Specifying an appropriate uncertainty description, or model, for each cost item is central to the use of Monte Carlo analysis. This in turn depends on the nature of the uncertainties with which you are concerned.
There are two types of uncertainty with regard to cost models, which we can describe as quantity uncertainty and scope uncertainty.
Quantity uncertainty is the uncertainty in the cost to complete a task resulting from your inability to predict the exact prices and quantities of the materials and labor that will be required to do the work, disregarding any uncertainty in the scope or extent of the work.
Suppose you are building a brick wall. The cost will depend on the price of bricks and cement and the cost of the labor to do the work, none of which you may be able to predict accurately in advance. Labor hours, for example, will probably depend on the skill levels and motivation of the actual individuals doing the work.
Quantity uncertainty, by itself, is just as likely to lead to an underestimate as an overestimate of the cost to complete a task.
Scope uncertainty is the uncertainty in the cost to complete a task resulting from your inability to predict the extent, or scope, of the work to be done.
Suppose you are renovating a house, and have prepared a budget based on a survey of the house. However, if when you start tearing down walls you discover some rotten timber that needs to be replaced, this will constitute an increase in the scope of the work, which will lead to increased cost.
While scope uncertainty can sometimes result in lower than expected costs, because the scope of the work is less than was estimated, more often the reverse is true - scope uncertainty results in higher costs. This is because there are many more ways in which a task can be more complicated than ways in which it can be less complicated. Scope uncertainty is therefore more likely to result in cost increase than cost decrease.