Control chart is a mechanism to understand process behaviour, predictability and stability over time. We do understand that any process has a certain amount of natural variability, but how can we tell if the process’s variability has gone “out of control”?

Control chart is a tool used in “Quality Control” for inferring an unplanned change has taken place in a process measured by a process continuous variable X. Example process variable could be but not limited to, like waiting time at a fast-food restaurant or at an airport check-in counter, schedule and cost variance over iterations, volume and frequency of scope changes over iterations, and other repetitive project management processes.

Control chart are normally developed for processes which are repetitive in nature, and expectation are set to perform around continuous process variable X.  A repeatable process is one in which process do the same thing in same way and produces the same results.

PMBOK® Guide Sixth Edition  defines Control chart as:

### “A graphic display of data over time and against established control limits, which has a centreline that assists in detecting a trend of plotted values toward either control limits”

A control chart has following components:

1. Centre line: Centre line in control chart is shown as desired ideal capability of a process. This is a graphical depiction of continuous process variable X. Centre line is the calculated mean of data points which are repetitive process output with time.
2. Specification limit: Specification limits are established normally after analysis of customer expectations, sometime mentioned in agreements. Penalties may be associated if data points exceed to specification limit.
3. Control Limits: Upper and lower control limits are established for the control chart and normally using statistical analysis or from historical records. Data points of a process are plotted to perform trend analysis toward either of control limits and with respect to centre line.

For repetitive process, the control limits are generally set at +_ 3 sigma around a process variable X or process mean i.e.  Centre Line. Upper control limit is drawn at 3 standard deviations above the process mean and lower control is drawn at 3 standard deviations below the centre line or process mean.

These limits are established to predict if process needs corrective action to bring process performance in line with needed stability and capability. Analysis of data points with centre line and control limits help us to prevent unnatural process performance with time. Control limits are more stringent from Specification Limits so that corrective actions are taken before data points start to reach towards specification limit.

Graphical representation of Control Chart Components:

How to determine process is “In Control” or “Out of control”:

Samples of data points as process output are taken and plotted over control chart, and then analysis is performed about how these data points are presented with respect to centre line and upper & lower control limit. Emphasis is to understand whether data points are within acceptable limits.

Data points within +- 3 sigma are thought as “in Control”, and within acceptable limits excluding the rule of seven (described later). Data points are within +-3 sigma means these data points are not crossing either of control limit. Anything beyond control limit requires investigation.

When 7 consecutive data points are presented on either side of mean, then “process is considered Out Control” based on heuristic of Rule of Seven.

In this case although data points are not crossing control limits but as repetitive process is not generating random output and this may be signal of problem in a process. Efforts are put to understand the situation and root of process problem.

In short, Process is considered out of control when data points are outside the upper or lower control limits and/or seven consecutive points are plotted on either side of mean i.e. center line. We need to investigate both of special cause variance.

Development of Control Chart:

As I mentioned earlier that control charts are used to show whether a repetitive process is “in control” or “out of control”, I am taking an example of a process to test repetitive weekly builds. On an average Friday EOD we need to finish weekly build. Now we need to understand the acceptable range, observations states that sometime we get late by 1 or 2 days and sometime build gets finish early by a day.

Process Owner may accept build within 1 day late or early, but mathematically how we can say that acceptable variation would be one day or two days?

And if any week builds are finished at a point, where need of corrective action is identified; control chart is used to understand mathematic identification of control limits and need of corrective action.

Suppose we have collected 30 weeks of data to understand whether or not process output is within acceptable limits.

Now we need to calculate average of slippage in build for 30 weeks: Average of slippage of data points in days i.e. 0.73 days.

Now Standard deviation is calculated, standard deviation means how much variation from the average:

σ = the standard deviation

x = each value in the population

x̄ = the mean of the values

N = the number of values

Using above formula standard deviation will be 5.132273364.

In order to get control limits we need to multiply standard deviation with 3, in this case 3 sigma value will be 15.39682009.

Now it is time to calculate upper and lower control limit:

Upper control limit will be addition of 3 Sigma and average slippage in weeks i.e. addition of 15.39682009 and 0.73. As a result we will get 16.13 as upper control limit

Lower control limit will be subtraction of 3 Sigma from average slippage in weeks i.e. subtraction of 15.39682009 from 0.73. As a result we will get -14.66 as lower control limit

As to summarize:

Here 3 Sigma is equal to 15.39682009, Average mean of slippage in days is 0.73 days, Upper control limit is 16.13, and Lower control limit is -14.66.

Now finally control chart can be developed using 2D line graph plot:

Control chart (x) using mean + 3 sigma and mean – 3 sigma control limits

Now analysis of chart needs to be performed, and noticed that there are two data points (two weeks) which are beyond the control limits and that is what we need to do investigation further. As I mentioned earlier that control limit help us to determine that whether or not corrective action are in need. When data points are beyond control limit, it shows that variability is not natural.

Analysis of standard deviation and control chart states that we have such a poor variation that may be 15 days late or early, we need to investigate root of the problem and here we can use other tool like “Cause and Effect” diagram, “Pareto Analysis” for the same. After root cause analysis and taking corrective action, we can draw the control chart again and removing the special causes (the two weeks) and finds out whether variation is reducing with time.

One important point is that as we need to remove special cause i.e. two weeks, we may chose brainstorming tool to understand what events held during those two weeks that are contributing to special cause variation. In agile methodology this can be done as part of Iteration retrospective. In this case objective of iteration retrospective would be to determine what needs be done to bring testing process under control.

Usage of Control Chart:

Control Chart is used in “Plan Quality” to understand what is needed to make sure that processes which are repetitive in nature will produce results within acceptable limits. Process improvement plan are developed accordingly. Quality policies are refined to get the desired output and metrics are defined to measure the process performance. Historical records of control charts plays an important role in development of process improvement plan, quality management plan and quality metrics.

Control Chart is used as a tool and technique during “Control Quality” to understand whether repetitive process producing results within acceptable range and in random manner, if not then investigation need to be performed to remove special cause variation.

In short, control chart is an effective tool to understand whether process is stable with time and producing results within acceptable limits and in random manner.

I hope this blog has sufficiently answered your all queries related to Control Chart. Good Luck with your PMP® Certification Exam.

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