Showing posts with label standard deviation. Show all posts
Showing posts with label standard deviation. Show all posts

Sunday, February 10, 2013

Interviewing

Interviewing is one of the techniques that are used in Quantitative Risk Analysis. As mentioned in the previous chapter, it is part of the Data Gathering and Representation Techniques sub-group. 

At a high level, we all know what Interviewing is, isn’t it? But, in this chapter, we are going to learn what we need to know about interviewing from Quantitative Analysis perspective. What information we are looking to get through interviewing and what we are supposed to do with that information are a couple of questions that will get answered in this chapter. 

Interviewing in general, is used to quantify the probability and impact that risks may have on our projects objectives. The information gathered during these interviews would be dependent on the type of probability distributions that we are looking to use. Typically, we will conduct such interviews with SME’s (Subject Matter Experts) to get their take on the risk and its impact. Don’t worry too much about probability distributions just yet. We will be covering it very soon. For now remember that the data we gather could vary based on the type of distribution we use. That should be sufficient to understand the forthcoming section. 

For commonly used distributions, we gather three point estimates through these interviews. The three point estimate is calculated using the PERT Formula. Are you wondering what PERT is? If you are someone who has not studied the PMBOK Guide fully yet, I strongly urge you to do that because, the PMI RMP Exam uses a lot of terms and concepts that are part of the standard Project Management Framework as per the PMBOK. Anyways, PERT stands for Program Evaluation and Review Technique. It is a technique used to estimate durations for activities. In my earlier series on PMP Certification I had covered it in great detail in the chapter titled Estimating Activity Duration

In short – As per the 3 point formula, we try to arrive at 3 different estimates: 
a. The Optimistic Estimate (O) 
b. The Most Likely Estimate & (ML) 
c. The Pessimistic Estimate (P)

The 3 point estimate is a weighted average of these 3 estimates and is usually more accurate. The formula is as follows: 

3 point estimate = (O + 4 * ML + P) / 6 

The range here between the optimistic and pessimistic numbers is the range of uncertainty for our estimate. The more the uncertainty, the greater the range. Remember, the chapter titled Managing Uncertainty? Uncertainty causes risks and the whole purpose of Risk Management is to keep this uncertainty to the minimum. 

Trivia
Whenever we calculate any numbers or values, we must always document how those values were derived, along with any assumptions or constraints that went into the calculation. 

Standard Deviation: 

The Standard Deviation (SD) is a measure of how far the actual estimate we have calculated is from the mean value. The formula to calculate SD is:

SD = P – O / 6 

Here again – P is the pessimistic and O is the optimistic estimate. 

An Example: 

Let us say, you are talking to an Engineer about construction of a brick wall. He is an expert and is going to give you his feedback during the interview. He feels that, the brick wall could be constructed in 10 days if everything goes smoothly but, if it rains then the construction may get extended to up to 20 days. He also feels that, the construction should be complete in around 15 days. 

So, as per this discussion: 

O = 10 days
P = 20 days and
ML = 14 days 

3 point estimate = (10 + 4 * 14 + 20) / 6 = 14.33 days 

SD = 20 – 10 / 6 = 1.667 days 

As per the 3 point estimate we can say that, the construction of the wall will be completed in 14.33 days while the standard deviation will be 1.667 days. The SD signifies the fact that the construction may get shortened or extended by this value based on the prevailing conditions. So, the work could complete 1.667 days prior to the planned 14.33 days or it could take 1.667 days more than the planned days. 

So, the expected construction duration will be 12.663 days to 16 days. 

Trivia:
All estimates provided must be justifiable. You can’t just take the word of the SME for the numbers. Ask them for justifications and note them down for future reference. 

In this chapter, we have covered a lot of items pertaining to interviewing, estimates etc. From the PMI RMP Exam perspective, you need to remember the following: 

1. Interviewing is a tool and technique that is part of the Perform Quantitative Analysis Process and a part of the Data Gathering & Representation Techniques sub-group
2. We use this technique to gather information using historical data (or SME’s) and help quantify the probability and impact of Risks on project objectives
3. Information gathered using this technique depends on the type of probability distributions used 
4. The 3 point estimate formula is: (O + 4 * ML + P) / 6
5. The Standard Deviation formula is: P – O / 6

Prev: Tools & Techniques Used in Quantitative Analysis - Introduction

Next: Introduction to Probability Distributions

Friday, May 6, 2011

Chapter 14: Other Terms Related to Project Management

As part of your preparation for the Project Management Professional certification, you will be encountering terms like Probability, Baseline, Project Team, Project Management Team etc. Even though these are straight forward terms and a majority of us already know what these are, it is best to cover them to help those few of us who don't know these terms.

So, lets get started!!!

What is Probability?

I do not want to relive the pain of studying Mathematics in School or College because math wasn't my strongest subject and most importantly I did not like my Math teacher. Jokes apart, certain terms related to probability are part and parcel of the life of a project manager. So, if you are someone like me who doesn't like math, just learn the basics that are required to carry out your job as the project manager and move on. Atleast that's what am gonna do!!!
Probability is defined as a chance that something will happen. The simplest example of probability is tossing a coin. The question is, when you toss a coin, what is the probability that the coin will land heads up? When you toss a coin, there are only two possibilities: It will land either heads up or tails up. So, either heads or tails will come up unless you cheat. The probability here is a 50-50 because there are only two options. In general, if there are ‘N’ possible outcomes of an event, and each outcome is equally likely, then the probability of one specific outcome is 1/N. So for 2 outcomes it is ½ or 0.5

Another useful concept in probability is the combined probability of several events. For example, if you toss two coins, the probability that the first coin will land heads up and the second coin will land tails up is 0.5×.05=0.25.

In general, to calculate the combined probability, you multiply the individual probabilities. If the probability that an event X will happen is a, the probability that event Y will happen is b, and the probability that event Z will happen is c, then the probability that all the three events (X, Y, and Z) will happen is a×b×c.

To summarize, the probability that a number of independent events will occur is calculated by multiplying the probabilities of occurrence of all the individual events.

Some other Probability Related Terms:

Random variable

A random variable can acquire any value within a given range or out of a set of values. For example, you can use a random variable to represent the results of rolling a fair die, which has six sides numbered by dots from 1 to 6. The possible outcome of rolling a die could be any number from the set of outcomes: 1, 2, 3, 4, 5, 6

Expected value

This is the expected value of an outcome. As an example, assume you get into a bet that you will win $10 if a coin toss results in heads, and you will lose $5 if it results in tails. Given that the probability for heads or tails is 0.5 for each, the expected value for the money that you will win is $10×0.5=$5, and the expected value for the money that you will lose is $5×0.5=$2.5.

Variance

The variance of a random variable is the deviation from the expected value. It is computed as the average squared deviation of each number from its mean. For example, assume that the values of a random variable are 2, 4, 5, 7, and 2 in five measurements. The mean value for these measurements is:
(2+4+5+7+2)/5=4

The variance of the spread of these values is:

V=σ2=[(2-4)2+(4-4)2+(7-4)2+(2-4)2]/5=3.4

Standard deviation

This is the square root of the variance—that is, σ. So, in our example, the standard deviation is the square root of 3.4—that is, 1.84.

Algebraic equations

Some questions in the PMP Exam will assume that you can do simple mathematical calculations. You should also have a very simple understanding of algebraic equations. You should be able to make simple manipulations, such as the following:

x = y/z implies y = x * z


Global Project Variables

There are some significant factors in projects and project management that vary their values throughout the project lifecycle. You must keep your eyes on these variables from the very beginning of the project:

Cost and number of team members (staff)

1. Usually Low in the beginning, maximum when the project is being executed, with a rapid drop when the project draws to a close.
2. Ability to influence the characteristics of the project product without significantly changing the cost.
3. Highest in the beginning and gradually decreases as the project progresses.

Risk and stakeholder influences.

Highest in the beginning and decreases as the project progresses. This is true about uncertainty, too, as risks arise from uncertainty.

Baseline

The project baseline is defined as the approved plan for the cost, schedule, and scope of the project. The project performance is measured against this baseline. The project baseline is also referred to in terms of its components:
1. cost baseline
2. schedule baseline and
3. scope baseline.

How would you know how your project is performing? You compare the performance against the baseline. Approved changes in cost, schedule, and scope will also change the baseline.

Previous: Relationship between Project, Program and Portfolio

Next: Project Management Office
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