# Determination of Reliability of Selected Case
## 3 Results and Discussion
This mathematical apparatus made it possible to calculate the reliability of entire furniture structures based on data on the reliability of individual connections and the type of structure connecting structural nodes. The developed mathematical model was next used during the design and programming of the web application. The web application was created in the high-level language Python, which is characterized by an extensive package of standard libraries. In addition, additional objects and methods of this language were used to perform the necessary calculations: scipy.stats.expon (exponential distribution) [33], scipy.stats.gamma (gamma distribution) [34], scipy.stats.lognorm (log-normal distribution) [35], scipy.stats.weibull_min (Weibull distribution) [36], and scipy.stats.rv_continuous.fit (distribution matching) [37]. The program has a built-in database based on open-source solutions. It enables, among others, self-adding, deleting, and updating data. The results from the presented laboratory reliability investigations of furniture joints constitute the basis for the web application and the calculations. The interface of the developed web application consists of two main modules. The first module allows users to present the designed furniture structures in the form of predefined views of 2D elements with the possibility of their parameterization. Importantly, it is a real-time, dynamic conversion of a 2D drawing. The second module is used to present data and the results of reliability calculations for both joints and the entire structure of the designed case furniture. In addition, the developed web application has several useful functionalities. It:  
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The second part of the settings allows the user to add additional furniture elements to the previously defined furniture construction. Among these settings, the user can add:  
* Vertical partitions;
* Partition walls;
* Horizontal partitions. When inserting additional elements, the web application indicates their dimensions by default, taking into account the previously defined thickness of elements and the overall dimensions of the furniture construction, also previously defined by the user. Additionally, the web application allows the users to choose the reliability structure. If the option of the parallel structure is selected, it indicates that the reliability-increasing reserve has been applied by using an additional connector together with the already existing connector. The second described module presents the results of the reliability calculations, namely, the reliability of the selected furniture joint, as well as the reliability of joints made of other materials and connectors, included in the program database. Thanks to this, the engineer can quickly assess the reliability of the designed furniture construction when using alternative materials or connectors. An important functionality of the developed web application is the ability to assess the failure-free service life of the furniture, which in practical terms can be used to determine the length of the warranty period. After making the calculations, the user can generate a full report containing the initial parameters of the furniture and the results obtained. In order to present the full potential of the developed web application, in the third stage of the investigations, various variants of reliability structures that can be applied in furniture construction, meaning serial and parallel reliability structures, were verified. In the analyzed example, in the first case, a serial reliability structure was adopted. Based on the conducted laboratory reliability tests and the developed mathematical apparatus implemented in the web application, it was possible to calculate the reliability of eccentric joints made of MDF of 18 mm (0.946). In the web application, as previously mentioned, the reliability of a whole case furniture construction depending on time can be determined as well.