Availability simulation model of complex electromechanical systems with the consideration of testability parameters

2.1. Overview of the corrective maintenance process

The corrective maintenance process can be divided into FD (fault detection), FI (fault isolation), and maintenance in sequence, which can be further described in specified details for different fault types. The detailed CM processes for different types of faults are depicted in the following steps:

Step 1: The fault signal is usually produced during the fault detection process. Fault detection is usually executed by BITE (built in test equipment) or expert with enough experience (which we call “artificial” method). However, the alarmed fault detected by BITE sometimes may be false, and this kind of fault is so-called “false-alarm”. So there are two kinds of fault called “false-alarm” and “true-alarm”.

Step 2: If the fault is true, this fault may be detected by BITE or artificial. If the fault is detected by BITE, it will be sent for BITE isolations, otherwise the system will go through artificial isolation process to locate this fault to one component; if the fault is a false-alarm, then it will go through the same steps as true faults, but the false-alarm will be found when performing the maintenance for “faulty component”.

Step 3: If the fault is detected by BITE, the system with fault signal will go through the fault isolation process to isolate this fault to one specified component. In ideal condition, the fault component can be obtained afterward. However, under some certain circumstances, only a fuzzy group in which the faulty component exists can be obtained. If the fault is isolated to a single component, faulty component will be replaced by a new one; otherwise, which component is faulty should be firstly checked out according to the following methods: considering the possibility of component failures, the failure-prone component should be detached and checked before the more reliable units. This helps to find fault more rapidly and decreases the number of unnecessary test operations.

From the detailed CM process above, we select three parameters to describe the numerical relationship of different kinds of faults. They are false alarm rate (FAR), fault detection rate (FDR) and fault isolation rate (FIR). FAR expresses the relationship of the false-alarms and the alarmed faults. FDR expresses the relationship of the detected faults and the true-faults. FIR expresses the relationship of the faults can be isolated to fuzzy group with ambiguity and the detected faults. Relationship of these three parameters determines the fault types, and obviously, CM processes for different fault types will be further influenced by the testability parameters. Relationships of fault types determined by testability parameters and CM processes were shown in Fig. 1.

Fig. 1Relationship of fault types determined by testability parameters and CM process

2.2. Stochastic maintenance functional block diagram

The relationships of complex maintenance tasks not only consist of logic sequence but also hierarchical structure. If one of many succeeding tasks is chosen to be accomplished after one function, the task will be determined by the certain extent of the function result. When the simulation is conducted on the basis of stochastic MFBD, the extent should be quantified to facilitate the determination of succeeding task. In order to solve this problem, the extent of function result is related to system design parameters and some testability parameters. These design parameters are then injected into stochastic MFBD to express randomness.

2.3. Math models

In this part, we purpose math models to describe CM. According to step 1 in section 2.1, the fault alarm may come either from BITE or artificial methods, then the probability of the above event can be calculated in fault detection model.

A binary variable $X$ is used to express whether the alarm is detected by BITE or artificial methods. The variable $X$ is equal to 1 if the method is BITE. Otherwise $X$ is 0.

The probability density function of $X$ can be calculated by the number relationship of different kinds of faults. The value of $p(X=i)$ is determined by ratios of corresponding alarm numbers to the sum of fault alarms. The calculation methods are shown in Eqs. (1), (2):

To convert the fault number relationships to testability parameters, we get the last form of equations as above. Eqs. (3), (4) converts the fault number relationships to testability parameters:

Taking Eq. (1) and Eq. (4) into consideration can be calculated by Eq. (5):

The integrated function of x can be expressed as follows:

Another five math models, false-alarm model, fault isolation and replace model and so on are presented in the same way as fault detection model.

2.4. Simulation models

Combining with Step 3 and Math Model, the stochastic MFBD expressing the fault isolation and replacement process can be constructed as shown in Fig. 2. Stochastic selection criteria for activities can be obtained from the method previous. The simulation models of fault detection and fault alarm are similar to this model and are omitted.

Fig. 2Fault isolation maintenance functional diagram block

Fig. 3Main procedure of simulation and structure of simulation software

3.1. Software structure

The software is composed of three subsystems, user system, data communication interface and simulation system. Users input parameters and get the simulation results by user subsystem which also shows some related information. Simulation subsystem is responsible for main process of simulation. The main procedure of simulation and structure of this simulation software is shown in Fig. 3.

3.2. Process interaction algorithm

Maintenance systems have a well-defined process, which can be captured using a discrete event simulation (DES) model. The equipment and components are modeled as simulation objects with characteristics such as a descriptive name, the time in operation, and a flag indicating whether a part is broken or not. PI is designed to describe the entity behavior without the need to establish the relationships of large amounts of events, characteristics of maintenance process that aim at describe entity-equipment behavior in its lifecycle. This simulation algorithm involves mission process, mission preparation process, mission turnaround process, CM process and resource process. Therefore, PI was selected as the simulation strategy.