Hello everyone, for our module here, I will be covering and talking about Program Evaluation and Review Technique. Which we refer to from, in this module and this course, as PERT. PERT, the initials on each of these words. So as introduction, what we cover so far? PERT charts, the activity on node, activity on arrows, the critical path method from the forward and the backward past calculations. We refer to sometimes for the activity on node the PDM, Presendence Diagram Method, or APD, Activity Presence Diagram and so on. All that we assume that all construction activities, the durations of these activities, remain the same and they are non-variable along the duration of the entire project, from the start to finish. If you want to think about that, this is quite not or unrealistic. So PERT technique or method introduces the uncertainty into the estimation of the construction activity duration in your schedule at the project scheduler. So unlike the CPM and the PDM, and even bar charts sometimes, of course, where a single duration is estimated for each activity, PERT considers three duration estimates for each construction activity in your project as following. The first one of the three duration estimates, we call it the ta, or the optimistic duration, which is the minimum estimated duration that an activity can be finished or be achieved. Or in other words, the ta, or the optimistic duration, is the best case scenario for that specific construction activity. Second is the tm or the most likely, which is the duration estimate, which can be achieved in the most likely scenario. As for the Pessimistic, or the tb, it is the maximum duration estimate that may occur in the worst case scenario on that specific construction activity. Then you, from these three estimates durations, you can then calculate the expected duration values of all the activities at your project. We refer to that expected duration in our course, in our module here, as te. After you are done with these calculations, then you can as simple as follow the CPM method calculations that early being described in the previous modules. And to show you how to calculate that te from these three duration estimates, you can then follow a very simple equation as following. So that expected duration, the equation for it is that te = ta which is the, what we said optimistic duration for the activity you are calculating, the expected duration for. Plus 4 times the most likely duration of that activity. Plus the pessimistic, or the worst case scenario, duration of that specific activity. And when you sum it all up, you divide it by 6 to find the expected duration. In definition, the expected duration is the average value of a probability distribution defined by the three estimates set that we just described in this equation here. Also, you have to have in mind that the expected duration, te, is always constant, so once you find the, or calculate, the expected duration, that constant number, you will use it for a follow up calculations on the PERT technique. For the purpose of this course and this module, and the specialization, I will not cover in details the behind mathematics on how we came up with such equations. I want you, as a construction manager, to understand the basic foundation of that scheduling tool itself, that PERT concepts, and how to use it, and it will help you in your project. And the same will apply for all the equations that we will go through, of course. Now let's take a quick example to calculate an expected duration for an activity. So, let's say if an engineer or an estimator, or maybe a superintendent, came to you and gave you three estimate durations of a concrete pouring activity for a big foundation, or slab, and they told you that the most optimistic duration to finalize that specific activity would be 4 days to pour all the concrete. The most likely is going to take you around 7 days. And the worst case scenario, you will not go above 12 days. So what you going to do here, in the example just want you to calculate what's the expected duration in that specific activity, which is concrete pour activity for the big foundation. We highlight the equation and take a minute, do the calculations quickly here. So the number would be 4 + 4 x 7, the most likely + 12, the worst case scenario. You sum it all up and divide it by 6. It give you 7.33 days, equal around an 8 working days as that expected duration for this specific activity.