain method. A similar investigation is made to analyze effect of various vaules M, N on the performances of adaptive X control chart with M&N switching rule. The results show that with application of M&N switching rule, the speed of detecting assignable cause is faster, but the economical performance doesn't chang significantly for adative X control chart. (5) Design of the adaptive X and R control charts with switching ruleNo matter the types of control charts, it is a problem that frequent changes in the valueds of the control chart parameters in the application of adaptive control scheme. So B&L switching rule and M&N switching rule are extended to the operation of the adaptive X and R control charts. The performances of the adaptive X and R control charts with switching rule are also analyzed.(6) ApplicationBy using the model of the proposed adaptive X control charts with switching rule, the actual control problem is studied. Comparaed the performance of the VSI X control charts with three switching rules, the optimal control shceme and design parameters are gived by using genetic algorithm aiming at more effective contol. It can instructe the actual application of switching rules.