In order to determine the productivity in joints/day, we have proceeded like the following:

1) Sum of the welding and grinding runtimes and unproductive times;

2) Definition of the effective workday, where we have considered the lunch break and work start and finish times;

3) Definition of the Standard Team;

Table 2. Statistical parameters of the sample runtimes.

Table 3. Start and end times of the effective workday.

4) Definition of the number of team involved in the process;

5) Productivity calculation in joints/day of all teams in the work front.

The calculation of productivity in joints is expressed through the Equation (1) below:

(1)

・ Welding Productivity (WP): considers the time per completed joint per welding team. This time is the denominator of the division by effective workday, producing the unit joints/day per team. To assess the productivity of the construction work with all teams, it is necessary to multiply it by the number of teams.

・ Effective workday: is the 10 daily hours of working of the studied construction work subtracted from the mobilization and displacement times where the team did not effectively started the service and the 1 hour lunch break.

・ Time per completed joint: is the sum of the opened arc time, grinding time and the unproductive times from the start of the open arc welding until the final grinding of finishing pass, in hours.

・ Joint: top, with a chamfering angle between 60˚ and 64˚, root opening between 2 mm and 2.5 mm. The weld volume deposited by FCAW is 86.7 × 10^{−3} dm^{3}, calculated in similar procedure as [23] .

・ Welding team: is the composition of the team working to weld a joint. The team of the studied work was composed of 2 welders, 2 grinders and 2 helpers.

・ Number of teams―in the construction work there were 5 welding teams with the same composition.

On phase 2 we aimed at gathering the productivity values in joints/day of the studied work taking into consideration a longer production period. These data have been achieved through registers of the Construction Work Daily Report document, which is used by the contracting party and the contractor to report the main occurrences. The productive data of 29 production days have been gathered following the aforementioned procedures.

3.3. Elaboration of the Productivity Control Chart

Aiming to develop a practical monitoring tool, quick in obtaining results and easy to understand, we chose to develop a control method similar to those based on the general theory of Shewhart’s control chart rules, that esablishes a central limit, to which corresponds the sample mean, and the upper and lower limits adding or subtracting the mean of a k constant multiplied by a sample standard deviation. The control charts quickly detect anomalies in the process, once it is a real time monitoring technique [24] . Although inspired by the control charts already mentioned, the methodology developed in this work adopted its own criteria, which have been considered more suitable for productivity monitoring.

The control chart has been elaborated in the following steps: definition of the productivity model equation; conduction of a Monte Carlo simulation on the productivity model established in the Equation (1) from the productivity data gathered at the worksite via monitoring of the productive runtimes, unproductive times, start and end in order to obtain the CDF curve; definition of the control chart upper and lower limits.

The simulation of the productive model established in the Equation (1) is ran by the version 6 of the Palisade Corporation’s @Risk software for Excel [25] . Figure 1 represents a flow chart of the Monte Carlo simulation to produce the control chart.

The simulation procedure with the Monte Carlo method is conducted as in the following steps:

1^{st}) Definition of the model input data. The input data are: welding time, grinding time, unproductive time, start time, end time, workday time deducted from lunch break, number of teams. The last two items are constant.

2^{nd}) Definition of the output data, which in this case is the Welding Productivity (WP) defined in Equation (1).

3^{rd}) Definition of the generating functions for the following variables: welding time, grinding time, unproductive time, start time and end time.

4^{th}) After the definition of the generating functions and their input in the productivity model, a simulation with the Monte Carlo method is made with 1000 iterations.

5^{th}) After the simulation, it has been verified whether the number of iterations was sufficient through convergence analysis made available by the computing software. In this case the result was positive and we proceeded to the next step. It is worth highlighting that, if the number of iterations was not sufficient, it would be necessary to raise it until a positive analysis of the convergence analysis took place, because, if it is not achieved, it is re-

Figure 1. Flow chart of the simulation.

quired the assessment of the possibility to select another generating function of each variable considered in the productivity model. Otherwise, a non-parametric distribution is used.

6^{th}) Once the previous steps have been conducted, a CDF curve is elaborated and the statistical parameters of the data obtained via simulation calculated.

On defining the generating functions in order to conduct the productivity model simulation, 3 different criteria have been adopted for each activity, taking into consideration the specific characteristics of each of them. Thereby, on defining the generating function of the welding times, a qui-square test, tool available in the @Risk6 software, was used. The function that showed the highest compliance was the Lognormal function for a significance level of 5% with the following main parameters: µ = 747.65 and s = 253.13. Regarding the grinding time, the Weibull function presented the best compliance with the sample data, for a significance level of 5% with parameters α = 2.5198 and β = 645.79.

For unproductive times, it was impossible to adjust the data with a CDF, because there was not compliance in the Qui-square test for any function presented by the version 6 of the @Risk software [25] . In Table 2, it is possible to notice a great value dispersion, resulting in a relevant amplitude between maximum and minimum, elevated dispersion attested by the analysis of the coefficient of variation and a bimodal behavior observed on the analysis of the distribution graph of the data gathered. The coefficient of variation is a meaningful way to determine which variable, in this case unproductive, has great dispersion. The variable with the smaller coefficient of variation, near 0, is less dispersed than the variable near 1.

It has been observed that the unproductive times result from many situations, for example, idleness, consumption materials waiting time, interruptions in order to reposition the tools, among others. In this sense, it has been concluded that the differentiated nature of the generating causes for the unproductive times is the main reason for the heterogeneous behavior in the sample and the difficulty on defining a generating function that would comply with the analyzed sample. Thereby, the solution adopted was to use the uniform distribution as a generating function, which attributes the same occurrence probability for the considered events. This function, which represents the behavior of the unproductive times due to various reasons, has been defined in the interval that corresponds to the minimum of 64 seconds and maximum of 1509 seconds, which respectively correspond to the shortest and longest unproductive time registered in this case.

The triangular function has been defined as generating factor for start and end times, which correspond to the preparations for the start and end of workday activities, taking into consideration the modeling impossibility of these processes. In this case, the main parameters of this distribution are: likely time, minimum time and maximum time, both for the start times and end times, presented in Table 3.

After defining the generating functions of the times considered in the welding process, the Monte Carlo simulation was ran in with the version 6 of the @Risk software for Excel with 1000 iterations, where the CDF and the generated data main statistics were obtained.

On the other hand, in order to define the control chart Lower and Upper Limits, the Probability criterion > 0% was adopted for the first one and Probability < 90% for the second one. These values have been extracted from the CDF curve. The upper limit setting in 90% aims at avoiding the use of data generated in the CDF, where the possibility of a discrepancy between the virtual data generated in a simulation and the ones originating from a real productive process increase. On the other hand, on setting the lower limit in 0%, the minimum positive value obtained in the simulation is attributed to the minimum productivity. We would also like to highlight that a similar criterion was used successfully by [12] .

3.4. Control Chart Effectiveness Test

We gathered the production of welded joints during 29 days in the Construction Work Daily Reports in order to verify the possibility of using the productivity control chart, which has been elaborated with data resulting from real time direct observation and register of the times considered in the welding operation in the workforce. Thereby, the production from each workday in joints/day has been registered and entered in the control chart. In case the productivity registered in a given day was out of both the upper and lower limits of the control chart, it was verified if any incident or occurrence has been registered in the Construction Work Daily Report. A comparison between the construction work productivity CDF curve in joints/day and the curve obtained through simulation, respectively presented in Figure 3 and Figure 4, was conducted to complement this analysis.

4. Results Analysis

From the CDF curve―Figure 2―obtained through simulation built based on direct observation and registration of both productive and unproductive times of the productive process, establishing the 0% quota of the CDF as lower limit corresponding to a productivity of 21 joints/day, 90% of the CDF, equivalent to 49 joints/day and the mean of 39 joints/day have been inserted as control chart limits presented in Figure 3.

The establishment of the upper quota in 90% of the CDF is due to the fact that values near 100% in the curve generated in the simulation present productivity results that do not represent a real productive process. In this article it has been established that this is the maximum value for the welding productivity as it is possible to note in Table 4.

The productivity data from the Construction Works Daily Report gathered during 29 production days have been inserted to assess the Control Chart capacity to detect variations in the welding productivity. Table 5 represents

Figure 2. CDF of the welding productivity indicator.

Table 4. Statistical parameters for the WP simulation.

the statistical parameters originated in the construction report and the result of the simulation. These data have been inserted in the Control Chart presented in Figure 3.

The analysis of Figure 3 shows that 86% of the elements of the productivity measured in the construction work are between the control chart minimum and maximum values and 14% of the elements are below mini- mum. Also, it is possible to notice that most values are below central limit.

During the analysis of the occurrence of points out of the lower limit and tending to be below the simulated mean, logistics problems in the construction work, deformations on the pipes to be welded, among other problems caused by the contractor management malpractices that were affecting the welding performance have been registered in the Construction Work Daily Reports. These problems are due to factors impossible to be encompassed by the experimental data gathering, because they are either special causes or welding process anomalies. From this result it is possible to conclude that this tool is effective on detecting the productivity variations, allowing corrective actions to be taken towards problems. On the other hand, it is possible to notice the effectiveness of the Monte Carlo simulation use in predicting the welding productivity behavior in accor- dance to what [11] -[13] have determined, once this control chart has been built from the CDF generated from the simulation obtained through data gathered by direct observation of the productive process of 29 joints. The evaluation period that encompasses the example of the control chart corresponded to the production of 824 joints registered in the Construction Work Daily Reports. Accordingly, it has been verified that the productivity model adopted in the Monte Carlo simulation, as well as the premises adopted in its building, both in the behavior of the productive times and unproductive times, presented adequate results. This analysis is reinforced when comparing the behavior of the WP obtained through Monte Carlo simulation CDF (Figure 2 and Table 4) and of the 29 days production corresponding sample, registered in the Construction Work Daily Reports (Figure 4 and Table 5).

It is possible to determine that in Figure 2, which presents the CDF built from the simulation based on the 29 joints experimental data gathered through direct observation and measurement of the productive and unproductive times of the productive process, the occurrence probability of the productivity data gathered in the construction work, which vary from 11 to 44 joints/day, is placed around 75%. Figure 4 represents the behavior of the productivity registered in 29 workdays and, in this case, the occurrence probability of the productivity

Figure 3. Control chart.

Table 5. Statistical parameters of 29 days productivity in the construction work.

Source: Construction Work Daily Report.

Figure 4. The welded joints productivity CDF during 29 days in the construction work registered in the CWDR

between the values from 21 to 44 joints/day is around 77%. Thereby, on comparing Figure 2 and Figure 4, it is possible to state that the curve generated in the simulation expresses the behavior of the productive process with reasonable precision.

5. Conclusions

By the results being achieved, it is possible to determine that the CDF curve generates through Monte Carlo simulation from the small samples gathered through direct observation of the productive process represents, with a good precision margin, the productivity of low alloy steels land pipelines welding process with the shielded flux cored wire process in the construction work.

The welding productivity model develops from the worksite welding direct observation with the registration of the productive and unproductive times, as well as the distribution models adopts in it in order to conduct the Monte Carlo simulation and welding productivity CDF building is successful in representing the productivity behavior in the construction work for the welding procedure being studied in this article.

The control chart, built from the CDF generated through a Monte Carlo simulation based on the productivity model and limits established in this work, has proven to be an effective tool on monitoring the welded joints productivity during construction work.

Cite this paper

Pedro MattosTabim,Miguel LuizRibeiro Ferreira, (2015) Productivity Monitoring of Land Pipelines Welding via Control Chart Using the Monte Carlo Simulation. *Journal of Software Engineering and Applications*,**08**,539-548. doi: 10.4236/jsea.2015.810051

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