Schedule risk is the risk that the project takes longer than scheduled. It can lead to cost risks, as longer projects always cost more, and to performance risk, if the project is completed too late to perform its intended tasks fully. Apart from the cost estimation and resource allocation used in CPM, most of the techniques used in quantitative cost risk analysis are different from those used in schedule risk analysis.

The earliest technique used for schedule risk analysis was the Gantt chart, developed by Henry Gantt in 1917. A Gantt chart gives a graphical summary of the progress of a number of project activities by listing each activity vertically on a sheet of paper, representing the start and duration of each task by a horizontal line and then representing the current time by a vertical line. This makes it easy to see where each activity should be and to show its current status. You can read more about Gantt charts on Wikipedia.

Many tasks require that prior tasks are completed before they can be initiated, but unfortunately, Gantt charts are not a good method of showing the interrelationship between tasks, so computers must be used to set up and maintain the network of tasks. One commonly-used technique is Program Evaluation Review Technique (PERT) which uses a detailed diagram of all anticipated tasks in a project, organised into a network to represent the dependence of each task on those that must precede it.

PERT can be used to analyse the tasks involved in completing a project, especially the duration of each task, and identify the minimum time needed to complete the total project. PERT makes it possible to schedule a project without knowing the precise details and durations of all the activities. You can read more about PERT on Wikipedia.

The Critical Path Method (CPM) is a similar project planning and management technique which also uses a network representation. Earlier versions did not try to estimate probability distributions for task durations, making it easier to derive the critical path, ie the set of tasks that determined the final project length. Various enhancements were made to CPM to allow alternative resource allocations to be explored, within specified cost constraints.

The increasing availability of computing power allowed led to the inclusion of probability distributions for task durations in CPM. This allowed Monte Carlosimulation to be substituted for the PERT assumptions. (Monte Carlo simulations are a type of algorithm used to simulate the behaviour of systems. They are described as stochastic or non deterministic because they are based on the use of random numbers. A stochastic model is a method of estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs.)
The addition of stochastic task durations means tasks can be placed on the critical path with some probability, also estimated using the Monte Carlo method. Stochastic CPM is now the preferred methodology for assessing schedule risk.