# Basics of Program Evaluation and Review Technique (PERT)

PERT is the technique used to find project completion time of “variable activities”. In PERT, the time is combination of three different time estimations. Following are the three different time estimation:

1. The optimistic time estimate (to): The minimum time required for the completion of the activity as per the predetermined condition.
2. The pessimistic time estimate (tp): The maximum time that activity will take under worst condition.
3. The most likely time estimate (tm): The time an activity will take if executed under normal condition.

## Important terms in PERT analysis:

1. Expected time or average time (te): Since there are three time values available in PERT, average time is to be calculate by following formula:
$t_{e} = {t_o + 4t_m + t_p \over 6}$
1. Variance (V): Variance is given by following formula:
$V = \Big({t_p - t_o \over 6}\Big)^2$
1. Standard Deviation ($\sigma$): Standard deviation is square root of summation of variance of critical activities. It is given by following formula:
$\sigma = \sqrt{V_1 + V_2 + V_3}$
1. Probability of completion of project (z): It is calculated in order to estimate that how many percentages are the chances of completion of project in certain time or given time (t). Let, tcp ​be the time of completion of project on critical path and t is any certain time or given time, then probability of completion of project in that given time t, is given by:
$Z = {t - t_{cp} \over \sigma}$