This work presents a review of the management of accumulated work as an integral and fundamental part of the maintenance function, which is not understood solely and exclusively as work not carried out in its entirety, but also refers to incomplete work or work done to means, that is, the important tasks that we leave for later, for carrying out urgent actions determined or typified thus in a subjective and erroneous way.
In general, the accumulation is due to the lack of follow-up and the improvisation of work due to inadequate planning caused by two main aspects; not working under any type of management methodology for maintenance and not having defined priorities for the work, supported by objective criticality models.
Any anomaly detected in an equipment and / or component that does not deserve to be corrected immediately and that its intervention can be scheduled, is considered as a pending repair activity, called Backlog. Timely generation allows setting correction conditions before failure occurs. It should be noted that as a Backlog remains in the system, without executing the required work, the equipment failure rate increases over time.
The job performs a backlog management review as an integral and fundamental part of the maintenance function. It is shown that Backlogs management should be the sole “capture source” of all detected, deferred and communicated flaws, and the management tool to conduct / guide maintenance routines through the analysis of their indicators and associated costs. A structure methodology of the Backlogs management system is delivered, through the number of states considered in the process and the construction of an associated Markov Model for better understanding. Additionally, it is shown that a critical factor in the management is the prioritization of the jobs, for which a procedure is proposed considering not only the age of the jobs detected,but also the comparison of their costs in order to determine the optimal strategy for the realization of the work requirement.
INTRODUCTION
The accumulation of work is not understood solely and exclusively to work not carried out in its entirety, but also refers to incomplete or half-done work, that is, important tasks that we leave for later, for carrying out determined or typified urgent actions thus in a subjective and erroneous way within companies. In general, the accumulation is due to the lack of follow-up and also to the improvisation of works due to an inadequate planning caused by two main aspects; not working under any type of management methodology for maintenance (TPM, RCM, etc.) and not having defined priorities for the work, supported by objective criticality models.
Any anomaly detected in an equipment and / or component that does not deserve to be corrected immediately and that its intervention can be scheduled, is considered as a pending repair activity, called Backlog. There are numerous definitions of Backlogs, such as: Maintenance work planned waiting to be scheduled, Jobs not completed on due date, among others. A relevant fact is that the definition used in a company is known by the entire organization, to avoid ambiguities and guarantee that a work requirement is authorized by becoming a work order.
The generation of Backlog can be carried out by anyone who detects an anomaly in a computer, and the only requirement that must be fulfilled is to present the background in a format called Backlog Form . Timely generation of Backlogs means evaluating an equipment failure and establishing correction conditions before failure occurs. Backlogs go through various states within the maintenance area, namely: they must be generated and entered into the administration system, validated and / or corrected, completed with the required spare parts, scheduled and executed under a prioritization delivered by the Engineering area Maintenance, as shown in Figure 1.
Figure 1: Accumulated work management process
The objectives set for this work are to carry out a review of the management of accumulated work as an integral and fundamental part of the maintenance function. A classification of the Backlog Management Systems was carried out, in relation to the possible states used by organizations for the management of accumulated work and the possible configurations that are feasible and their relationship with an associated Continuous Markov Chain. From the Markov model, the stationary probabilities were found for the case of a cumulative work management system with 7 states like the one shown in the following Figure 2.
Figure 2: Feasible configuration for 7 states of backlog management
The model used corresponds to a Markov Chain in continuous time, commonly used in the field of Operations Research to describe and predict the behavior of certain systems under conditions of uncertainty over time. The use of these models has been adequate to model population dynamics, waiting systems, inventory control, maintenance and replacement of equipment and in support of decision-making in administration, engineering and medicine, among others.
In general, the techniques currently used to optimize maintenance management are classified into two large groups:
- Methods based on minimization of objective functions from linear and nonlinear programming methods Methods based on Markov Models
A Markov model is a graphical representation consisting of nodes (or states) and arcs (or transitions between states), as represented in Figure 2. The crucial hypothesis in a Markov model is that the system is completely specified by nodes, and that the past history of the system is irrelevant for future transitions. For example; aging can be represented by discretizing the life of the component in separate states and estimating the probabilities of transition between them. Interventions that leave the equipment as new can be represented by a transition to the first discretized state. Gertsbakh (1977) provides a list of maintenance optimization problems solved with Markov models.This type of model provides a simple representation that allows estimating the objective function as a function of the decision variables without having to perform Monte Carlo simulations or multiple integrations on all possible events (finite horizon of analysis).
Finally, it is shown that from the definition of the Markov model carried out by an organization it is possible to determine an inventory equation of the accumulated work, and extract management indicators to measure the efficiency of the maintenance area, and that as the model enriches the quality of the indicators is higher, in relation to the targeting of the problems in the respective areas involved. In addition, an objective criticality prioritization procedure was carried out, incorporating the analysis of the costs of the works and the possible maintenance strategies to follow for the realization of the work requirement.
METHODOLOGY
A bibliographic review and field research was carried out in different companies, mainly mining companies, to observe the way in which they are managing the accumulated work. Based on this information, the Backlogs Administration process was designed at level 2 (for 7 states), using the ISO 9001: 2000 documentation methodology, in order to have a clear knowledge of the tasks, roles and responsibilities that each one of the states.
Using this information, the Continuous Markov Model associated with the accumulated work administration states is built, the possible configurations are studied and a classification is made in relation to the number of states used for management. Applying the theory of Markov chains, some natural questions that arise in this type of model are answered. Computational tests were carried out using the MATLAB application to obtain the long-term transition probabilities in order to observe the consistency of the proposed model.
An analysis of the work prioritization techniques is carried out, in order to propose a reduced management model for the prioritization of accumulated work.
RESULTS AND DISCUSSION
Few tools are as useful for managing the amount of maintenance work and its efficiency as Backlog Management. Of course, in many companies today the administration of Backlogs must be improved, since they are generally drowned in their own data having dramatic effects on the delivery of the maintenance service. Although the situation may seem random and chaotic, there are several common symptoms of mismanagement of Backlogs, such as: duplicate work orders (with effects on reordering materials, parts, and additional planning efforts), non-standardization of texts when entering the backlog format, no indication of resource requirements, poor coding of work orders, spare parts, and tools, among others,little focus on priorities, many non-prioritized work orders, many tasks not saved in the backlog system, and jobs not required.
The objective of backlog management is: To be a key contribution to Maintenance and Repair tasks by proactively directing work toward repairs before failure to match Maintenance performance goals.
In general, scheduled and unscheduled shutdowns should be used to inspect equipment (window of opportunity), detect anomalies, and generate Backlogs. Operators, technicians and inspectors should be the main generators of Backlogs. The Planning and Scheduling area must intensively use the windows of opportunities to schedule the execution of the Backlogs, and maintain exhaustive control of their status.
There are organizations that use Backlog management with three, four and more states. Table 1 shows the possible configurations that are generally presented in companies for Backlog Management. Which have their advantages and disadvantages in relation to the number of tasks, roles and responsibilities that each state contains.
Table 1: Possible settings for backlog management
| 3 States | 4 States | 5 States | 6 States | 7 States |
| Generation
Wait Spare Parts Wait Execution |
Generation
Wait Spare Parts Wait Execution Elimination / Execution |
Generation
Approval Wait Spare Parts Wait Execution Elimination / Execution |
Generation
Approval Wait Spare Parts Wait Execution Execution Elimination |
Generation
Fingering Approval Wait Spare Parts Wait Execution Execution Elimination |
Note that in the classification of 4 and 5 states, we have considered the Elimination / Execution State, hinting that there are organizations that consider only the Execution state and not the Elimination state, leaving these backlogs historically in the database of the teams, I have inversely, the Elimination State over the Execution State.
In general, the inventory of accumulated work for these configurations can be obtained with the expression:
P t = P t −1 + G t - EJ t - E t t = 1, K, n (1)
where: P t = Number of pending Backlogs, G t = Number of Backlogs generated, EJ t = Number of Backlogs executed, E t = Number of Backlogs eliminated, in period t. With this expression (recursive), assuming P 0 = 0, we can calculate general indicators, such as: Total Pending, Generated, Executed and Eliminated Backlogs by period, equipment, system, components, etc. It should be noted (assuming a 7-state configuration) that the pending Backlogs from the previous period entered into the administration system are randomly distributed in the states of Typing (d t), Approval (a t), Waiting for Spare Parts (ert) and Awaiting Execution (ee t). So we can write:
P t = d t + a t + er t + ee t t = 1,2,3, K (2)
From (2) it is possible to determine other important management indicators such as: the level of service of the typing area, the number of hours - men needed to carry out the total accumulated work, the hours - required machines that have their immediate effect in availability, the level of winery service, among others. Note that if fewer states are considered, equation 2 is reduced, obtaining less reliable and / or focused indicators. With this we can build reports like those in Figure 3, to have a better appreciation of the management of accumulated work.
Figure 3: Generic Backlog Management Reports
On the other hand, to answer other natural questions that arise from Backlog management, we introduce the concept of the Markov Chain. The state of the system at time t is denoted by X (t), and we are interested in estimating the probability that the system is in a specific state at time t. The crucial hypothesis we are using is that the system is completely specified by the states (nodes), and that the past history of the system is irrelevant to future transitions. Considering Table 1, we see that there are several configurations for the Markov Chain associated with the model that have an effect on the way of managing the accumulated work, and that in turn there are several feasible cases in each of these configurations to be implemented or used by organizations,An example of this will be presented in the case study later.
A fundamental element is to have a prioritization criterion for the analysis of Backlogs, which helps reduce the levels of backlog of work. Said prioritization of accumulated activities is usually done under a criterion of age or aging of the required service, or using a risk matrix, or a decision number constructed with some variables of risk, consequence, probability of failure and time, among others. All these forms of prioritization are not associated with a maintenance strategy. A procedure for making decisions in the administration of accumulated work is presented below, Figure 4:
Figure 4: Backlog prioritization procedure
CASE STUDY
As an example of the above, consider the configuration for 5 states given in Table 1, then we can have the following cases or feasible situations presented in the following Figure 5.
Figure 5: Feasible configurations for 5 states
In this case, the approval status of the generated Backlogs shown in Table 1 is incorporated. Once the Backlogs are generated, they are immediately entered into the administration system by the generators (either manually, by electronic OT device or data entry operators not identified by the current configuration). In cases 1 to 3 we see that the Backlogs are technically rectified (generally by Team Analysts), when a Backlogs is not approved it is immediately eliminated, but in cases 4 and 6 the alternative is given that when there are doubts about the anomaly detected or there is a lack of information to give a verdict, these can be returned to the Generator to complete the missing information. Now if the Backlogs are approved and they do not require spare parts, they are sent directly to the Waiting for Execution state,otherwise they will go to the Waiting State for Spare Parts. Note that in cases 2, 3, 4, 5 and 6 there is an alternative that those Backlogs that are complete and awaiting execution, the spare parts are occupied by other jobs, which forces the Backlogs to return to the Waiting Spare state, and being in this state they can also go to Eliminated if the equipment fails or the Backlogs is absorbed by a major work such as a component change, or preventive maintenance, the same situation occurs for those Backlogs awaiting execution. In cases 5 and 6, the alternative is given that those who are entering the Backlogs to the system can immediately delete them if they are duplicated (the anomaly had already been detected and reported).We see that case 6 is the most general situation that occurs when considering 5 states for Backolgs Administration.
On the other hand, for the case of 7 states like the one shown in Figure 2, suppose that the residence time in the different states are exponentially distributed with mean 1 / µ i i = 1,2, K, 7, and that with probability α i goes to the next state or is eliminated. The following transition probabilities are obtained:
The value of π 1, written in simplified form, is given by:
where the values of A i correspond to the components that accompany the values of the probabilities π i, i = 2,3,4,5,6,7, in the above equations. Using the MATLAB application, simulations can be performed to obtain these transition probabilities in the long term in order to observe the consistency of the proposed model.
CONCLUSIONS
The customer's assessment of the management of the maintenance area is strongly based on the work that is pending (Backlogs). We can say that a very high percentage of the success of maintenance management is based on good Backlogs management. That is why the analysis of the Backlog management indicators is crucial for the success of the maintenance area management. And the richness of the indicators in this area depends on the number of states considered for management, which are graphed in the inventory equations that can be constructed.
It is observed that each feasible configuration for the management of accumulated work can be represented by a Markov Chain, with different properties, classes and types of states. A common occurrence is the presence of one or two absorbing states (Elimination and Execution). In this case, we can write the transition matrix in the form: P = é ë Q 0 R I ù then in the long
We obtain term: lim n → ∞ P n = é 0 0 (I - Q I ) -1 R ù û. This means that once the
Stationary situation, the fixed point vector will be canonical, equal to the limit distribution and independent of the starting point, topos the non-absorbent states of the chain will be absorbed by the absorbent state. That is, all the states will be empty except the absorbing state that will monopolize the entire population, or what is the same, will have probability one. With this methodology we can answer the following questions: (1) what is the expected number of times that each state is entered? (2) how many periods (average time) is expected to pass in a certain transitory state before absorption to take place? (the average time that we will spend in a transitory state are given by the ij-th elements of the submatrix (I - Q) −1), (3) what is the probability that we end up in each absorbing state? (The absorption probabilities are given by the ij-th elements of the submatrix (I - Q) −1 R). Several computation runs were carried out in MATLAB making changes in the conditions of the starting transition matrix, obtaining the mentioned results.
A procedure is provided for the prioritization of accumulated work, which is a fundamental element that incorporates an initial prioritization based on some criteria of age or aging of the required service, or using a risk matrix (Pareto), etc., but incorporating a second criterion that is fundamental, the observation of the costs of the works, to determine the execution strategy of the requested work, this because it is not about executing jobs to be executed, but about optimizing the maintenance service.
From the analysis of Backlog management, multiple opportunities, improvements, redirections, optimization of maintenance management, among others, can be extracted, which allows us to affirm that Maintenance Management depends to a high degree on Backlog Management and in a sense a little broader are synonymous.
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