## 1 Introduction  
Cyber-physical systems (CPS) are a paradigm which emphasizes interaction and interoperability between microscopic components of a real physical system and a cyber system. The CPS technology, which is capable of modeling the complex systems, is particularly well-suited for safety-critical applications or mission-critical applications such as electric power generation, transmission and distribution grids, and transportation systems. Many studies on the CPS field are being undertaken to fully meet non-functional requirements such as safety, security, and dependability. The key to avoid catastrophic consequences and provide safety for such systems lies in achieving a high level of dependability. In order to support the intended functionality even in the presence of the faults in the physical system, CPS should be designed with fault tolerant control, of which the core process is fault diagnosis. A fault, which can make CPS fall into an abnormal state, may naturally occur and leads to failures or errors that eventually prevent continuing intended operations. Faults may be caused by many factors such as environment uncertainty and defective components. To maintain safe control, they should be detected explicitly or implicitly in fault diagnosis before performing fault recovery. Permanent faults from defective components are very dangerous because they cause fatal consequences during operation of CPS. If we examine a set of specific conditions that appear explicitly, it is relatively easy to detect these faults rather than detect transient faults. In contrast, it is not easy to detect transient faults because they appear stealthily and may not affect the safety of CPS immediately. One transient fault does not greatly affect the safety of automotive CPS at the moment but continuous or intermittent faults might result in changing the state of the physical system gradually. In this work, they are considered critical faults. However, it is difficult or impossible to identify when transient faults affect the physical system and how much the cumulative number of transient faults influence the physical system [1]. Transient fault detection is more of a challenge due to those characteristics. There are a few studies on transient fault detection in which they focus on the interaction and consistency of the multiple inputs (i.e., multiple sensors) for the same physical variable. The method using the interaction of variables has a fatal drawback that it does not work in the presence of a majority of faults [2]. A cost-effective and space-saving way to detect these faults is to adopt an analytical redundancy approach, which takes advantage of a mathematical model mimicking the targeted physical system, and is referred to as a model-based approach. A basic idea of this approach is to check consistency. The consistency checking is achieved by monitoring the difference between the real measured variable of the physical system and the estimated variable derived from the model-equation-based computations. The monitored difference, called residual, is treated as a fault indicator. Performance of this approach depends on how well the targeted system is modeled by capturing the physical system and how elaborated a given threshold used to monitor its consistency is. The model-based fault diagnosis commonly  
To provide enhanced dependability for model-based fault detection and safety for CPS, it is necessary to develop a new threshold generation method that should be adaptive to the operation of the physical system, the uncertainties, and the time-varying data. For the threshold generation, rather than catching the difficulties inherent in obtained data or designing the elaborate state-observer, we solve the problems with an intuitive and simple way that is to treat the obtained data as the normal data with the acceptable uncertainty if we can be sure that data with any uncertainty does not adversely affect the operation of the system.