This paper presents a methodology to compare two welding processes, namely SAW (submerged arc welding) and GMAW (gas metal arc welding) and to select the best one for a given application. The selection was based on double criteria: operational costs and non-quality costs. The former is related to the normal costs evaluated in such kind of decision, like consumable cost, labor cost, etc. The latter is the financial loss suffered by the client every time response variable drifts away from its target value or presents variability. The non-quality costs reduction is fulfilled through the proper adjustment of the process variables, in such a way that deviations from the target are minimized while robustness to noise and to process variable fluctuations is maximized. Since this a multi-response, multi-objective problem, the optimum solution is a compromise. Prior to comparison, the two welding processes were optimized. The results indicated that the non-quality costs for the SAW process are slightly higher, but these are compensated by its lower operational costs. Therefore, the SAW process has the lowest total cost and, consequently, it is the best process for the given application.
The quality of a welded material can be evaluated by many characteristics (or responses), such as bead geometric (penetration, width and height) or mechanical properties. These characteristics are controlled by a number of welding variables, and, therefore, to attain good quality, it is important to set up the proper welding process variables. But the underlying mechanism connecting them (welding variables and quality characteristics) is usually not known.
In the optimization of a given welding process, the quality engineer is generally interested in the achievement of the three objectives below [1]:
1.
minimize target deviations;
2.
maximize process robustness to noise factors (minimize variability);
3.
maximize process robustness to process variables oscillations.
The targets are the ideal values for each response. To minimize target deviations means to produce units with their responses as close as possible to the ideal values. The noise (variability) is caused by the effect of non-controllable factors, such as weather condition. To maximize robustness to noise means to produce units relatively insensitive to these non-controllable factors.
The process variables are the controllable factors, i.e., product or process variables that can be controlled. In the welding process under investigation, typical variables are welding voltage, wire feed speed, welding speed, etc. The process variables should be adjusted in order to achieve objectives 1–3. However, during the production phase, changes in setup, operators, raw material supply, etc., may compromise holding the levels of some (or all) process variables at fixed levels. Therefore, it is also desirable to develop robustness to process variables fluctuations. This means that when the process variables experience small variations from their optimal setting, the quality responses will not degrade.
To achieve these three, sometimes conflicting, objectives, Ribeiro and Elsayed [2] proposed the following five steps optimization methodology:
(1)
Problem identification: list process variables and quality characteristics of interest (and for the latter, define target and priorities). Defining the proper targets is crucial. Engineer must be sure that the chosen targets are in harmony with the customer requirements.
(2)
Experimental design: study the problem and choose the proper experimental design to collect data concerning mean and variability. The levels of the process variables must be chosen carefully in order to properly investigate the region of interest. Also, it is important to collect enough data to allow variability modeling.
(3)
Response modeling: build mean and variance models for each response. To perform step 3 the engineer must be familiar with model building techniques. Building models for each response separately, the engineer has the opportunity to learn important facts about the process under study. Barbetta [3] proposed an iterative technique for building models of mean and variance. At first, the variance model is built with a statistic made from the calculated variance and from the quadratic error (taken from the mean model). Then the mean model is recalculated using the variance statistic values as weights when finding the new mean regression parameters, in a technique known as generalized least-squares (GLS). This technique is a variation of the common ordinary least-squares (OLS). The procedure is repeated at least twice or is finished by visual analysis of residual error and R2 index.
(4)
Objective function definition: the gradient loss function is based on the function proposed by Taguchi to quantify the non-quality costs [4]. These costs may be defined as the financial loss suffered by the client every time response variable drifts away from its target value or presents variability. Eq. (1) presents the objective function:
The proposed optimization methodology can be considered effective in providing a representative value of the total costs involved in welding applications (operational costs and non-quality costs). Therefore, it can be used to compare different processes options and help choosing the most suitable. In the present case, it was found that the best process for the given application was the SAW: despite its higher non-quality costs, its lower operational costs provided the superiority over the GMAW process. However, two questions should be emphasized.
The targets should be chosen with great care, since a poor defined target can lead the remaining quality responses to undesirable values. And other important concern is the procedure to define the constant K, responsible for the transformation of the Z function in monetary values. Further work is needed in order to define better methods to relate rework, customer dissatisfaction and other non-quality items with monetary values for the Z function.
