Availability model based on task and risk model based on safety for condition based maintenance

2.1. Availability model based on task

In some cases, we can not only consider component economic efficiency, but also pay more attention to the task indicators. For example, we are more focused on availability and reliability of the aircraft, artillery and firearms in the battlefield, rather than how to reduce the cost. The economic factors will be considered only on the premise of ensuring availability. Then, the availability model based on task is needed to be established.

In an update cycle, the working time is consisted of as follows:

where $T_i$ is optimal maintenance interval and $t_i$ is the $i$th monitoring time of system.

The time definition for a maintenance cycle is shown as follows:

where $T_p$ is an average maintenance interval and $T_f$ is average time for corrective maintenance.

The availability model is obtained as follows:

2.2. Risk model based on safety

In practice, the safety of the component is the most important. The purpose of maintenance decision-making is to realize accurate, timely and effective maintenance with decreasing maintenance costs at the same time. However, it does not mean that safety can be ignored. Once the safety problems occur, it may threaten the life safety of operating personnel or cause serious los. As a result, risk model based on safety need to be considered firstly.

The reliability or failure probability can be selected as the objective function in risk model based on safety. The optimal maintenance interval is determined through lower the fault probability of component to a pre-determined level. Assuming that component risk $\alpha$, the failure rate cannot be higher than the risk $\alpha$ in every monitoring process. Therefore, the probability of component not failure is:

It can be described via the remaining useful life:

The maintenance interval of risk model based on safety can be obtained by Eq. (5) when the remaining useful life has been known.

The maintenance decision-making usually takes reliability or risk rate as the objective function under the security requirement. So, the failure probability reduced to an acceptable level is used to determine the optimal maintenance interval.

3.1. The introduction of experiment

In the experiment, the gear box was driven by a electromotor, and a load was added to simulate the real working state of the gearbox. The gearbox is shown in Fig. 1, and test results are shown in Table 1.

Fig. 1The experiment of gearbox

3.2. The results analysis

In the experiment, we assume that $T_p=$ 5 hours, $T_f=$ 15 hours and the risk is $\alpha =$ 0.05. The results of availability model based on task is shown in Fig. 2.

Fig. 2The results of availability model based on task

The results of availability model based on task is shown in Table 2, which we can determine the maintenance interval. When maintenance interval that determined by availability model is earlier than RUL, the decision for system is obtained via availability model. On the other hand, when maintenance interval that determined by availability model is later than RUL, maintenance decision-making is obtained based on RUL. As we can see from Table 2, maintenance interval is earlier than RUL at all time, so optimal maintenance interval for maintenance decision is all based on availability model.

In the risk model based on safety, we assume that risk $\alpha =$0.05. Then, the result of maintenance decision-making based on risk model can be obtained which is shown in Fig. 3. As we can see from the figure, the safety index is higher with the decrease of the maintenance interval, which is consistent with our subjective experience. When $1-\alpha >$ 0.95 is satisfied, we will get the most optimal maintenance interval.

Fig. 3The results of risk model based on safety

The results of risk model based on safety is shown in Table 3, which we can determine the maintenance interval. As we can see, the results based on risk model is earlier than the RUL of the gearbox, so it is necessary to propose maintenance decision based on risk model.