## 5 Discussion  
In a construction project where time really means money, schedule management is crucial. Therefore, predicting the probability of time overruns plays a key role in project success or failure. It is also much easier to manage what can be quantified. Therefore, project managers should know the probability of time overruns so that they can take the necessary preventive or corrective actions. Researchers have developed various quantitative methods for assessing time schedules in construction projects. The aim is to examine the reliability of the project schedule taking into account available probabilistic information accounting for potential disruptions that may occur during project execution. We use the Time-at-Risk (TaR) metric, which is a static  
Figure 8: Deviations in time schedules for the project implementation stage (PIS). Figure 9: Individual project stages can be visualised in terms of the distribution of changes in the assumed time schedule on the timeline of the entire project. measure of risk. More specifically, it is a quantile that reflects a particular feature of the probability distribution of the underlying value, i.e., time changes of the whole project and the contributions of its individual stages. In this respect, a quantile represents a certain part of the data set (time duration of all project stages) and indicates how many values in its distribution are above a certain threshold value. This paper shows a practical application of the TaR approach, which provides a realistic view of the feasibility of project schedules within anticipated time windows. In short, we used this approach to assess the reliability of performing a project according to the anticipated schedule time span. The analysed case was the construction of a residential complex (Fort Bema, situated in the Warsaw-Bemowo district), realised on 148 hectares of land and comprising almost 120,000 m\({}^{2}\) of usable floor area of residential units. The construction of such a large residential complex took a total of 128 months. In particular, TaR allows visualising the risk of time changes related to the project as a whole, as well as to each individual stage. TaR enables the assessment of the uncertainty surrounding each project. It is a tool that helps managers create a realistic project plan that can be used as a guide to manage individual project stages/phases or even specific tasks, as well as to monitor the entire project and its expected completion time. This method, in combination with Monte Carlo simulation, where time lags (i.e., deviations in the execution times of specific stages or even tasks/activities themselves) are sampled, allows for arbitrary assumptions tailored to the specifics of each stage/task. The MC method allows for certain assumptions about the distribution of time offsets in specific stages of the project. For example, triangular distributions can be assumed instead of PERT distributions for short phases such as the realisation of the opportunity study (OS) or for the conceptual phase (CONC), while Weibull distributions can be used for the other longer implementation stages (such as the arrangement stage and execution of construction documentation [ASECD], or the project implementation stage [PIS]), as they are inherently characterised by fat tails on the right (and thin tails on the left) side of their distributions [67; 86]. According to [PERSON] [86], the variation in the duration of activities/processes is best described by a Weibull distribution. However, we use PERT-distributions since they are easier to implement in the R package and they give the possibility to individually define the extremes and the most likely value, which has already been defined for the project under study. Viewing a construction project through the prism of a series of sequential or parallel stages of the investment process makes it possible to improve the quality of implementation of the entire project.