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PERT is one of those mysterious aspects of project management that many will choose to avoid.

It deals with uncertainty and requires a little bit of statistics.

PERT stands for **P**rogram **E**valuation and **R**eview **T**echnique.

It was developed around 1958 as part of the development of the Polaris submarine project.

The special aspect of PERT is that it takes into account the inherent ‘uncertainty’ of making estimates of task durations.

Many project schedules are put together by asking an experienced person for his or her judgement on the time it will take to complete a task.

From this approach we end up with rigid values for task durations. It does not mean that they will be wrong it just means that the estimate is expected to be correct based upon the individuals experience.

Other aspects of risk management are covered in 'The Complete Risk Management package'.

Some people find PERT very useful and others less so.

The fact that it deals with uncertainty can lead to improved aspects of the project management control process.

Because PERT considers uncertainty it allows managers to assess the overall duration of one or a series of tasks.

With this information a manager will be able to see if these tasks could move from non-critical to critical given adverse conditions.

This sort of information will be very valuable for contractors, extremely concerned with maintaining or improving on their schedule.

In addition, if we look at the total project duration you will be able to get data on the likelihood of completion within a range of values.

This will be extremely useful when you are talking to clients and considering costs and the effects of overlap with other projects.

In order to fully appreciate what PERT can achieve you must be familiar with a few simple statistical terms.

It might help to show these terms based upon a series of data.

If we have a set of data values of:

23, 22, 31, 27, 28, 22, 34, 27, 24, 25, 23, 21, 29, 32, 24, 27, 21, 18, 26, 27

These values are unordered. It is a good idea to rewrite the values in order.

18, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 27, 27, 27, 27, 28, 29, 31, 32, 34

All of these examples can be found in the Excel file ‘stats.xls’ as part of the product package.

Statistics is concerned with the behaviour of a large number of items and not just one.

These are often termed a ‘population’. For example, boats in a race, 1000 screws, 5000 sheep etc.

This is the total of all of the individual values divided by the number of values.

For example,

The sum of 18, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 27, 27, 27, 27, 28, 29, 31, 32, 34 = 511

The number of values = 20

Thus the mean = 511 / 20 = 25.55

This the middle value when all values are arranged in an order from low to high.

If there are an even number of values as above then it is the average of the middle values.

For example,

18, 21, 21, 22, 22, 23, 23, 24, 24, **25**, **26**, 27, 27, 27, 27, 28, 29, 31, 32, 34

Here, as we have an even number of values 25 and 26 are the middle values.

Hence, the median value is (25 + 26) / 2 = 25.50

Had the final value of 34 been absent the median would have been = 25.

This is the value that occurs the most.

For example,

18, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, **27**, **27**, **27**, **27**, 28, 29, 31, 32, 34

Here, 27 is the mode value as it occurs the most at 4 times.

This is just the largest value – smallest value = 34 – 18 = **16**

The variance is a measure of the ‘spread’ of the values about the mean.

It is calculated as:

Σ (x - y)2/n OR Σx2/n - y2

Where:

Σ = the sum of the terms (Greek capital sigma)

X = a value

Y = the mean

n = the number of values

For example.

18, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 27, 27, 27, 27, 28, 29, 31, 32, 34

Using the formula Σx2/n - y2

Σx2 = 13367

Σx2/n = 13367 / 20 = 668.35

Y2 = 652.80

So,

Σx2/n - y2 = **15.55**

The variance is also the square of the Standard Deviation.

It is a measure of the range of variation from an average of a group of measurements.

It can be very useful as it can be shown that:

68.27% of all measurements fall within **one** standard deviation of the mean.

95.45% of all measurements fall within **two** standard deviations of the mean.

99.73% of all measurements fall within **three** standard deviations of the mean.

The standard deviation is the square root of the Variance.

Hence for our example of:

18, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 27, 27, 27, 27, 28, 29, 31, 32, 34

The mean = **25.55**

Standard deviation = **3.94** (the square root of 15.55 the variance)

Thus, values within **one** standard deviation are:

From 25.55 – 3.94 = 21.61

To 25.55 + 3.94 = 29.49

Hence, 68% of the values will lie between 21.61 and 29.49

There are 14 values in this range = 70%.

For **two** standard deviations the range is 17.67 – 33.43

There are 19 values in this range = 95%.

For **three** standard deviations the range is 13.73 - 37.37

There are 20 (all) values in this range = 100%.

The 20 values we are using in the above example have been derived from repeating a task **20 times** and measuring a value each time.

The total number of values therefore being 20. In this example we are saying that on 68% of the occasion that we carry out the task the result will lie between 21.61 and 29.49 and outside of this range on the other 32% of occasions.

When we carry out a project we in effect carry it out usually **once only** so we have to be careful in saying there is a 68% probability of a total project duration (for example) lying between two values. This would be the case if we were able to carry out the same project many times.

In effect when someone estimates a task duration value they are doing this on the basis of experience by mentally simulating what is likely to happen if they repeated it many times.

Risk management in general is covered in more detail in 'The Complete Risk Management package'

PERT as applied to task duration is tackled next.