### Reliability considerations for mechatronic systems on the basis of astate model

*Talal Arnaout*

*, Peter Göhner*

*, Hans-Joachim Wunderlich*

*and Eduard Zimmer*

#### Abstract

the reliability related technical peculiarities from each discipline, and unify them in a way suitable for mechatronics as a whole. As we are dealing with the reliability of mechatronic systems, we ought to find initially a definition that could be representative for all the functional subsystems. Searching the literature, we could realize a set of relevant definitions, which could be stated as follows: - Reliability is the ability of an item to work properly [Bi04]. - Reliability is the probability that the system produces correct output [VP93]. - Reliability is the probability of non-failure of an item for a given period of time, and for certain operational and environmental conditions [Bi04, VDA00]. - Reliability is probability that an item performs a required function under stated conditions for a stated period of time [Bi04, Bi86, DIN95]. - Reliability is the probability of survival against failures or malfunctions, which mask out one or more functions, or limit them in unspecified\&Error: Mismatch between font type and embedded font file Error: Mismatch between font type and embedded font file nbsp;ways [VDI86]. The tenor of these different definitions is the same, as they refer to the time-dependent probability that a unit remains functional. However, we have adopted the last definition as our standard definition, due to the following: First, the definition relates the reliability 107 to the survivability of a function, which in turn governs the operability of an item to execute a specified task. Second, it expresses the effect of a malfunction, whether permanent or temporary, on the whole system and on other functions. And third, since functionality is a common concept between the three disciplines, this definition could serve as a basis for mechatronic systems. Based on this definition, we have developed a model that could represent the nonfunctionality of a mechatronic system. For this model, we had the following points in mind: - The impairment of a certain function should be considered, rather than the failure of a complete unit. This considers transient errors, which are common in electronics. - A distinction is to be looked upon between dormant and active faults. Here software has been borne in mind, since dormant errors, i.e. bugs, can be present, and only under certain circumstances these errors result in a failure. - The complexity of mechatronic systems is to be broken down by extracting the basic fundamental functions of the different units. This helps in contemplating the failure behavior per function and assessing the consequential influence of such a failure on other functions. Accordingly, a functional orientation is very suitable to analyze the operability. Looking into these three points, we can deduce that a function could exist in any of three states, depending on whether a failure has occurred or not: fault free (state 0), faulty (state 1), and failure (state 2). In most cases, the system is presumed to have state 0 as an entry state to the model. In the following section, we will detail how we realized our model, which is depicted in figure 1. However, first we need to define the used terms. According to [Av97, La92, Pr96] failure, error and fault could be defined as follows: - Failure: A failure is the inability of a function to deliver an output according to the specifications. - Error: The error is the noticeable deviation or discrepancy in the output of the function from the specification. - Fault: The fault is the flaw or defect that occurred to the function, causing the error at the output. It could be classified as dormant or active, and temporary or permanent. 3 Model Realization In order to come up with a representative model that describes the behavior of failures in mechatronic systems, we focused our analysis on some particular cases and observed their respective failure behavior. It is easier to visualize the problem through an example, whose failure behavior is depicted in figure 1. We consider a CNC (computer numerical control) lathe machine, starting our analysis with the mechanical subsystem. The 108 subsystem is initially fault-free, hence in state 0. Assume a shaft, which is currently not in use, breaks. Thus, the subsystem has acquired a fault in one of its parts, which when accessed will deliver an erroneous behavior. Hence the system moves to state 1. No Call No Fault Function Fault 0

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