Selection of Welding Process for Repairing Shredder Hammer by Integrated Data Envelopment Analysis (DEA) and P-robust Technique

The Selection of the welding process is one of the most significant decision-making problems, and it involves a wide range of information following the type of product. Hence, the automation of knowledge through a knowledge-based system will significantly enhance the decision-making process and simplify for identifying the most appropriate welding processes. The aims of this paper for explicates a knowledge-based system developed for recognising the most suitable welding processes for repairing shredder hammer by using data envelopment analysis (DEA) and p-robust technique. The proposed approach is used for ranking six welding processes which are commonly used, namely shielded metal arc welding (SMAW), flux cored arc welding (FCAW), submerged arc welding (SAW), oxyacetylene gas welding (OAW), gas tungsten arc welding (GTAW), and gas metal arc welding (GMAW). In order to determine the best welding process among competitive welding processes for repairing of shredder hammer, ten parameters are used, namely the availability of consumable, welding process type (manual and automatic), flexibility of welding position, weld-ability on base metal, initial preparation required, welding procedures, post-weld cleaning, capital cost, operating factor, and deposition rate. Furthermore, the sensitivity analysis of regret value (p) is investigated in three cases proposed.


Introduction
Thailand is the fourth-largest sugar producer and the second largest sugar exporter in the world [1]. In the sugar industry, the shredder hammer is used to shred sugarcane billets and pulverise sugarcane billet into a fibrous mat [2]. Generally, the shredder machine has 90-250 of shredder hammers that rotate on a rotor at around 1000 RPM, and it can process sugarcane at 7,000-15,000 tonnes/day [3]. The shredder machine is essential for the sugar industry, but the cost that involved in the operation of shredder machine is expensive because the service life of shredder hammer is relatively short.
The shredder hammer needs to be checked for balance to prevent something that can damage the machine. The vibration monitoring system is the system for check balance of shredder hammer, if the shredder hammer broken during operation, this machine has to stop. The shredder hammer consists of carbon steel as the base metal, and hard-facing is stacked on the base metal using welding process. The hard-facing is a form surfacing that is applied to reduce wear, abrasion, impact, erosion, galling, and cavitation [4].
Typically, the selection of welding process depends on experiences or follows the general application in the similar companies. However, this strategy often ignores many criteria or parameters that can be affecting the suitable welding process selection. Therefore, knowledge management is a critical element for a better decision. The knowledge from an expert will significantly benefit if using the advanced method for analysis it.
A little of research has been done about welding process selection, but none of them deals with selecting welding process use hard-facing for repairing shredder hammer. Darwish [5] studied about welding process selection used confidence level for each qualifier. Ravisankar [6] used analytic hierarchic process (AHP) as a method for welding process selection of high strength aluminium alloys to fabricate butt joint. Jafarin and Vahdat [7] Studied about the selection of welding process selection used AHP at high-pressure vessel manufacturing. Balasubramanian [8] used AHP for welding process selection of hard-facing on carbon steel. As is seen, The AHP method is a popular method for welding process selection, but the issue of AHP is the weight of criteria by a judgment of decision maker. It means if the judgment is changed, the final ranking will change as well. So the limitation of AHP depends on the decision maker's judgment.
This paper aims to propose welding process selection for repairing shredder hammer by integrated data envelopment analysis (DEA) and p-robust technique to support a decision of welder, manufacturing, and supplier. Data envelopment analysis (DEA) was introduced by Charnes [9] to obtain the efficiency score of decision-making units (DMUs) by comparing how creatively this DMU transform inputs into outputs. Moreover, DEA does not need a decision maker to set the weight to the inputs and the outputs. Due to in this paper uses group decision-making and the information of experts is valuable, integrated DEA and p-robust are used to consider all the opinion of expert without losing any information.

Determination of the experts
An expert is someone that has extra weight because of their qualifications, experience and other signal authority [10]. Due to decision-making is involving a wide range of information, five opinion of the expert from academia (theory) and five opinion of the expert from welder (practice) will be used. Furthermore, the experts should have enough knowledge about welding process, procedures for repairing shredder hammer and all of the parameters that be used for welding process selection in this research.
Due to use many experts opinion for making decisions, this is very potential to happen dissent of experts. Although expert opinions differ from each other, the final decision must be robust in the uncertain situation. Therefore, data envelopment analysis (DEA) and p-robust technique are applied to deal with this problem.

Data envelopment analysis (DEA)
CCR (Charnes-Cooper-Rhodes) model is the most common DEA models. Suppose there are h DMUs, each of DMUs have n inputs ℎ (i = 1,...,n) and m output ℎ (r = 1,...,m). The efficiency of DMU is the division of the weighted sum of outputs (virtual output) by the weighted sum inputs (virtual input). Supposed DMU has efficiency score equals 1 (E h = 1), it means the DMU is efficient; otherwise, it is inefficient. The following model is referred to as input-oriented DEA model: Subject to: The notations are representing in Table 1.
DEA can be used as a tool for making decisionmaking process because of some advantage of this method as mention in the previous research [11,12]. The main problem with this method when we use group decision making is model (1) only to achieve the ideal efficiency scores based on each expert's opinion separately. If we want to get the average score, it needs to run the model (1) several times and then get aggregate the final score. The aggregate result should satisfy against the overlapping opinion of the expert, which is known as "ambiguity". In this situation, it is necessary to Table 1. List of notation in the proposed model.

P-robust technique
Make the final decision End Table 3. Description of criteria for evaluating the welding process.

No
Criteria Description 1 weld-ability on base metal Weld bead appearance, porosity, lack of penetration, etc. 2 Initial preparation required Setting welding parameter (voltage, current, welding speed, gas flow rate, and wire feed, etc.), electrode or filler metal preparation, cleaning the base metal. 3 Welding procedures Preheating requirement, number of passes required, interpass temperature maintenance and post-heating requirement. 4 Post-weld cleaning Slag removal, spatter removal and gridding the weld reinforcement. 5 Capital cost New equipment cost. 6 Operation factor Welder skill's need. 7 Availability of consumables Electrodes, filler wires, fluxes, shielding gas, etc. 8 Welding process type The capability welding for manual (case 1) or fully automatic (case 2 and 3). 9 Flexibility of welding position Flat, horizontal and incline. 10 Deposition rate Penetration in crack, and repair rate (pieces/hours).
have the p-robust technique to overcome these problems. The integrated DEA and p-robust technique can analyse different opinion of experts all at once and also satisfy the ambiguity.

DEA and p-robust technique
Integrated DEA and p-robust technique are introduced by Fasanghari [13]. In this paper, the efficiency score of DMUh for each expert is an independent scenario. Suppose that we have a = 1,2...,A set of scenarios, and ℎ * is the ideal efficiency of hth DMUs in ath scenarios associated with ath expert. In order to resolve ambiguity in the group decision making, the efficiency score will be controlled by a relative regret. The relative regret is a relative difference between the aggregated solution and ideal solution. The model of integrated DEA and probust technique as follows: Subject to: The model (2) is a kind of stochastic programming that has the objective function for maximising the expected efficiency of oth DMU. Where is the weight of ath opinion of experts and ∑ ℎ ≥ =1 (1 − ) ℎ * , ∀ donates constraints associated with all opinion of experts. The constraints do not allow a value more than (p*100) % of the ideal efficiency score for the final efficiency score. The value of p is flexible for control the relative regret. The constraint becomes inactive if p = ∞ and the score become infeasible if p is very small. The information of expert's opinion is valuable, this method very suitable to use analysing all the opinion of expert without losing any information. Therefore, this method can control the relative regret to increase accuracy and satisfaction of the group decision making.

Selection of welding process
The application that was investigated is the shredder hammer as given in Figure 2. The base metal that is used for the shredder hammer is medium-low carbon steel, and the specifications are presented in table 2. As mentioned before, hard-facing using welding process is used for repairing the shredder hammer. During a discussion with the experts and consider some critical point in the welding process selection for repairing shredder hammer, this paper proposes six welding process be investigated. Namely shielded metal arc welding (SMAW), flux cored arc welding (FCAW), submerged arc welding (SAW), oxyacetylene gas welding (OAW), gas tungsten arc welding (GTAW), and gas metal arc welding (GMAW). Some critical criteria that are considered in the welding process selection for repairing shredder hammer are taken from Ferjutz and Davis [15], as given in Table 3.
Due to the primary goal of DEA is to determine the efficiency of decision-making units (DMUs), while multiple criteria decision making (MCDM) is used for ranking or selecting from a set of the alternative that has conflicting criteria. The "methodological connection" is necessary used for apply DEA as MCDM. The methodological connection between MCDM and DEA is to specify maximising criteria as outputs of DEA and minimising criteria as inputs of DEA [14]. The criteria that bigger value is better called maximising and the criteria whose lower is better called minimising.
Based on methodological connection, the inputs of DEA are initial preparation required, welding procedures, post-weld cleaning, capital cost, and operation factor. Furthermore, the outputs of DEA are weld-ability on the base metal, availability of consumables, easy of manual or automation for welding process, the flexibility of welding position, and deposition rate.

Result and discussion
Due to the capital cost and welder skill are criteria that be affected by the investor. So these situations can change in several conditions. Therefore, this paper is done in the three cases, shown in Table 4. First of all, we solve model (1) to get the ideal efficiency score ( ℎ * ) from 10 experts without considering p-robust constraint to control relative regret. The results are shown in Table  5 for three cases. Based on the outcome, many welding processes get the efficiency score of 1 according to the opinion of 10 experts. Due to the score of efficiency for three cases have many scores of 1, it means the  discrimination power of basic DEA is not satisfying and impossible to decide about the best welding process for each case. Therefore, the final of efficiency score should be only one score and robust. These mean that the final efficiency based on ten experts should not change to various inputs and outputs of DEA in the uncertain situation.
After solving model (1), we need to solve model (2) to get final efficiency score for each case with same inputs and output like when solving a model (1). Let the regret value (p) for case 1 equal to 0.15, regret value (p) for case 2 equal to 0.19, and regret value (p) for case 3 equal to 0.22. Let the weight of experts' opinion have the same value (w1, w2, …, w10 = 0.1), and the result is showed in Table 6 or Figure 3. As it can be seen from Table 6 or Figure 3, case 1 denotes SMAW has the highest score with the final efficiency score of 0.996. OAW is the second one with the final efficiency score of 0.995 and GTAW is the third one with the final efficiency score of 0.976. In case 2, SAW has the highest score with the final efficiency score of 0.996. FCAW is the second one with the final efficiency score of 0.994, the third one is GMAW with the final efficiency score of 0.990, and the last one is GTAW with the final efficiency score of 0.969. In case 3, FCAW has the highest score with the final efficiency score of 0.994. GMAW is the second one with the final efficiency score of 0.992, GTAW is the third one with the final efficiency score of 0.978, and the last one is SAW with the final score efficiency score of 0.879.
In case 1, the highest final efficiency score belongs to SMAW and OAW (see Table 6 or Figure 3) because they are a success to satisfy capital cost and welder skill needs with the lower value than GTAW. For GTAW has the lowest final efficiency score because of GTAW also has the lower value of deposition rate than SMAW and OAW. So when capital cost and welder skill needs are limited by using manual welding, the value of SMAW and OAW will rise rapidly.
In case 2, the highest final efficiency score belongs to SAW (see Table 6 or Figure 3) because of SAW has the lowest value of welder skill need than another welding process. However, the final efficiency score of SAW and FCAW is not too much different because the capital cost value of FCAW is better than SAW.
In case 3, when the parameter like welder skill needs is not limited, the final efficiency of SAW decrease rapidly because of the superiority of SAW is only in the welder skill needs. Moreover, the final efficiency score of SAW lower than GTAW because of GTAW better than SAW in term of the flexibility of welding position (especially in horizontal position and incline position).
As can see from three cases above, the suitable welding process can change because of the different parameter that uses. The three problems shown are a common problem in manufacturing especially for repairing the shredder hammer.   Fig. 3. The graphical final efficiency score in 3 cases. Now, this section study effect of relative regret value on the final efficiency score. As mentioned before, "the regret value and p-robust constraint" control the relative difference between final efficiency score ( ℎ ) and the ideal solution from a experts ( ℎ * ) or known as "relative regret". Table 7 shows the sensitivity analysis for three cases that we proposed. As we can see it the Table 7 (1 − ) ℎ * , ∀ } does not allow the final efficiency score more than (p*100) % of ideal efficiency. Due to the lowest acceptable of regret value of case 1 is (p) ≥0.15, it means "the p-robust constraints and regrets value" able to handle up to 15% of relative regret. Also, case 2 can handle up to 19% of relative regret and case 3 can handle up to 22% of relative regret. However, notice that a large regret value (p) has a side effect of the inconsistency of experts' opinion in the results.

Conclusions
Welding process selection usually depends on experiences or general application in similar companies. However, this approach mostly ignores many criteria that can be affecting the suitable welding process selection. In this paper, ten opinions of expert will be analysed by integrated data envelopment analysis (DEA) and p-robust technique to select welding process for repairing shredder hammer. The most advantage of the proposed approach is that regret value (p) and p-robust constraints that control the relative regret base on ten opinions of experts. The result should not change to various inputs and outputs of DEA in the uncertain situation. The main contribution of this study can support the decision of welder, manufacturing and supplier base on three cases proposed concerning limitation of capital cost and welder skill. For future research, the approach can be used for welding process selection in another area like a storage tank. Furthermore, because of the discrimination power of this method can be said still low, TOPSIS method can be used and combine with our proposed approach to get more discrimination power.