Statistical-Economic Design of Control Chart If The Vector of Target Values of Multi-Variables Shifts With Time

Abstract

INTRODUCTION Mao (2019 a) presents a new quality control technique. The optimization adjustment interval of one dimensional quality characteristic are extended to multi-dimensional case in which the vector of the quality characteristics or important financial indices of firms shifts with time due to seasonal changes or cyclical change of economic environment, and also there are time-varying correlated among each other. The statistical-economic design of a multivariate special triangle control chart is proposed to control such kinds of processes. An application is illustrated to monitor the soundness of insurers of U.S. Optimal solutions of control region, power of finding out assignable cause(s), sample size and sample interval are found out. In business process, the process means shift gradually with time. For instance, the means of some performance type financial indices gradually increases or some consumption type financial indices gradually decrease And we must distinguish three different situations. One is that the shift of the means is resulting from the normal growth and development of firms and another is that it is due to the unnormal events happening in firms, such as, the underwriting premium or liabilities suddenly increases in a very short time to very high level and even excesses the normal underwriting capability. Since the quality of underwritten insurance policies is not good, it will cause very big insolvency risk to insurance companies. The third situation is that the process is affected by some causes and the financial indices shift gradually from the targets due to seasonal changes or cyclical change of economic environment. And these changes are unavoidable within an allowable range. The important thing for insurance companies is to use suitable control techniques to dynamically control the means of important financial indices under the target level, find and correct unnormal situations as long as the control chart alarms the signal of out of control. It is obvious different from production process where in any situation that the target means is always a constant even though the quality characteristics change with time due to tool wearing or some other reasons such as material consumption. This is because the engineering specification limit or region is fixed. The control target is to keep the process means at the target value presetting by adjustment the process cyclically. Mandal (1969) (also see Montgomery (2009) ) suggests ABSTRACT In this paper, the statistical-economic design of a multivariate special triangle control chart is proposed to control the processes of the quality characteristics or financial indices shifting with time. A multi-objective programming with several constraints is used to determine optimal solutions of control region (probability of false alarm), the power of finding out assignable cause(s), sample interval and sample size. An application of the statistical-economic design of a Multivariate special triangle control chart is illustrated to control the soundness of insurers of U.S