# How to Optimize the Implementation of ITIL through a Process Ordering Algorithm
## 4 Results: Comparative of Sequences in a Real Case  
As mentioned before, there is not a generic methodology to sequence ITIL processes which takes into consideration the parameters of each company. A solution for this has been developed and it lays on data gathered from different companies. This information allows a candidate sequence to be proposed for a company depending on the size, industry, age, and other parameters. Of course, this solution generates a sequence for each company that aims to implement ITIL. It is necessary to compare the results of such optimal implementation with the sequences obtained in the literature review. The objective of this comparative is to determine if the sequence is significantly different from the ones proposed by different authors. The proposals of sequence selected are S1: [9], S2: [13], S3: [32], S4: [21], S5: [2], and S6: [31], as these proposals include a greater number of processes. To determine if the proposed sequence and the reference sequence are independent, Spearman contrast and Kendall contrast were used. In both cases the null hypothesis is that both sequences (the reference one and the proposed one) are independent; and the alternative hypothesis is that both sequences are related (that is, there is not a significant difference). The level of confidence used was \(\alpha\) = 0.1. For every real company, an optimal sequence is obtained and, so, the comparation with the referenced sequences may lead to one of next results: The optimal sequence is significantly different from the reference sequence or the optimal sequence is not significantly different from the reference sequence. In addition, even in this second case it may occur that selected processes for implementation are the same, but they are selected in a smoothly different order (not statistically different). As an example, a real, small, and young IT consultancy company located at Madrid (Spain) with less than nine employees was selected for testing. The algorithm is required to propose an optimal sequence considering five criteria (staff, IT employees, company age, industry, area). The application of the algorithm requires a database with data from other companies and make calculations with them (more information about this issue in Appendix A). The order of processes obtained is (just the 10 first processes are shown):  
1--continuous improvement; 2--management of catalogue; 3--incident management; 4--validation and testing; 5--availability management; 6-- service portfolio management; 7--financial management; 8--configuration management; 9--transition management; 10--access management. Results of the comparative with other sequences are shown in Table 1:  
From Table 1, it is relevant to conclude that the optimal proposed sequence is significantly different from the first five reference sequences and, at the same time, is optimized for the criteria given by the company. For the sequence S6, the optimal sequence has a \(\rho\) value out of the limits (that is, we cannot accept the null hypothesis), although the value is quite close to the limit; nevertheless, for the Kendal contrast the \(\tau\) value is clearly inside the limits (which allows us to accept the null hypothesis). Let us remember that the optimal sequence selects processes iteratively, so the global degree of the ITIL implementation on a company is maximized when compared with similar companies in terms of size, IT size, age, industry, etc. This optimal sequence is significantly different from the published sequences by different authors. The significance of the experiment is based on the fact that companies obtain a sequence of processes to implement ITIL at very low cost (no experts are needed), defining the criteria for optimization and considering the degree of implementation already reached at the moment.