**4. Maintenance solution framework**

The optimized maintenance scheduling framework is recommended to be built using ant colony optimization model using structured content found in a typical maintenance ecosystem.

The first step is to predict the failure based on survival analysis, with certain confidence level before its occurrence. The next step is to combine the predictive maintenance and preventative maintenance schedule using optimization model. This optimization model determines which equipment should be assigned to which day in the maintenance workshop bay for minimizing waiting time, maximizing production and ultimately increase the availability.

In the solution framework, two types of maintenance activities are considered: first preventive maintenance which is based on the recommendation of OEM. The second maintenance is predictive maintenance which is based on probabilistic failure. The next section will cover the derivation of predictive maintenance schedule.

### **4.1 Predictive maintenance schedule**

The predictive maintenance schedule is derived from Cox regression model which gives survival probability distribution function. The Cox regression model is shown in below

*The Application of Ant Colony Optimization*

$$H(t) = H\_0(t) \exp\left(\beta \mathbf{1} Y \mathbf{1} + \beta \mathbf{2} Y \mathbf{2} + \cdots + \beta n Y n\right) \tag{3}$$

Where the expected hazard is *H*(*t*) at time *t*, the baseline hazard is *H*0(*t*) and it represents the hazard when all of the independent variables) *Y*1,*Y*2,...*Yn* when they are equal to zero. Based on the collected data the model estimates *β*1,*β*2,...*βn*.

The expected hazard function increases as the days progress. This function is converted to survival days and remaining useful life (RUL). RUL is defined as the duration left for the occurrence of breakdown based on the probability threshold of failure i.e. how many days when the cumulative probability falls below 60%. The RUL has been extensively used in calculating the reliability-based research in the mine system to derive the occurrence of the failure, so the appropriate action can be taken proactively

This survival data (predictive failure day) is used in combination with the preventive maintenance, production schedule and other constraints to optimizing the maintenance schedule.

### **4.2 Optimization of maintenance schedule**

The optimization of maintenance schedule requires to determine the optimal maintenance day for each truck in a time horizon so that the maintenance time, production loss is minimised while meeting the preventative maintenance schedule requirements and minimizing the probability of failure (predictive maintenance – survival days). In the above sections we discussed on the application of ACO in the context of SMTWTP.

In order to formulate the problem using SMTWTP, it is assumed that there is one workshop and it has one bay for carrying out maintenance activities (single machine). One truck is represented as one job and a fleet has n trucks which need to be scheduled for maintenance. Based on historical analysis, the time for each job i.e. time for carrying out maintenance activities is available (processing time *p*<sup>j</sup> ). The due date (*dj*) of processing is provided by the preventive maintenance schedule for each job (truck). The completion time of job *j* is defined as *Cj*. The earliness of job is defined as *Ej*, if the job is completed early and the tardiness of job is defined as *Tj*, if the job is completed late. The probability of failure (*fj*) at *Cj* is provided by the predictive maintenance schedule (RUL). The cost functions (*w*) for earliness and lateness take the probability of failure (*fj*) into consideration.

*An Innovative Maintenance Scheduling Framework for Preventive, Predictive Maintenance… DOI: http://dx.doi.org/10.5772/intechopen.103094*

The objective is to find the truck fleet maintenance scheduling sequence that minimizes the function as below.

$$|\mathbf{1}|d\_j|\sum\_{-j}w\_jE\_j+\bar{w}\_jT\_j\tag{4}$$

where

*d <sup>j</sup>* – due date of job (preventative maintenance scheduled day for truck) *w*\_ *j* – unit cost of earliness i.e. cost of maintenance too early based

*E <sup>j</sup>* = max{0,*d*<sup>j</sup> �*C*<sup>j</sup> }; earliness of job

*T <sup>j</sup>* = max{0,*Cj*�*dj*}; tardiness of job

*w <sup>j</sup>* – unit cost of tardiness i.e. cost of lost production if failure before maintenance (*f*j)

*N* = {1,...,*n*}; *n* trucks (jobs) have to be sequentially processed (1 job = 1 truck maintenance activities) at workshop (1 bay)

This function can be modelled to minimizes the total weighted earliness tardiness (*z*) as below

$$z = \min \sum\_{j \in N} w\_j E\_j + \bar{w}\_j T\_j \tag{5}$$

Mainly there are three key requirements of the ACO algorithm.


Applying the ACO algorithm, in the initialization step, a colony A of m ants is generated, where each ant corresponds to a random feasible solution. The next is the iterative step where the acquired knowledge (pheromone level) is fetched and job assignment attractiveness is calculated. Next the ant generations are merged and only the best ants are retained for the optimal solution. Lastly pheromone evaporation and deposit are updated and the process continues till the maximum number of Generations are reached.

```
ACO pseudo code
Input parameters
• N, is a set of n trucks (jobs that need to be processed in workshop)
• C, the number of colonies
• n, the number of ants in the colony (i.e. size)
Output solution
```
At the end of step 2.3 to further enhance quality of the solution i.e. the retained n ants and speed up the convergence towards near optimal solution, a local search criteria can be applied. Hybrid approaches with local search criterial include beam search [20], scatter search, tabu search [27], threshold accepting [28], and neighbourhood search [29]. These search criteria help to efficiently guide the ants movements towards global optima. In the paper by M'Hallah and Alhajraf [30] ant colony systems for the single-machine total weighted earliness tardiness scheduling problem, they provide empirical evidence of using variable neighbourhood search (VNS) to improve the overall quality of the retained ants and converge towards a near global optimum.

By applying ACO to SMTWTP, the total cost for early or late maintenance is reduced by optimally assigning the truck to the workshop for maintenance activities based on the preventive maintenance schedule and predicted maintenance (RUL).
