Tuesday, 13 October 2015

The Purpose of Project Control

The purpose of the project control or implementation phase is four-fold:

  • To observe the work in progress.
  • To ensure that it follows the plan sufficiently closely.
  • To understand the underlying problems when it does not.
  • To take appropriate action when necessary.

The Medical Analogy
The whole process is not very different from the case of a medical doctor presented with a patient with symptoms. The doctor examines, compares results with expectations (as provided by medical science), diagnoses illnesses and prescribes treatment.
Project managers play the doctor role, examining the project (patient), looking for symptoms (poor progress, excess expenditure, time delays), seeking reasons (inefficient or absent resources) and administering antidotes (extending durations, providing additional resources).

In the project management context, the four steps mentioned above are:
1. Monitoring
2. Tracking
3. Interpretation
4. Taking corrective action

Monitoring requires continual observation and measurement of the 'actuals', that is actual starts and finishes, actual effort, actual progress and efficiencies. It requires a systematic reporting system involving the participation of team members who provide feedback on a periodic basis.  It is akin to a doctor taking one's blood pressure.

Tracking involves the ongoing recording and comparison of these 'actuals' with the plan, searching for significant departures as an early warning of problems. Only by maintaining an ongoing record of results can trends and patterns be detected. The table below shows a typical representation of data collected for a given progress measure for a particular task.  These are shown in the 'Actual' column.  The 'Baseline' shows the originally forecast values while the 'Forecast' (which means the current forecast), while it must agree with the actuals (there being no better forecast than the actuals when something has already happened), projects into the future values which take into account what has happened to date.    Tracking is the act of monitoring and comparing on an ongoing basis, much the way a doctor would take more than one reading of blood pressure, perhaps even over several days or weeks before acting.












Interpretation is the attempt to understand why deviations from the plan are occurring. This is analogous to a medical officer reading an X-ray image and arriving at a diagnosis.  This can be assisted by certain reporting parameters which are designed to indicate possible reasons for emerging problems.   These include Earned Value analysis and critical ratio analysis, topics to be covered in future articles. In this case the actual values recorded are trailing the baseline (originally predicted) values somewhat consistently, indicating an ongoing problem regarding the rate of work.

This could be due to lack of skill, greater resistance encountered on the job, or a mis-estimate of the work originally. The forecast column indicates that at roughly current rates, the task will run late. The last row also indicates that additional work will be required for the task.

Finally, taking action means moving in a manner to modify the current forecasts - the administering of medication.  In the project context, possible actions could include adding resources, extending durations or deadlines, overlapping tasks formerly arranged in sequence, changing the team or even modifying the nature of the task.

Taking Corrective Action Part 2

We continue with our examination of the corrective action alternatives that are available to a project manager when progress begins to lag behind expectations as shown in the diagram below. In the previous article we looked at the implications of extending the duration on the first task, leading either to a delay in the project finish or at least a reduction in the amount of contingency available.

Option C: 

Overlap some tasks.This is a popular method since it saves time but may not add to the cost. However, we might ask after the reason for the presence of the planned predecessor for task 2 in the first place - given that we now seem willing to dispense with it. What was its importance and what is implied by its omission? These questions need to be considered before we simply overlap tasks. The other disadvantage is that if the same resources are required on the now overlapping tasks, a conflict is caused and this would have to be resolved.
Option D: 

Modify the methodThis simply suggests that we tackle the task differently, even though it has already started. This might involve the use of better processes, more appropriate technology, higher skilled people or a total re-think of the overall approach. Of course it would have been better to identify these improvements earlier but we will exploit good ideas whenever they strike us. The method is too general to lay out specific consequences but they could include delays while we procure equipment or train staff, cost-overruns incurred in that procurement or training, the need to gain approvals for the new approach - among many other possibilities.

Option E: 

Add Resources (Crashing)To crash a project means to add resources to one or more critical tasks in an effort to shorten their durations leading to a contraction of the entire project. The primary consequence here is of course a cost increase. This is due to a variety of factors. The time reduction is rarely inversely proportional to the resource increase (the law of diminishing returns) leading to inefficiencies and hence cost increases. Also, as teams grow there need to be additional supervision, catering, transport and other services that incur new costs. The source of these additional resources may also become an issue. Are they available? Do we draw them off other projects that will then suffer from their absence? On the other hand, if we plan to make use of the same people in the form of overtime, do we risk their fatigue leading to potential safety or quality problems?
The question may then arise as to which task to crash. Planning to wait until the last task might be risky, while crashing the first one might not achieve acceptable results as it is already partially complete. We might rather select task 2 and use the interval before it starts to identify and prepare the additional team members so that they will be performing to maximum productivity on that task. This case is shown in the diagram below. We therefore plan to allow it to start late but finish on time, thereby preserving the original project end date. 

Option F: 

De-ScopingThis usually means doing less, delivering a smaller slice of the deliverable (and consequently associated project benefits) than originally promised. This of course should not be done without negotiation which again has consequences in terms of quality, client expectations, credibility and professional reputation.

Options G: 

Motivate the TeamIf we look after our team members in the good times they might just look after us in the bad ones! Appealing to their sense of loyalty and commitment to the project and the organisation might yield additional effort in well-led teams. Of course there is a penalty. We are consuming goodwill which will need to be replenished by acknowledgement, reward, time-off or other means.

Taking Corrective Action Part 1

So far in this series of articles on project control, we have used a medical analogy to guide our approach. We began by showing that all maladies on a task can be attributed to one of four types of problems, or a combination of them. Then we formulated questions, much the way a doctor would, in order to determine which of these offer the most likely source of what ails the task.

In this article, we turn our attention to the types of actions project managers take in order to solve problems. Unfortunately, again like medical treatments, these can often have side-effects. Therefore, when contemplating which line of action is the most appropriate, the project manager is thrust into a classic decision-making situation in which he or she is required to consider options, examine their associated consequences and pick the alternative which in some sense minimises the potential damage to the project.Let us examine a typical situation. Consider the diagram below:
The lower bars represent the baseline (i.e. the original plan) while the upper reflect the current best forecast. At present these agree. Now imagine that half of the planned duration of the first task has elapsed and that we are told that the job is only 30% complete. Notice that we have allowed a contingency period between the dates of scheduled and promised completion.If we expect the progress measure to run proportionately with time, then it appears that we have a problem. Of course we don't always jump to action. It may be that the best alternative at present is to nothing and wait for developments. However, if things don't improve of their own accord, we shall at some stage wish to intervene.

In attempting to identify the most appropriate action, it is always important to determine the nature of the problem caused. This is why we ask the questions we do at each update period (see previous article). However, this does not always indicate how we should solve it. After all, it might be that our choices are constrained by external factors such as availability or time and we may simply need to fix things as best we can given these factors.The following is a selection of potential actions and their corresponding effects. It is not possible to identify the 'best' option without considering the circumstances and context in which a particular project is taking place. We present them only to stimulate thought. Of course you would have to weigh up their relative merits and select what appeals most to you. Or perhaps you can come up with actions of your own.

Option A:
Extend the Task Duration We may choose to lengthen the task, i.e. allow the team more time to complete the work. The situation is described in the diagram below. However, the move could lead to a number of problems. Firstly, the team members scheduled to work on succeeding tasks (tasks 2 and 3 for example) would now need their commitment to the task to be extended but they may not be available for the extended part and would have to be replaced.If they are available, there is the possibility that the tasks on other projects they were otherwise scheduled to work on during the new dates would be left without resources, leading to disruptions and delays there. Also, extending the task duration might mean that additional effort (relative to the baseline) is required to be expended, implying an increase in costs. Finally, we are required to consume some of the contingency time we had made available to the project, thereby making it a little bit less secure.

Option B: Extend the DeadlineIn this case, we assume that no contingency was allowed at all and so we are required to advise the client or other affected parties that the project finish date would be delayed.

In this case all of the negative implications discussed under option A would apply with the additional inconvenience to be experienced by the client as well as the probable loss to our credibility and professional reputation.

Using Critical Ratios to determine project health

Earlier in the series we saw that the purpose of monitoring progress on a task is simply to ensure that it performing according to expectations.  These are set by the plan, specifically the baseline that represents the original forecast for the schedule, the cost, the use of resource and the delivery of quality.  Where performance deviates from those expectations we need to identify and understand the causes.   We saw in an earlier blog (link) that these causes are confined to a handful of broad areas, involving the productivity of the resources, their rate of attendance, and the punctuality of the start.  Of course these can each be analysed to reveal a variety of sub-causes which will need to be addressed.  Also, the deviations could also be due to an expansion or contraction of the scope which we will handle at the end of this post.

It is important that monitoring is performed at the lowest level available in the WBS, that relating to tasks or activities.  This is where the data is most precise and the focus most clear.   Individual task performance may itself not be of much interest to stakeholders who are probably after similar reporting at higher levels of the WBS.  However, the accuracy available there is achieved by aggregating the results recorded for their constituent individual task behavior.  Hence we cannot do without a careful analysis of task behavior. In what follows, we introduce measures designed to reflect the degree to which the broad causes mentioned above are responsible for any deviations from the baseline. 

Consider a case where it is reported that we have achieved 30% of the actual progress on a task, measured in some appropriate way.  We shall call this the ‘Actual Progress’ or ‘AP’.  To be more precise this is the Actual Progress (to this date) from the point of Actual Start. Suppose further that we know from the baseline data that we ought to have achieved 50% completion by now – that is had everything gone according to plan.  We shall call this figure the Baseline Progress or BP, which can also be described as the Planned Progress (to this date) from the point of Planned Start.   A natural way of quantifying this situation is to form the expression for what we shall call the (overall) Schedule Factor SF by means of the expression   


 Clearly a value of 1 for this ratio would indicate that the task is performing according to expectations while if it rises above 1 performance is better than expected.   In the case we are considering, the value computes to 30%/50% or 0.6 which indicates that problems exist.   

Defining a Punctuality Factor ratio
Let us first examine the case where the entire reported progress deficit is due to the late start.  This implies that there are no problems in the implementation of the task itself once it has got going.  Put another way, ignoring the late start, 30% is precisely the progress we should have expected at this stage.  Let us call this the (currently) Expected Progress (EP), that is, the progress currently expected ignoring the effects of an early or late start.    Alternatively we could say that the EP is the Planned Progress (to this date) from the point of Actual Start. The situation would appear as shown in figure 1.
Note:    Since the measure of progress should relate to some quantitative or qualitative indication of output produced relative to the total expected, there is no particular requirement that it accord with the proportion of the task duration that has already expired.  That is, progress is not assumed to be linear with time.  It follows that in general the progress bars shown within the task bars are not necessarily expected to coincide with the reporting date.  

It seems reasonable then to describe the effect of the late start, a value we shall call the ‘punctuality 

factor’ (PF) as again giving a value of 0.6 which provides a full account of the overall schedule deficit we saw in equation (1) since we are assuming no problems were found in the implementation of the task.   

Defining a Duration Factor Ratio
Note the difference between ‘Actual Progress’ and ‘Expected Progress’.  The former represents what we have actually achieved while the latter reflects the performance that should have been achieved, ignoring variations in start times.  In the case we are considering they are numerically equal because we are assuming that all of the delays can be attributed to the late start.  This suggests that a ratio describing the performance of the task itself, expressed in terms of the health of its duration prospects relative to the original baseline forecast, sh should be

 Again, this compares, to this date,  the Actual Progress compared to the Planned Progress, both measured from the point of the Actual Start and in this case gives a value of 1 indicating that all is proceeding according to plan on the task itself, late start notwithstanding. Now let us suppose that the delayed start does not fully explain the deficit and that problems were found in the implementation of the task. Consider the case below where Actual Progress is only 20%, and since the Expected Progress is 30%, on current trends the task duration itself will be extended and add further delay to that expected due to the late start.

Figure 2:  Schedule deficit due to delay and productivity loss
Here we find the DF equal to or 20%/30% = 2/3 indicating that if current trends continue, an extension in duration would result. From our definitions of SF, DF and PF it is clear that     
so that SF = 2/3 * 0.6 = 0.4 

Equations like (3) reveal the entire point of this analysis.  It is one thing to know that the task if falling behind (0.4 being a very low ratio compared to 1), but quite another to understand its underlying causes. The decomposition of SF into its two constituents provides the means for understanding their relative contributions to this poor state of overall schedule health.   Specifically, overall schedule performance is seen to consist of two effects, the duration and punctuality performance.   This makes sense.  How well a swimmer performs relative to the overall time expected in a race depends upon both the quality of the start at the gun and of performance across the pool.   This sort of analysis provides swimming coaches and project managers with valuable insights into the causes of variations from the expected.

Note that from equation (3) we can see that the duration and punctuality factors can compensate for each other.  For example an SF value which would otherwise suffer from a late start of say PF = ¾ could be rescued by a task performing better than expected by a factor of 4/3, restoring it to a value of 1 or par.  On the other hand, these two effects can re-enforce each other.  An early starting task (say PF = 4/3) along with this good task progress performance would provide a very healthy overall schedule factor SF of 4/3 * 4/3 = 16/9 = 1.77. 

Defining Attendance and Productivity ratios
In a very similar way, we can break open the Duration Factor measure in an effort to understand the factors that influence it.  Clearly one such factor would be the degree to which resources are working on the task relative to what was expected in the baseline.  Following our definition of DF, let us define an Attendance Factor ratio as


where Actual Effort reflects the actual hours recorded and Expected Effort those that should have been recorded (if all human resources scheduled in the baseline plan had shown up for work) both since the point of Actual Start. 

Let us suppose that this ratio is found to be 0.8, implying that there was a 20% loss of resources.  Assuming that the size or scope of the task has not changed (a factor we shall treat later), any departures of DF from unity not explained by this absenteeism can only be attributed a drop in productivity – something we shall call the ‘Efficiency Factor’, (EF).  Consider the ratio

 From equations (2) and (4) it is evident that

 which can also be written as

Now we know that the Progress/Effort ratio is a measure of productivity or efficiency and so EF can be interpreted as the productivity compared against that expected in the original baseline forecast.  It follows that   
The dependence of duration on productivity and resource attendance is true for all productive processes.  For example, economic output is measured this way.  Similarly, a swimmer’s progress across the pool is a function of the productivity of each stroke (distance achieved by each) multiplied by the number of strokes (resources inputs). Of course, as we saw, her overall time (schedule performance factor) would also be affected by any late start compared to other racers. This is confirmed when we combine equations (3) and (5) to produce     
In our example, we therefore have


In this case the poor schedule performance is due to three factors all performing badly.  The task started late, has lost resources and those that have worked have done so at below-par productivity. 

Equation (6) therefore illustrates the main constituent factors contributing to schedule performance and allows us to see the relative responsibilities that each has to any divergence from the expected value of 1. 

Relationship with Earned Value
Readers familiar with Earned Value Analysis (EVA) methods will see some similarities in the process described above.  The obvious differences lie in our focus on work hours rather than costs which dominate the EVA approach.  We also introduce additional factors such as DF, PF and AF for which there are no equivalents in EVA, although these could be very easily introduced as discussed in our paper delivered to the Australian Institute of Project Management Conference, Canberra, October 2008 entitled ‘Towards a Complete Earned Value Analysis’. Where the two systems overlap, it is clear that our value for EF is analogous to the CPI (cost performance index) in EVA, representing a cost efficiency factor and SF is analogous to SPI (schedule performance index), representing a time efficiency measure.   

The Effects of Scope Change
One of the additional factors introduced in our paper related to the effects of scope change.  It is clearly possible to be falling behind on progress relative to a scope that has grown since the baseline was set, without being formally recognized in that baseline.  In a treatment slightly different from the one we gave in that paper, we could introduce a measure M to reflect the magnitude of the work to be completed according to the baseline.  This could be measured in relevant units depending upon the nature of the task.  If M’ is the new size of the task, resulting from a change in scope, we could introduce the factor KF = M/M’ to reflect this.  We can now modify the SF value in (6) to become

Thus if M is greater than M’, reflecting a situation of scope creep or some other mechanism for its increase, KF is smaller than 1 and SF is further reduced.

Estimating Durations - A General Framework Part 2

A Framework for Estimating Task Durations

In this post we shall construct a framework to host the duration estimate and it to the painting task discussed in the previous post.  However here we will take a more general approach, identifying the building blocks that will provide the platform for all estimates.  The chief characteristic of our framework is that it explicitly recognises and identifies the major factors that will influence the duration.  These are:
a)      The size of the task.
b)      The availability and productivity of resources, both human and equipment or materials.
c)       Interruptions and delays from both within the task and without.
Let’s examine these in the context of the paint job, but this time slow down the calculations a little, making some refining modifications as we go.
The task size was given as 450 square meters to paint (3 coats for a 150 square meter space – assuming that each coat requires the same effort.   There we had
Effort Task Productivity
Let’s assume that this calculation was made on the basis of using a short-handle brush for the entire job and suppose further that longer-handle rollers can increase productivity by 10%.  We can incorporate this into our model by introducing a materials resource factor (MRF) which here would be 1.1 giving us
Effort Task Size equals 35 work hours 01
where we have rounded the result up to the nearest whole number.
Let us further suppose there is now a full time and a half-time painter are available up to do the work, giving us a crew size of 1.5 full time equivalents (FTEs).   To convert effort to duration we needed to consider the number of painters available per unit of duration, which we will call ‘attendance rate’.   The relationship between duration and effort is given by the general expression;
Effort Driven Duration
Where was this step in our initial presentation of the problem?  In that case there was only one painter and then, as is clear from the above equation, effort and duration are numerically equal although they have different units of dimension (work-hours vs hours).  This part of the duration may be thought to represent ‘effort driven’ effects.  Now we have
Effort Driven Duration equals 24 hours
which has been rounded up as always.
It is important to remember that by adding to the team size (attendance), we could have some (possibly negative) effect on the productivity. This is the ‘law of diminishing returns’ effect.  On the one hand, perhaps there is some synergy between the two individuals which would raise this value and therefore reduce the effort while on the other hand they could provide obstructions to each other, thereby lowering the value and increasing the effort required.  Also, there could be a difference in their relative skills, requiring us to use an average value to reflect this.  In our example we will use the original productivity.
Remember that we added half a day (say 4 hours) for various small but important sub-tasks, which we will call ‘time-driven’ effects since they are expressed in the form of additional duration.  This gives us a new value of 28 hours and with a half-day allowed for contingencies giving us a final result of 32 hours.  At seven hours per day, this is approximately 5 days.   In general then we have
Effort Time effects contingencies
Formally by combining the general formulae above we obtain
Duration Task Size Contingencies
From now on, we shall combine all of the time effects, including contingency, call them ‘External Factors’ and simply write
Duration Task Size External Factors
This provides not just a formula for calculation but a framework to guide our thinking.  All duration estimates can benefit by this kind of systematic thinking.
As we hinted in the previous post, the major challenge is bound up in defining the size of the task.  We are almost ready to tackle this hurdle in the posts that follow.

Estimating Durations - A General Framework Part 1

Estimating Durations

As project managers, we are expected to provide competent forecasts for a whole range of activities in each of our projects without necessarily having the degree of subject expertise that specialists can command.   Yet the influence of duration estimates, in particular, plays a vital and central role in the project plan.   From the diagram below it is clear that they affect both cost and schedule and therefore cash-flow.   However, they also influence the number and timing of the resources required.  Given also that resources are frequently shared across projects, poor estimates begin to affect areas outside of the project.  Pressures of time also lead to increased risk and reduced quality.  There is also a psychological aspect.  Teams and clients are happier when the schedule is relatively robust and a sense of stability and control is felt.  Poor estimating can produce the opposite.
(Click diagram to enlarge)
Effects of Duration
Estimation is therefore a fundamental source of error in the planning and control of all types of projects.   In many industries, it is seen as particularly difficult, a view that often causes it to be reduced to guesswork.  While the complexity of duration estimation is beyond question in many types of work, rather than leading to an attitude of resigned ignorance, this should stimulate a serious attempt to adopt a rigorous and diligent approach toward reducing the kind of errors typically made.  What we need is a general framework and a process both of which can be applied universally.  The development of these is the focus of this chapter.  Before embarking on this, however, we shall review the common errors made.
In this series of posts, we will introduce a general framework for estimating all task durations.  It will focus on the key parameters and provide a process which can be followed each time, using appropriate degrees of detail, accuracy and precision.
To begin with, we will examine a fairly straightforward case.  Consider the single task of painting a 150 square meters of wall space in a room, with three coats needed.  Although there would be associated activities within the larger project such as preparation and procurement, the durations for these would be estimated separately.  Suppose that we have discovered that a single painter has a productivity of about 12 square meters per hour worked, allowing for climbing, ladder-moving and taking care of parts near corners, windows, floors and ceilings.  This tells us that this painter would require about 37.5 work hours of effort to complete the job (450 square meters including the three coats divided by 12 square meters per hour). Suppose there is only one painter available for the job.  The ‘effort-driven’ component of the duration would therefore be approximately 37.5 hours, which at 7 hours per day of activity would require almost 5.5 days.  However, there would be some additional sub-tasks required, perhaps removing and restoring furniture and protecting floors and perhaps some brief time-consuming non-activity such as allowing the paint to dry between coats.  While these could be incorporated by means of a slightly lower productivity rate, we shall treat them as ‘time-driven’ effects choose to add half a day hours of duration to our result to account for them.  Finally, we should allow for some contingencies such as problems with access and other unexpected obstacles – make this a further half day giving us a total of approximately 6.5 days of duration.  This is summarised in the diagram below.

Diagram of estimate calculations
It is not hard to see that this process can be generalised for any type of duration.   This we shall do in the next post.  The biggest challenge will be we shall face is to define suitable output units in non-physical type of tasks, those that involve work such as design, writing, research, analysis and software development.  We shall deal with that challenge in posts to come.

Diagnosing Project Problems

In the previous article in this series on Project Control, we saw that a useful analogy can be made with problems of diagnosis encountered by a medical doctor. In this case, the project manager is the doctor, the project is the patient and the symptom may be 'slow progress'.
For example, when a doctor faces a patient with a temperature, he or she has certain hypotheses in mind as to what could be causing this. There might be several typical causes and a doctor would know this from training and experience. In the same way, we as project managers, faced with a report of 50% progress on a task that has consumed 75% of the allotted duration and 80% of allotted resource hours, would use our background and experience in order to understand the cause.
This is not as difficult as it sounds. For while there could be thousands of specific reasons why the task is behaving the way it is, it can be shown that there are only four types of reasons for this behaviour. This provides a very good starting point in trying to understand the problem before we can fix it.
We call this the SEAM method to help remember the four types. They are:
  • Start Variation
  • Efficiency
  • Availability
  • Measure Problems
Let us examine these one by one:
Start Delay
This one is easy and obvious. In general it is possible that a late start to the task has contributed to the poor progress shown thus far. It is also possible that the problem is not even at this task. Some previous task, perhaps even in some other project may have been delayed, causing our team to delay their start on our task. This is worth knowing.
This type of explanation for poor progress is wide and varied. We are thinking here about a drop in the expected rate of production, regardless of what it is this task is producing on its way to completing its deliverable.
It may be square meters of wall space painted, chapters written in a major report. The team doing the work have either not quite sufficient skill, have encountered unexpected resistance to the work (heavier materials, more complex research matter), or perhaps have found conditions to be unexpectedly difficult.
The word 'unexpected' here reveals why we package these productivity or efficiency problems under the heading of 'estimating'. For we, the project manager, are ultimately responsible for anticipating these problems. This does not mean we are being clever in hindsight. Estimating is difficult and we are not beating ourselves up over this. Prediction is difficult. This is the future we were talking about. Nonetheless, there is no point in evading the issue. We simply wish to understand the nature of the problem, document it, revise our estimate, and have this become part of our corporate memory so that we shall do better in future.
This seeks to link the drop in expected progress to a drop in expected resource numbers actually working on the job. We may have lost some of the team due either to illness, the need to attend to higher priority tasks or similar reasons.
Measure Problems
The final possible explanation for the apparent slow progress might be that it is just that - apparent only. For it may be that the way in which progress is being measured does not necessarily reflect the way the work is going.
The measure we are using may be one that does not move at a constant rate with time. For example, the team may take a little time to settle down, conquer a learning curve, or perhaps spend the first few days on the task doing important, necessary preparatory work that does not show up in the 'score'. Perhaps they spent the first day on a writing job doing important research but wrote nothing.
If the measure of progress used was number of sections written or something similar, we can see that this is not an adequate measure although it may be the best one available. In short, there may not be a problem. If the team thinks it can finish the task in the allotted time, we can put down the apparent progress degradation to the difficulty in measuring.
Therefore, as a first step, we need to establish which of the SEAM explanations best supply a cause for the specific task we are examining (there could be more than one cause of course). This is done by means of further examination and well aimed questioning. Armed with this guide, we can investigate the specifics of the matter in a more focused manner, identify the appropriate treatment, conscious of the likely associated side effects. Just like our doctor friend.
These are issues which will occupy the next articles in this series.