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## 5th Edition PMBOK® Guide—Chapter 6: Modeling Techniques

This post covers Modeling Techniques, one of the types of tools & techniques used in the final planning process under Schedule Management, process 6.6 Develop Schedule.

1. What-If Scenario

The purpose of the technique is to refine the schedule model by accounting for the effect of various risks or scenarios on the project schedule, such as: What will happen if there is a delay in the delivery of a major component?

The idea is that the effect on the project schedule of various scenarios or risks are assessed. How vulnerable is the schedule to these adverse conditions? Can contingencies or response plans be prepared to reduce the impact to the schedule of these various adverse conditions? Contingency reserves that pay for these contingencies or response plans may be needed to be added to the project estimate to get the cost baseline.

If the scenario is tied to a certain activity or stage of the project, and that scenario does not occur, then the contingency reserves tied to that scenario may be deemed no longer necessary, and can be used to reduce the cost baseline. Also, the potential negative impact on the schedule may be deemed no longer necessary, which can be used to reduce the range for the duration of that particular activity.

This shows that, as the risk on a project gets reduced throughout a project, this also reduces the uncertainty in both the budget and the schedule.

2. Simulation (Monte-Carlo Analysis)

A three-point estimate gives a range of durations for each activity, the tP or pessimistic estimate, the tO or optimistic estimate, and the tM or most likely estimate. What happens when you get a large number of activities, each with their own set of three estimates for the activity durations? How do you determine the likely duration of the project of the whole?

One way is through simulation, which takes the various activities and performs a calculation simulating various possible outcomes for each activity, and then based on this simulation of the individual activities, calculates the possible outcome for the overall project. The most common form of simulation of this type is Monte Carlo analysis. When you are doing a problem in the form of Estimated Monetary Value in risk management, you are doing a very simple form of this simulation using only two scenarios. If you can imagine extending this type of calculation for scenarios involving hundreds or more activities, you can get an idea of what the Monte Carlo analysis does and why it takes a computer to figure it out.

3. Conclusion

These modeling techniques offer a layer of refinement to the estimate of the duration of the schedule by showing the affect of risk. This is important because it not only makes the schedule more robust, i.e., able to be executed under adverse conditions, but can also become a tool in managing the risk on the project as well as its schedule.

The next tool and technique to be reviewed is that of leads and lags. Unlike modeling techniques, leads and lags are a tool that lends itself to questions involving calculation on the exam.

## 5th Edition PMBOK® Guide—Chapter 6: Resource Optimization Techniques

The duration of a project activity will depend on the availability of resources you can apply to that activity. That is why the process 6.4 Estimate Activity Resources comes before process 6.5 Estimate Activity Durations.

Once you get a schedule model together, you may have to adjust it depending on the supply and demand for resources not only within the project, but between projects in a company. That’s why you may need one of the following resource optimization techniques: resource leveling and resource smoothing.

1. Resource leveling

This is used when critical resources are shared between projects or are overallocated either a) to one or more activities that are concurrent within a project or b) to one or more concurrent projects within an organization.

Thus the demand for resources outstrips the supply, and resource leveling is done to make sure that the supply meets the demand. In practical terms, it often happens like this. If Resource A is assigned to an activity on project #1 for eight hours a day, and resource A is shared between two different projects, project #1 and project #2, then resource leveling would then assign resource A to project #1 for 4 hours a day, and to project #2 for 4 hours a day. Notice that, in terms of project #1, this would double the amount of days it would take to do a particular activity using Resource A.

In fact, it is worthwhile noting that because it necessarily increases activity durations, resource leveling can even have an affect on the critical path of a project.

2. Resource smoothing

This is when the requirements for resources on a project are kept within certain predefined resource limits, for example, if Resource A is only working part-time on a project, the number of hours that Resource A is assigned to the project may be limited. The difference between resource smoothing and resource leveling is that resource smoothing is only used on activities that have float, so they cannot affect the critical path of a project like resource leveling can.

I hope this post clears up the difference between resource leveling and resource smoothing because the terms sound similar, and in fact, are both used for the same general purpose, to adjust the demand for resources on a project with a given supply. The difference between them comes to the fact that resource smoothing is used only for activities that are not on the critical path, whereas resource leveling has no such restriction, and can indeed affect the critical path of a project.

The next post covers the subject of modeling techniques used to model the effect of various risks on the duration of a project.

## 5th Edition PMBOK® Guide–Chapter 6: Critical Chain Method

One of the tools and techniques used in the process 6.6 Develop Schedule is the critical chain method. Unfortunately, it can be easily confused with the similar-sounding critical path method, which was covered in the last two posts.

The purpose of this post is to explain briefly what the critical chain method is, how it is distinguished from the critical path method, and how the addition of buffers used in the critical chain method differ from merely padding the estimates, a practice frowned upon by PMI.

1. The Critical Chain Method

First of all, why do you need the critical chain method in the first place? In the critical path method, you are given the durations of each individual activity as definite amounts: 7 weeks, for example, to complete activity A as opposed to 5 weeks to complete activity B.

However, when you start to use three-point estimates, you realize that the duration estimates for activities are better expressed in terms of a range of durations: 5-9 weeks, for example, to complete activity A as opposed to 3-7 weeks to complete activity B.

Because the activities themselves have a range of durations, once you figure out the critical path based on, say, the most likely durations of activities, you will have a float for activities on the non-critical path which now will also have a range. There is therefore some uncertainty about the durations of the individual activities and the total duration of a non-critical path. Buffers are added to account for this uncertainty. So if an activity has a float of between 1 and 3, you would place a buffer from 1 and 3 weeks to make sure that the non-critical path feeds into the critical path at the correct time.

There are two kinds of buffers: feeding buffers for each of the non-critical paths, and then a project buffer at the end of the critical path, which the project manager can use to make sure the project finishes on time.

2. The Critical Chain Method vs. the Critical Path Method

The critical path method deals with definite durations, whereas the critical chain method is used to add buffers that account for uncertain durations (i.e., those that can be expressed as a range). It adds a level of flexibility to the critical path method, if you want to put it in those terms.

How does adding a buffer in the critical chain method differ from simply padding an estimate? Padding an estimate means adding an arbitrary, across-the-board percentage to one’s estimates. Padding is therefore an extremely blunt instrument for making sure your project is done within the schedule. It is wasteful, in that it may add to estimates of certain activities that don’t require any such “padding.” And the arbitrariness means that there really is no basis other than guesswork in how much you add to the estimates.

With a buffer, you are adding extra built-in time to the non-critical paths of the project a) at the precise point where they are needed and b) in the precise amount which is needed. So it is a scalpel as opposed to the blunt instrument of padding, and is therefore approved by PMI, whereas padding is frowned upon by PMI.

The next post deals with the next tool and technique of this process, called resource optimization techniques. What the project requires on an optimum (8 hours a day, 5 days a week) schedule and what resources are actually available on a day-to-day basis may be two different things, and this technique reconciles the project durations to the reality of resource availability on that particular project.

## 5th Edition PMBOK® Guide—Chapter 6: Critical Path Method SHORTCUTS

In the last post, I discussed the formal method for determining the critical path of a network using the forward and backward pass method. This also gives you the float of each activity on the network. Recall that the float of any activity on the critical path is by definition equal to 0, the float of any activity on a non-critical path is the number of time units it can be delayed without affecting the successor activity.

There is a shortcut alternative which I found saves a lot of time, which is especially important when taking the PMP or CAPM exam.

Here’s how it works.

1. Draw the network diagram for the problem.

2. List the potential paths for the project and their durations.

3. Whichever path you find as a result of step 2 has the longest duration is the critical path.

4. Label ALL activities on the critical path as having float of 0.

5. Calculate the float of the non-critical paths found as a result of step 2 by taking the duration of the critical path minus the duration of that path.

6. Take the non-critical path with the next highest float above 0.

7. Label all activities on that non-critical path with the float of that path EXCEPT for those that you already labeled as a result of step 4.

8. Taking the non-critical path with the next highest float above the one you found as a result of step 6.

9. Label all activities on that non-critical path with the float of that path EXCEPT for those that you already labeled in a previous step.

10. Continue until all activities are labeled.

Let me illustrate.

Here is a chart with the activities of a project. Answer these questions.

1. What is the critical path of the project?

2. What is the float of each activity?

 Activity Predecessor Duration Float Start None 0 A Start 2 B A 9 C B 18 D A 6 E D 10 F A 4 G F 14 H E, G 8 I C, H 9 J I 5 End 0

If you draw the network diagram, you get the following  three paths and their durations.

Path #1: A-D-E-H-I-J , Duration = 2 + 6 + 10 + 8 + 9 + 5 = 40

Path #2: A-F-G-H-I-J, Duration = 2 + 4 + 14 + 8 + 9 + 5 = 42

Path #3: A-B-C-I-J, Duration = 2 + 9 + 18 + 9 + 5 = 43

The longest path is path #3, with duration 43. This is the critical path and all activities have a float of 0.

Let’s look at path #2, which has the next smallest duration of 43, and a float of 43 – 42 = 1. All of the activities on path #2 that are NOT ALREADY accounted for in path #3 (the critical path) are assigned a float of 1. That means F, G, H are all have float of 1.

Finally let’s look at path #1, which has the next smallest duration of 40, and a float of 43 – 40 = 3. All of the activities on path #1 that are NOT ALREADY accounted for in either path #3 or path #2 are therefore assigned a float of 3. That mean D and E have a float of 3.

So the finally answer is the duration of the critical path is 43, and the chart below contains the float of all the activities.

 Activity Predecessor Duration Float Start None 0 N.A. A Start 2 0 B A 9 0 C B 18 0 D A 6 3 E D 10 3 F A 4 1 G F 14 1 H E, G 8 1 I C, H 9 0 J I 5 0 End 0 N.A.

If you would have done that same problem with the forward and backward pass, it would have taken a LOT longer.

The next post will cover the critical chain method; it sounds like the critical path method, but is a different technique altogether, with terminology involving “buffers” borrowed from lean manufacturing.

## 5th Edition PMBOK Guide–Chapter 6: Critical Path Method

1. Introduction

The critical path method is one of the techniques used in the process 6.6 Develop Schedule.   The procedure of using a forward and backward pass to calculate the early start, early finish, late start, and late finish of the activities is the standard way to find out which activities are on the critical path.   The difference between either the late start and the early start, or the late finish and the early finish, give the float of each activity.  If the float is 0, then this means that the activity cannot be delayed without delaying the successor activity.   If the float is some positive number, say 3, this would mean that the activity can be delayed 3 time units (days, weeks, or whatever your network diagram is using as units of time) before the successor activity is delayed.

2. Critical path method illustration

To determine how long a project will take, you need to find out the critical path, that is, the sequence of activities in the network diagram that is the longest. Other paths along the network will yield sequences of activities that are shorter than the critical path, and they are shorter by an amount equal to the float. This means that activities that have float could be delayed by a certain amount without affecting the schedule. Activities along the critical path have a float of zero. This means that any delay along the critical path will affect the schedule.

Here’s an outline of the critical path methodology.

a. You create a network diagram of all the activities.

b. You label each activity with the duration derived from process 6.4 Estimate Activity Durations.

c. You do a forward pass to determine the early start and early finish date of all activities, from the start of the project to the end of the project.

d. Once at the end of the project, you do a backward pass to determine the late start and late finish date of all activities, from the end of the project to the start of the project.

e. For each activity, you use the results of c and d to calculate the float of each activity.

f. All activities that have 0 float are on the critical
path for that project.

Let’s take a look at the methodlogy in general.

Step 1. For each activity, create a matrix which will contain the duration, the early start, the early finish, the late start, late finish, and float for a particular activity.

 Activity Number Duration Early Start (ES) Early Finish (EF) Late Start (LS) Late Finish (LF) Float

Here are the meanings of the numbers in the boxes:

Activity Number: you can label them A through Z, or 1 through N, just as long as each activity has a unique identifier.

Duration: this is the number that you should get as an output of the 6.4 Estimate Activity Durations process.

Early Start (ES): The Early Start is the number you begin the analysis with to do the forward pass. It is defined as 0 for the first activity in the project. The Early Start for subsequent activities is calculated in one of two different ways, which will be demonstrated below.

Early Finish (EF): This is the next number you go to in the forward pass analysis. It is taken by adding the number in the ES box plus the number in the Duration box.

Late Finish (LF): The Late Finish is the number you begin the analysis with to do the backward pass. It is defined to be equal to the number in the Early Finish box for the last activity in the project. The Late Finish for preceding activities is calculated in one of two different ways, which will be demonstrated below.

Late Start (LS): This is the next number you go to in the backward pass analysis. It is taken by subtracting the number in the Duration box from the number in the LF box.

Float: Once ES, ES, LF, and LS are determined, the float is calculated by either LS – ES or LF – EF. Just remember that a piece of wood will float to the top of the water, so the float is calculated by taking the bottom number and then going upward and subtracting the number that’s on the top of it.

Step 2.

For activity A, the first activity in the project, ES = 0.

 A 0

Step 3.

Then EF for activity A is simply ES + duration. Let’s say activity A takes 5 days. Then EF = 0 + 5 = 5.

 A 5 0 5

Step 4.

The forward pass for activity A is complete. Let’s go on to activity B.

Since activity B has only one predecessor, activity B, the ES for activity B is simply equal to the EF of activity A, which was 5.

 B 3 5

Then the EF for activity B is taken by adding the ES of to the duration of activity B or 3, giving EF = 5 + 3 = 8.

There’s one more situation that we have to discuss and that is if an activity has more than one predecessor.

Let’s assume the durations for each activity are as follows:

 Activity Duration A 5 B 3 C 6

Assume Activity A and Activity B are both done concurrently at the start of the project, and both need to be done in order for Activity C to start. Well, before we do the formal forward pass analysis, what does logic tell us. Activity A takes 5 days; Activity B takes 3 days. Both activity A and B have to be done before Activity C can take place. In this case the start date of the project is considered to be 0. Can Activity C take place on day 3, when activity B is done? No, because Activity A isn’t completed yet, and you need BOTH A and B to be done. The earliest possible start date for Activity C will be day 5, because only on that date will both A and B be done.

So this illustrates the other way of calculating ES for an activity B. If there are multiple predecessors, then the ES is equal to the LARGEST of the ES of the predecessor activities.

Step 5.

Now, let’s assume we are at the end of the project at activity Z.

 Z 5 95 100

EL = ES + duration gives us EL = 95 + 5 + 100. So the project will take 100 days according to our forward pass calculation.

Now, we have the backward pass.

We start this out by stating as a principle that the late finish or LF date for the last activity in the project is equal to the EF date.

 Z 5 95 100 100

Then, of course, the late start date or LS = LF – duration = 100 – 5 = 95.

 Z 5 95 100 95 100

Step 6.

Now we go in the reverse direction towards the beginning of the network diagram, this time filling out the bottom LS and LF boxes for each activity.

If the activity has one successor, then the LF for the predecessor activity equals the LS for the successor of activity. But if there are more than one predecessor activity, then here’s what you do. For the forward pass, you take the highest EF of all predecessors.

For the backward pass, you take the lowest LS of all successors. Let’s see how this works.

Let’s assume the forward pass is done on A, B, and C. We do the backward analysis and we get to the following point. What is the LF of activity A?

 A B C 5 3 4 0 5 5 8 5 9 6 9 5 9

Well, activity B and activity C are both successors of A. In this case, activity B has an LS of 6 and activity C has an LS of 5. The earliest LS is therefore 5, and so LS of activity A is 5.

 A B C 5 3 4 0 5 5 8 5 9 0 5 6 9 5 9

Step 7.

What is the float? Take LF – EF (or LS – ES) for each of the activities.

 A B C 5 3 4 0 5 5 8 5 9 0 5 6 9 5 9 0 1 0

So the float of B is 1, and the float of A and C are 0. Therefore A and C are on the critical path, and activity B is on a non-critical path.   If you needed to compress the schedule, you would do it with activities A and C that are on the critical path.  If you shortened B by one day, however, it would not shorten the overall schedule at all, but would just reduce the float from 1 to 0.

3.  Exam questions

Oh, PMI just loves giving questions on the critical path, and they can be time consuming.  When taking a test with 200 questions, every minute counts, so how can you answer questions on the critical path without having to go through this long and time-consuming process?   HINT:  Most critical path questions can be answered without the forward and backward pass methodology.   How?  Read the next post to find out!

## 5th Edition PMBOK® Guide: Chapter 6: Process 6.6 Develop Schedule

1.  Introduction

The purpose of this process is to put everything together from the first five time management processes and create a schedule model.  This terminology is new with the 5th Edition:  what does this mean apart from the schedule.  There is schedule data which goes into making the schedule, and then there is the presentation of the schedule, typically in the form of a Gantt chart or some other visual representation that is easy to understand.

The reason why it is referred to as a schedule model, it to distinguish it formally from the schedule data and schedule presentation, but to remind the project manager that it is based on assumptions that may change, or risks that may occur during the course of the project.

2.  Inputs, Tools & Techniques, and Outputs
This list of inputs, tools & techniques, and outputs is the most complicated of any of the other five planning processes in Time Management because it is in fact the culmination of all of them.

The inputs come mostly from the outputs of other time management processes, but also include outputs from scope, risk, and even human resource management.

 6.6  DEVELOP SCHEDULE INPUTS 1. Schedule Management Plan Identifies the scheduling method and tools to be used, and how the schedule is to be calculated.  It is an output of process 6.1 Plan Schedule Management. 2. Activity List Identifies activities that will be included in the schedule model.  This is an output of process 6.2 Define Activities. 3. Activity Attributes Provides details to be used to build the schedule model.  This is an output of process 6.2 Define Activities. 4. Project Network Schedule Diagrams Contains the logical relationships between predecessor and successor activities used to calculate the schedule.  This is an output of process 6.3 Sequence Activities. 5. Activity Resource Requirements Identifies types and quantities of resources required for each activity used to create the schedule model.  This is an output of process 6.4 Estimate Activity Resources. 6. Resource Calendars Contains information on the availability of resources.  This is an output of process 6.4 Estimate Activity Resources. 7. Activity Duration Estimates Contains quantitative assessments of the likely number of work periods required to complete an activity.  This is an output of process 6.5 Estimate Activity Durations. 8. Project Scope Statement Contains assumptions and constraints that can impact development of the project schedule model.  This is an output of process 5.6 Define Scope. 9.. Risk Register Identified risks and their characteristics affect the schedule model.  This is an output of Risk Management. 10. Project Staff Assignments Specifies which resources are assigned to each activity.  This is an output of Human Resources Management. 11. Resource Breakdown Structure Provides details by which resource analysis can be done.  This is an output of process 6.4 Estimate Activity Resources. 9. EEFs Scheduling standards Scheduling tool Communication channels 10. OPAs Project calendars Scheduling methodology TOOLS & TECHNIQUES 1. Schedule network analysis Technique that generates the schedule model:  it includes Critical path method Critical chain method What-if analysis Resource optimization techniques and calculates early and late start and finish dates of project activities. 2. Critical path method Through a forward and backward pass analysis, it calculates early start, early finish, late start, and late finish dates for all activities to find the critical path, the longest path through a project which consequently yields the shortest possible project duration. 3. Critical chain method Allows project team to place buffers on any project schedule path to account for limited resources and project uncertainties. 4. Resource optimization techniques Used to adjust schedule due to demand and supply of resources: Resource leveling Resource smoothing 5. Modeling techniques What-if scenario analysis:  used to assess feasibility of the project schedule under adverse conditions Simulation:  calculates multiple project durations based on different sets of assumptions (Monte Carlo analysis) 6. Leads and lags Develops viable schedule by adjusting the start time of successor activities. 7. Schedule compression Shortens project duration without reducing the project scope in order to meet schedule constraints. Crashing:  adds resources Fast-tracking:  activities normally done in sequence are now performed in parallel for part of their duration 8. Scheduling tool Automated scheduling tools contain the schedule model and expedite the scheduling process. OUTPUTS 1. Schedule Baseline The approved version of the schedule model by which performance of the project will be measured.  Can only be changed through formal change control procedures. 2. Project Schedule The schedule baseline refers to the schedule model, whereas the project schedule refers output of the schedule model.  It can be represented in the following ways: Bar charts Milestone charts Project schedule network diagrams 3. Schedule Data Information used to describe and control the schedule: Resource requirements Alternative schedules (best case vs. worst case, resource-leveled vs. non-resource-leveled, etc.) Scheduling of contingency reserve 4. Project Calendars Identifies working days and shifts available for scheduled activities of the project. 5. Project Management Plan Updates Schedule baseline Schedule management plan 6. Project Documents Updates Activity resource requirements Activity attributes Calendars Risk register

The various tools & techniques will take a series of posts to discuss because they are so vital in understanding how a schedule is put together.  Plus, they tend to be favorite topics for PMP and CAPM exam questions, so there is another pragmatic reason for discussing them in detail.

The schedule data, schedule presentations, and schedule model are all outputs of this process.  The schedule model is the schedule baseline, against which the actual performance of the project is measured in the monitoring and controlling processes of schedule management, which are covered in the post covering process 6.7 Control Schedule.  This will be covered after the tools & techniques for this process, starting with the next posts on schedule network analysis.

## History of Christianity: Lecture Four–The Earliest Traditions about Jesus (part 2)

This is a summary of the fourth part of twenty-four in the course on the New Testament presented by The Teaching Company.  The lectures in this course are by Prof. Bart D. Ehrman, the James A. Gray Distinguished Professor of Religious Studies at the University of North Carolina at Chapel Hill.  His expertise is in the Greco-Roman cultural environment of early Christianity and the textual criticism of the New Testament.  For those who are interested in purchasing this course and listening to the complete lectures, please go to http://www.thegreatcourses.com.

This second post contains the last half of this lecture.

6.  Authorship of the Gospels

Why would the fact that stories normally got changed over time have any effect on the Gospels?  After all, they were not written by hypothetical businessmen but by disciples of Jesus and their close followers, in other words, by eyewitnesses and those who knew eyewitnesses.  In fact, the question of the authorship of the Gospels is not that simple.

All four of the Gospels that were later attributed to Matthew, Mark, Luke and John were in fact written anonymously.  These books later came to be ascribed to people named Matthew, Mark, Luke and John:  two of Jesus’ disciples and two friends of his apostles.  Matthew, the tax collector, and John, the beloved disciple, were two of Jesus’ disciples.  Mark, who was thought to be the secretary of the apostle Peter, and Luke, who was thought to be the traveling companion to the apostle Paul, were two friends of Jesus’ apostles.  These attributions of the Gospels to these four men were not originally in the Gospels themselves, but rather arose in the 2nd century AD some decades after the Gospels themselves were written.  There are good reasons for doubting that these ascriptions are accurate.  Even though Jesus and his followers originally spoke Aramaic, a language that is closely related to Hebrew, the Gospels were written in Greek.

Moreover, Jesus’ own disciples, at least according to New Testament accounts, were by and large lower-class uneducated peasants.  According to the Book of Acts, Chapter 4, both Peter and John, two of Jesus’ principal disciples, were known to be illiterate.  The Gospel authors, on the other hand, are highly educated and literate.  In addition, all of these Gospels are written in the 3rd person.  Never does a Gospel author says, “and then Jesus and I went up to Jerusalem.”  These books do not appear to have written by Jesus’ own disciples.  They were later ascribed to apostles by later Christians, Christians who were interested in securing their authority as canonical scripture.  These traditional ascriptions, however, are late and questionable.

Who then were the authors of these books?  We can’t really say, other than that they were relatively highly-educated literate Greek-speaking Christians living several decades after Jesus who had heard numerous reports about his life from the various stories that had been passed down by Jesus’ followers and had written some of these reports down.

7.  Evidence for the Contention:  The Death of Jesus according to Mark

Is there any evidence for this view that the stories in the Gospels were changed over time?  Prof. Ehrman illustrates the kind of evidence that is widely available to scholars by looking at just two brief accounts.  The first account has to do with a relatively simple and minor question:  when did Jesus die?

Before going into this example, Prof. Ehrman has to stress the point that historians have to look at what seems to be minutiae in order to make a big point.  It is like the investigation of a murder case.  There may be a highly significant murder case but the inspector who comes into the room, instead of being aghast at the immensity of the crime, starts looking for fingerprints or strands of hair, which would seem small and insignificant in comparison with the crime that has been committed.  Historians are like that:  they have to look for little things in order to explain something big that has happened, because a little thing may have big implications.

When did Jesus die?  Each of the Gospels narrates the events.  Two of the Gospels, the earliest one, Mark, and the latest one, John, provide the dates for Jesus’ death.  All of the Gospels agree that Jesus died at some time during the feast of the Passover, the annual festival that was celebrated in Jerusalem by Jews to commemorate the events of the Exodus from Egypt.  The festival had as its background the story of God’s deliverance of the people of Israel from their slavery in Egypt under Moses as recorded in the Hebrew Bible in the book of Exodus.  In the 1st Century, Jews would come from all over the world to celebrate this feast.  When they came to Jerusalem, they would purchase a lamb that would be eaten at the celebration in the evening.  The lambs were sacrificed in the Temple in the afternoon before the Passover where the lambs were actually eaten.  The day when the lambs were sacrificed was therefore called the Day of Preparation for the Passover.  It is important to recall that in Jewish reckoning, a new day does not begin at midnight as it does for us, but whenever it gets dark.  That’s why the Jewish Sabbath begins on Friday evening when it gets dark and continues until Saturday evening until it gets dark.  The lambs during the Passover feast then were sacrificed on the Day of Preparation for thee Passover; they were taken home and cooked for the evening meal, and when it got dark it would then be the next day and the lambs were would be eaten for the Passover meal on the Day of Passover.

Let us return now to the Gospel accounts.  In the earliest account of Jesus’ last days, the account found in Mark, the sequence of events leading up to Jesus’ death are clearly laid out.  The day before Jesus was arrested, Jesus’ disciples ask him where he wants to prepare to eat the Passover meal (Mark 14:12).  He gives them their instructions.  That night, in other words, on the Day of the Passover, they have the meal in which Jesus takes the symbolic food of the Passover Feast and instills new significance in them.  He takes the unleavened bread and says “this is my body which is given for you.”  He takes the cup of wine and says “this cup is the new covenant in my blood.”  Afterwards, Jesus goes out to pray.  He is betrayed by Judas Iscariot and handed over to the Jewish authorities for trial.  He spends the night in jail.  The next morning, that is, the morning after the Passover lambs have been eaten, Jesus appears before the Roman governor Pontius Pilate who finds him guilty of criminal charges and orders him executed.  Jesus is taken immediately off and crucified and we’re told when this was:  at 9:00 in the morning (Mark 15:25).  This is a very clear dating of when Jesus died.

8.  Evidence for the Contention:  The Death of Jesus according to John

Our last Gospel, the Gospel of John, also provides a precise dating for the events.  The sequence of events in John is in many ways similar to that found in the Gospel of Mark, but there are striking differences as well.  Here, too, Jesus has a last meal with his disciples, but there is no word of it being the Passover meal.  The disciples in this Gospel never ask where they are to prepare the Passover and Jesus does not speak about the symbolic foods, giving them new significance.  After the supper, Jesus again goes out to pray.  He is betrayed by Judas, is arrested, spends the rest of the night in jail.  The next day he appears before Pontius Pilate and is ordered to be executed.  We are then told precisely when it happens in John 19:14:  on the Day of Preparation for the Passover at 12:00 noon.  How could it be the Day of Preparation for the Passover, when according to Mark’s account, Jesus lived through that day, he had the Passover meal with his disciples that night, and was put on the cross the next morning on the day of Passover itself.  In John’s Gospel, though, Jesus was executed before the Passover meal even began.  How does one reconcile this discrepancy?  Well, it probably can’t be reconciled literally, although people try all the time.  It is worth noting, though, that the Gospel of John, which has Jesus did on the afternoon before the Passover, has him dying precisely when the Passover lambs, the lambs of God, were being slaughtered in the Temple.  Moreover, this Gospel is the only Gospel that refers to Jesus himself as “the Lamb of God who takes away the sins of the world” (John 1:29 and 1:36).  In other words, in John’s Gospel Jesus is identified as the Lamb of God and he died precisely when on the day and at the time when the lambs are being killed in the Temple.  It appears highly probable that John changed the day and the hour historical time of Jesus’ death in order to emphasize a theological point, to show that Jesus really was the Passover Lamb.

This shows that in John’s Gospel we have accounts that have been changed in order to make theological points.  We could show example after example of similar things happening throughout the Gospels, where it appears that you have a story told in two different accounts with differences between them, and the differences make sense in light of the theological views of the authors.  A natural assumption is that this kind of changing of the accounts, which you can show without much doubt in the written texts, was also going on at the oral stages, as people were telling stories about Jesus and modifying them in order to make their points.  Sometimes the Gospels tell different accounts of the same stories precisely because they derive from different oral versions of the same story.

9.  Further Evidence for the Contention:  The Birth of Jesus in Matthew and Luke

You can see this for yourself by comparing almost any two accounts of the same story in the Gospels.  The birth stories of Jesus in Matthew and Luke are a good example.  If you make a list of everything that happened to Jesus at his birth in each of the stories and compare the two lists, you find that the Christmas story that Christians celebrate every year on December 25th is a conflation of these two accounts.  You can see the similarities and the differences between these two accounts.  For example, what was Joseph and Mary’s home town?  If you read Luke, it was Nazareth.  If you read Matthew, it was Bethlehem.

10.  Conclusion

It’s undoubtedly true that the Gospels of the New Testament contain stories about Jesus that are historically accurate, but they also contain stories that appear to have been modified as Christians told and retold the stories over the decades between Jesus’ death and these first accounts of his life.  One of the tasks will be to decide which of the stories in the Gospel represent historically accurate materials, and which ones represent stories that have been modified in the process of retelling them.  Our first task will be to look at the Gospels themselves to see what they have to say about Jesus, to see what their perspectives were.

The next lecture in the series will discuss the first Gospel to have been written, the Gospel according to Mark.

## History of Christianity: Lecture Four–The Earliest Traditions about Jesus (part 1)

This is a summary of the fourth part of twenty-four in the course on the New Testament presented by The Teaching Company.  The lectures in this course are by Prof. Bart D. Ehrman, the James A. Gray Distinguished Professor of Religious Studies at the University of North Carolina at Chapel Hill.  His expertise is in the Greco-Roman cultural environment of early Christianity and the textual criticism of the New Testament.  For those who are interested in purchasing this course and listening to the complete lectures, please go to http://www.thegreatcourses.com.

This post contains the first half of the lecture.

1.  Introduction

The previous lectures have focused on the cultural background of Jesus’ life, starting with the Greco-Roman world and early Judaism.  This lecture starts looking at the New Testament itself, beginning with the four Gospels of Matthew, Mark, Luke, and John.

What kind of books are the Gospels?  Are they historically accurate biographies of Jesus, written by people who actually saw him do the things that he did?  Or are they filled with legends and myths?  Or are they fictions created by his well-intentioned followers?  In short, are they facts or fictions, or a combination of both?

2.  Dates of the Gospels

One way to begin to answer the questions in the last paragraph is to look at some historical data:  the dates that the Gospels were written as compared to the dates of the events that they narrate.  Virtually all scholars agree that Jesus died some time around the year 30 AD.  The Gospels were probably written about 30-65 years after Jesus’ death.  Most scholars are reasonably sure that Mark was the first Gospel to be written, around 65-70 AD.  Matthew and Luke were probably the next Gospels to be written, around 80-85 AD.  The Gospel of John was probably the last Gospel to be written, some time around 90-95 AD.

Most scholars agree on these dates.  What scholars do not agree on is the significance of these dates.  Prof. Ehrman wants to discuss the time gap between the death of Jesus and the first accounts of his life.  This gap of between 30-65 years is significant for our understanding of these earliest accounts of Jesus.  In modern terms, it would be as if the earliest accounts of the presidency of Lyndon Johnson were written in this year.  Some of you may be thinking, that’s not a big time gap because many people remember his presidency quite well, but what if there no written sources between the time of his presidency and the present day?

That would only be comparable to the gap between the death of Jesus and the writing of the Gospel of Mark, some 30-35 years.  What if the gap were as long as that between the death of Jesus and the Gospel of John, some 60-65 years?  That would be the equivalent of someone writing about the Great Depression of the 1930s with no earlier written resources.  This demonstrates that the 30-65 year time gap between the death of Jesus and the writing of the Gospels is significant.

3.  The Significance of the Time Gap

So you can see how the stories propagate from town to town.  But the people who are converting are doing it based on the stories they have heard from people in their own town.  However, these stories cannot have been told by the eyewitnesses themselves, because the religion is increasing geometrically and therefore propagating too quickly to be simply based on eyewitness testimony.  The people who are telling the stories were not there to see these events happen, and they didn’t know anybody who had seen these things happen.  Prof. Ehrman stresses that the Empire itself did not convert to Christianity until much, much later.  But there were pockets of Christians who were starting to emerge in this period in various locales throughout the Mediterranean.

4.  Contention:  stories about Jesus were changed

What happened to the stories as they were being narrated by these people at this time?  Prof. Ehrman’s contention is that the stories got changed as they got told time and time again.  The stories of Jesus were modified as people told them year after year.  Sometimes the changes to the stories would have been purely accidental, just as every story gets changed as it gets told from one person to another.  He relates the children’s game “Telephone” where a group of children sit in a circle and one child tells a story to the next child and so on around the circle.  By the time it gets back to the child who told the original story, it has become a different story.  Imagine playing the game of “Telephone” for 50 years involving thousands of people in different countries using different languages.  Prof. Ehrman says it is reasonable to assume that the story told would get changed.

Sometimes the stories get changed because people wanted to change the story.  After all people are telling stories about Jesus expressly because they want to convert others to believe in certain things and to act in certain ways.  The stories were told to promote faith in Jesus and to promote the right kind of faith in Jesus.  Was it possible that sometimes the stories were changed precisely in order to make Jesus look even better than he did before, or to stress a particular theological point about the importance of Jesus.  There is historical evidence that stories were changed in these ways.

5.  Objections to this Contention

There are objections to this idea that the stories about Jesus were changed as they came to be circulated by word of mouth.  Some people state that the stories could not have been changed in such a short amount of time, especially when there were eyewitnesses around who could verify the account.  The logic behind this objection is that there were eyewitnesses around who would have been able to check to make sure that the stories being about Jesus were correct.  Prof. Ehrman does not put much stock in this objection, however, because it does not take much time to change a story; moreover, the presence of eyewitnesses does not usually have a lot to do with the accuracy of an account.  Stories can change overnight.  Even today, we can occasionally read a newspaper article or hear an account on the radio or television which turns out later to be wrong.  Some of Prof. Ehrman’s colleagues refuse to give interviews on the radio or television because they do not trust that their views will be accurately presented.

As to the other point of the objection, the mere presence of eyewitnesses cannot guarantee the accuracy of an account, especially in a world before mass communications existed.  There’s no way to guarantee that eyewitnesses will be around to guarantee that the telling of a certain story is accurate.

The second objection that people raise to the idea that the stories of Jesus got changed is that in ancient societies which were oral cultures, people had better memories than people do today who live in modern societies which are written cultures.  In other words, people in oral cultures had an ability to tell and recall stories accurately.  Since they had better memories, they had better accuracy when they told stories.

Unfortunately for this view, anthropological studies done in the past 20 years have shown convincingly that this is not the case at all.  In fact, the very concern for verbal accuracy that lies behind this theory is a concern that exists exclusively in written cultures like our own.  It is only in written cultures where one can actually check the accuracy of something that is said.  Since you can check in written cultures the accuracy of something that is said, we believe that statements ought to be accurate.

In oral societies it turns out there is no natural assumption that stories should remain unchanged.  In fact, anthropological studies have shown that the assumption in oral societies is that stories should be changed depending on the audience to whom a story is told.  So it appears that stories were changed as they were told by word of mouth from one person to another.

The next post will contain the second half of the lecture.

## 5th Edition PMBOK® Guide—Chapter 6: Comparison of Estimating Techniques

1.  Introduction

The last post covered the time management process 6.5 Estimate Activity Durations, and among the tools & techniques, which are listed below for reference, are the various techniques for estimating activity durations.

 6.5 ESTIMATE ACTIVITY DURATIONS TOOLS & TECHNIQUES 1. Expert judgment Expert judgment can be used by using historical information to give duration estimates from similar projects.  It can also used to reconcile different estimating methods. 2. Analogous estimating Uses a measure from a previous similar project to estimate the duration or cost of the current project in a top-down approach. 3. Parametric estimating Uses an algorithm to estimate the duration or cost of the current project based on historical data from previous similar projects. 4. Three-point estimating A single-point activity duration estimate can be improved by using the most likely, the optimistic (best-case), and pessimistic (worst-case) estimate for each activity.  These three estimates can be combined by using the triangular or beta distribution formulas. 5. Group Decision-Making Techniques Team-based approaches can be useful for improving duration estimates. 6. Reserve analysis Duration estimates can use “contingency reserves” for risks in the risk register that the “known-unknowns” of the project.

Estimates made by individual experts use the technique of expert judgment (tool #1), and opposed to this are group decision-making techniques (tool #6), which create estimates in a brainstorming fashion by a group.  This post will contrast the three estimating techniques of analogous (tool #2), parametric (tool #3), and three-point estimating (tool #4).  The remaining reserve analysis technique (tool #6) is particularly useful in conjunction with three-point estimating.

2.  Analogous, parametric, and three-point estimating

The reason why I am creating this post is because the PMBOK® Guide definitions of analogous and parametric estimating both use the words “parameters” and I thought, well, there’s a potential source of confusion right there.  So I am going to compare these definitions below to help the reader distinguish between them.

 Estimating Technique Explanation Kind of projects used for 1. Analogous Uses actual duration of previous, similar projects as basis for estimate of duration of current project. Previous activities are similar in fact. 2. Parametric Uses statistical relationship between historical data and other variables. Previous activities in similar in appearance. 3. Three-point Improves single-point estimates by using three estimates:  most likely, optimistic, and pessimistic. Can be used for projects that are new.

Analogous and parametric estimates are examples of top-down estimates, the first being on the basis of the entire project and the second being on the basis of some sort of unit measure (dollars per square foot, hours per line of code, etc.).  They both use historical data, with parametric estimates taking longer, but being more accurate than, analogous estimates.

Three-point estimates are example of bottom-up estimates, which are obtained from analyzing individual work packages.  The single-point estimates are enhanced by using risk analysis to figure out how much each estimate would take in a best-case (optimistic) and worst-case basis (pessimistic).

They are the most accurate of the three techniques above, but they also take the most amount of time to complete.  It is entirely possible that you could use all three techniques in different stages of planning, the analogous and then parametric estimates to get a preliminary estimate, and then the three-point estimates to get a more refined estimate.

3.  Three-point estimates

The three-point estimate relies on three different estimates:

 Estimate Explanation 1. tO Optimistic Based on realistic analysis of the resources likely to be assigned, their availability, and their productivity. 2. tM Most Likely Based on analysis of the best-case scenario. 3. tP Pessimistic Based on analysis of the worst-case scenario

However, they can be combined into the three-point estimate in two different ways:

 Estimation distribution type Expected Duration (tE) 1. Triangular distribution (tO +   tM + tP)/3 2. Beta distribution (PERT technique) (tO + 4tM + tP)/6

The triangular distribution is simply the average or mean of the three separate estimates.  The beta distribution, based on PERT (Program Evaluation and Review Technique), assumes a great deal of confidence that the most likely estimate tM is accurate.  This allows the distribution to give 4 times more weight to tM than to either tO or tP.  The way to remember the denominator of this formula is to realize that there are the equivalent of six terms rather than three in the numerator, if you consider the 4tM to be the equivalent of four terms, tM + tM + tM + tM.

After a brief interlude this weekend, I will continue next week with a summary of the last planning process, 6.6 Develop Schedule, which puts together all of the other five planning processes in the Time Management knowledge area to form the project schedule.

## 5th Edition PMBOK® Guide—Chapter 6: Process 6.5 Estimate Activity Durations

1. Introduction

Once the amount of resources that can be assigned to a project are known as a result of process 6.4 Estimate Activity Resources, then you can estimate the activity durations in the current process 6.5 Estimate Activity Durations.

2.  Inputs, Tools & Techniques, Outputs

The inputs come from previous processes in Time Management, such as 6.2 Define Activities and 6.4 Estimate Activity Resources, as well as from Scope and Risk Management. Risk Management is particularly important when it comes to the three-point estimating which take best-case and worst-case scenarios into account.

 6.5 ESTIMATE ACTIVITY DURATIONS INPUTS 1. Schedule Management Plan Identifies the scheduling method and tools to be used, as well as the level of accuracy used in creating activity duration estimates. 2. Activity List Identifies activities that will need duration estimates. Provides data to be used in estimating the resources required for each activity. This is an output of process 6.2 Define Activities. 3. Activity Attributes Provides data to be used in estimating the resources required for each activity. This is an output of process 6.2 Define Activities. 4. Activity Resource Requirements The estimated activity resource requirements will affect the duration of the activity. This is an output of process 6.4 Estimate Activity Resources. 5. Resource Calendars The availability of the resources will affect the duration of the activity. This is an output of process 6.4 Estimate Activity Resources. 6. Project Scope Statement Assumptions and constraints are considered when estimating activity durations. This is an output of process 5.6 Define Scope. 7. Risk Register Identified risks and their characteristics affect the schedule module. This is an output of Risk Management. 8. Resource Breakdown Structure Hierarchical representation of resources by category and type, typical categories being: labor, material, equipment, supplies. Output of process 6.4 Estimate Activity Resources. 9. EEFs Duration estimating databases Productivity metrics Published commercial information 10. OPAs Project files (duration information from previous projects) Project calendars Scheduling methodology TOOLS & TECHNIQUES 1. Expert judgment Expert judgment can be used by using historical information to give duration estimates from similar projects. It can also used to reconcile different estimating methods. 2. Analogous estimating Uses a measure from a previous similar project to estimate the duration or cost of the current project in a top-down approach. 3. Parametric estimating Uses an algorithm to estimate the duration or cost of the current project based on historical data from previous similar projects. 4. Three-point estimating A single-point activity duration estimate can be improved by using the most likely, the optimistic (best-case), and pessimistic (worst-case) estimate for each activity. These three estimates can be combined by using the triangular or beta distribution formulas. 5. Group Decision-Making Techniques Team-based approaches can be useful for improving duration estimates. 6. Reserve analysis Duration estimates can use “contingency reserves” for risks in the risk register that the “known-unknowns” of the project. OUTPUTS 1. Activity Duration Estimates The duration estimates may include a range of possible results. 2. Project Document Updates Activity attributes Assumptions made during the activity duration estimate

The tools and techniques are varied in terms of complexity and accuracy, and a comparison of these techniques will be taken up in the next blog post.

The outputs of the activity duration estimates are used directly in the next and final planning process for Time Management, 6.6 Develop Schedule.