Bar chart; expected time and variance

Bar chart

A bar chart shows each activity as a horizontal bar on a time scale; the length of the bar is the duration. Example: house project (weeks).

                 0   4   8   12  16  20  24  (wk)
                +------------------------
A Site clearing |#                       
B Excavation    | ##                     
C Foundation    |   ###                  
D Plinth beam   |      ##                
E Walls+columns |        #####           
F Roof slab     |             ###        
G Plumb/electric|             ###        
H Plastering    |                ###     
I Floor,doors   |                   ###  
J Painting      |                      ##
                +------------------------

Advantages

• Simple to prepare, read and understand, even for non-technical persons.
• Shows start, finish, duration and overlap of activities on a time scale.
• Cheap and quick; needs no special training.
• Good for presenting the summary to top management and site staff.
• Progress can be marked on the bars and compared with the plan.
• Useful for resource scheduling on a time scale.

Disadvantages

• Does not show the logical dependence between activities, so the effect of a delay on other activities is not seen.
• Critical activities and float are not shown, so the manager cannot say where attention is needed.
• Not suitable for large and complex projects; the chart becomes crowded.
• Difficult to update; any change in logic needs redrawing.
• Durations are single-point values; uncertainty is not considered.
• Does not show resource or cost relations.

Expected time and variance (PERT)

Given: optimistic time $t_o = 6$, most likely time $t_m = 8$, pessimistic time $t_p = 12$.

$$\begin{aligned} t_e &= \frac{t_o + 4t_m + t_p}{6} = \frac{6 + 4(8) + 12}{6} = \frac{50}{6} = 8.33 \\ \sigma &= \frac{t_p - t_o}{6} = \frac{12 - 6}{6} = 1 \\ \text{Variance} &= \sigma^2 = 1^2 = 1 \end{aligned}$$

Answer: $t_e = 8.33$ and variance $= 1$ (standard deviation 1).