Función de las tareas escolares en el proceso de aprendizaje

It is practically impossible to simulate all possible age configurations a decent number of times. The total number of possible age configurations for T1, T2, T3 and T4 is:

∑ ∑ (𝑖 ∗ (𝑛1 − 𝑖) + 1) ∗ (𝑗 ∗ (𝑛2 − 𝑗) + 1)

𝑗=𝑛2

𝑗=1 𝑖=𝑛1

𝑖=1

With n1 as number of possible threshold ages (in years) for T1, n2 as number of possible threshold ages (in years) for T3, and T2>T1 and T4>T3.

Total number of possibilities for n1 = 43 and n2 = 73 is 110.941. The values for n1 and n2 are

determined by using the maximum ages the soft part can reach during the simulation period 1994- 2065: the maximum useful lifetime of a regulator soft part could reach is assumed to be 42, as is shown in Section 2.5, and maximum age a monitor soft part could reach is larger than the number of years between 1994 and 2065 and therefore 72 is the maximum age the soft part can reach during the simulation. Next to the possible replacement ages that follow from the maximum ages that the parts can reach, the replacement ages 43 (regulator) and 73 (monitor) are added to represent the scenario that no opportunistic or preventive replacement is performed on the regulator (monitor). Because the number of possible configurations is large, the concept of response surface

methodology is used in order to select a smaller experimental area. This method uses factors, which are the input parameters and assumptions composing a model, and responses, which are the output performance measures (Law, 2015). Using these factors and responses, quadratic regression models can be found. The next paragraph explains how this is done. More explanation of the response surface methodology can be found in Law (2015). The same holds for the following concepts that are introduced in the rest of this Section: Latin hypercubes, stepwise regression method and quadratic regression models.

First, Latin hypercube designs are developed. Then, responses are determined by taking the average of 1.000 replications per design point in these Latin hypercubes. Then, quadratic regression models are found by using the concept of stepwise regression. In the first step of this stepwise regression method, all 14 factors (T1, until T4, T12 until T42, and the interactions between T1 and T2, T1 and T3, T1 and T4, T2 and T3, T2 and T4, T3 and T4) are included. In each following step of the stepwise regression analyses, it is checked whether the P-value of any factor is higher than the removal level

64

of 0.15; if not, the stepwise regression method is finished, otherwise, the factor with the highest P- value is deleted and the regression analysis is performed again. This is done until there are no factors with a P-value higher than 0.15. Directly after each removal of a factor, the adjusted R-square values are evaluated, in order to estimate the fit of the regression model. After the last step of the stepwise regression method, the fit of the regression model is checked on other design points in the area of the Latin hypercube. These comparisons are done as follows: design points are chosen that were not used as design points in the initial Latin hypercubes, and their simulation results are compared with the results of using the factor values for each of these design points in the fitted regression model. When the responses of the simulations are comparable to the results of the regression model for the same design points, the fitted regression model is considered to be valid.

The method described in the last paragraph, is performed in two iterations: first, a relatively broad experimental area is chosen as input for the Latin hypercube design, and based on the results of the first regression model, a smaller experimental area is chosen as input for the second Latin hypercube model. Motivation behind this logic is that on forehand, there is not much information about the location of the global costs minimum; after the first iteration, there is more information and it is possible to focus on a smaller area.

Objective of the described method is to find a relatively small number of configurations that are all close to the optimal solution as indicated by the fitted regression model. When a relatively small number of configurations is found, the selected configurations are all simulated with 3.000 replications. These 3.000 replications are sufficient to meet the convergence criteria as given in Appendix Q. After obtaining the averages of the 3.000 replications for each configuration, the optimal configuration is determined. Two-sample t-tests for equal means are used to determine whether the differences between the expected total costs per configuration are significant at an alpha level of 0,05. More information about this method can be found in Snedecor & Cochran (1989). 5.2 Adjustments to the model as described in Chapter 4

As mentioned in the introduction of this chapter, the objective of the analyses in this chapter is to find the top 5 best configurations in terms of total costs related to soft parts of regulators and monitors. In order to focus on the costs and benefits of preventive and opportunistic replacement of soft parts only, a number of adjustments is done to the basic model as described in Chapter 4. These adjustments are the following:

 only costs related to regulator soft parts and monitor soft parts are taken into consideration. This means that only the replacement costs of scenario 1, OM and PM of regulators and monitors are taken into consideration, and the failure costs due to gas leaks and transport breaks caused by regulators and monitors;

 all supply disruption input parameters are set on “False”. This means that all required soft parts are considered as always available at the OEM. As explained in Chapter 4, OM and PM replacements of soft parts of certain regulators and monitors are only beneficial when there are no permanent supply disruptions of the soft parts of these regulators and monitors; Motivations are in the next paragraph. Changes in the code behind the model are shown in Appendix I.

65

The motivation behind implementing these rules is that the replacement costs of complete regulators and monitors is much higher than the replacement costs of soft parts. When the

replacements of complete component would be taken into consideration as well, the main factors in the model would be the number of required replacements of complete regulators and monitors. To measure the effect of opportunistic or preventive replacements, the large influence of the complete component replacements would require very large numbers of replications. Because, as explained in the introduction of this chapter, the main goal of the analyses in this chapter is to find the optimal age replacement configuration, the other costs are not taken into consideration. After determining the optimal age replacement configuration, the effects of implementing the optimal age replacement configuration in the standard settings (so, without using the described adjustments) are given in Section 5.4 and in the sensitivity analyses of Chapter 6.