Application of two linear methods for fault detection

Since 1960 and with the advent of cheap and high-speed microcontrollers the growth of automation began in industry. The unavoidable consequence of this issue was the application of automatic supervision and monitoring in all critical systems. This brief preface would persuade us to consider the fault detection and fault tolerant systems as major and speculative issues in engineering One of the most important in which the methods of fault detection are frequently applied is petrochemical systems where the failure of the systems wastes 10 billion dollars annually in this industry in the United States solely.[1]