Control Chart as a Component of Seven Basic Quality Tool

A control chart, a valuable quality tool in the PMP exam, helps us gain insights into the behaviour, predictability, and stability of a process over time. While every process exhibits some inherent variability, it is crucial to identify when this variability exceeds acceptable limits, and the process goes “out of control.”

So, in the context of the Project Management Professional (PMP) exam, a Control Chart can be defined as –

A visual display of data over time against established control limits. In addition to the control limits, the control chart incorporates a central line (depiction of the mean value) to facilitate the identification of trends. Chart shows how the plotted data spreads across the centerline and if these data approaches the control limits. When data points fall outside the control limits or show a lack of random output in a repetitive process, it reflects a deviation that needs corrective action.

 Control charts allow project managers to detect and address any unexpected deviations or changes, enabling timely intervention to maintain quality and stability. These are primarily used to monitor the output variable of repetitive activities, but they can also track cost and schedule variances, among other factors.

In addition to control charts, there are several other essential quality tools that project managers can explore. For further information and insights on these tools, you can refer to the following series of blog posts:

1. Histogram As A Component Of Seven Basic Quality Tool
2. Check Sheet as a Component of Seven Basic Quality Tool
3. Pareto Chart – An Effective Graphical Tool to Resolve Problems
4. Scatter Diagram: Scatter Plot and its Development
5. Flowchart as an Integral Component of Seven Basic Quality Tools
6. Cause and Effect Diagram- Fishbone Diagram Analysis

These resources will provide detailed insights into each tool, its purpose, and how they can be effectively utilized in project management.

In control charts, a process continuous variable X measures if the process is out of control. Now, let’s see what could be the examples of continuous variables (X) related to the control chart:

1. Waiting time at a fast-food restaurant or an airport check-in counter: This variable measures the time customers spend waiting in line before they are served. By tracking and analyzing waiting time data on a control chart, we can evaluate the efficiency of service delivery and identify any significant deviations from the expected waiting times.
2. Schedule and cost variance over time or iterations: Monitoring a project’s schedule and cost variance allows us to assess how the actual progress and expenditure compare to the planned values. Project managers can identify trends, patterns, or outliers that indicate potential issues or opportunities for improvement by plotting these variables on a control chart over time or iterations.
3. Volume and frequency of scope changes over time or iterations: Changes in project scope can impact the project’s timeline, resources, and deliverables. By tracking the volume and frequency of scope changes on a control chart, project managers can evaluate the stability of project requirements and assess if excessive or unexpected changes are occurring. This helps in managing scope creep and ensuring the project stays on track.

Using control charts for these variables visually represents the process behaviour. It helps detect when the process variability exceeds acceptable limits, indicating the need for corrective actions or adjustments.

Control charts are typically developed for processes that meet the following criteria:

1. Repetitive production of manufactured lots: Control charts are particularly useful for processes that involve the repetitive production of items or lots. This means that the process is characterized by consistent and repeated production cycles or batches.
2. Expectations of performance around a continuous process variable (X): Control charts are designed to monitor and assess the performance of a process based on a continuous process variable, denoted as X. This variable can be a measurement such as time, dimensions, weight, or any other quantifiable characteristic that is critical to the process.

A control chart consists of the following components:

1. Centre line: The center line represents the desired ideal capability of a process. It is based on the calculated mean of the data points representing a graphical depiction of repetitive process output with time. We can say it presents a continuous process variable (X) over time, reflecting the expected performance level.
2. Upper and Lower Specification Limits: Specification limits are established based on customer expectations and are often included in agreements or contracts. These limits define the acceptable range of the process variable, and exceeding them may result in penalties or dissatisfaction from the customer.
3. Upper and Lower Control Limits: Upper and lower control limits are set on the control chart. These limits are determined through statistical analysis or historical records. They help in analyzing the trend of data points relative to the center line and identify any significant deviations or shifts in the process.

 Graphical representation of Control Chart Components:

For repetitive processes, the control limits on a control chart are typically set at ±3 sigma around the process mean, also known as the Centre Line. The upper control limit is drawn at 3 standard deviations above the process mean, while the lower control limit is set at 3 standard deviations below the process mean.

We establish these limits to predict if the process needs corrective action to improve performance in line with the required stability and capability. Analysis of data points with the center line and control limits helps us to prevent unnatural process performance with time. Control limits are more stringent than Specification Limits. So that we can take corrective actions before data points start reaching the specification limit.

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

1. Plotting Data Points: We collect samples of data points from the process and plot them on a control chart. The control chart consists of a centre line and upper and lower control limits.
2. Analysis of Data Points: We analyze the data points in relation to the centre line and control limits. The emphasis is on determining whether the data points fall within acceptable limits.

 Data points that fall within ±3 sigma (standard deviations) of the centre line are considered “In Control.” This means the data points are within acceptable limits and do not exceed the control limits. However, we exclude the rule of seven for this determination.

The Rule of Seven – If seven consecutive data points appear on either side of the mean (centre line), we consider the process “Out of Control” based on the heuristic of the Rule of Seven. This indicates that even though the data points may not cross the control limits, the lack of random output in a repetitive process suggests a potential problem.

An “Out of Control” process has either data points outside the acceptable limits of ±3 sigma or seven consecutive data points appearing on either side of the mean (centre line). This situation shows special cause variances.

In Summary, Special Cause Variances can be seen when a data point falls outside the control limits on a control chart or when there is a pattern or trend in the data, such as seven consecutive data points falling on either side of the mean (Rule of Seven).

3. Investigating Process Problems (Special Cause Varainces): When special cause variance is present in a process, further investigation is required to identify and address the underlying root causes of the variation to bring the process back into control.

 Let’s consider an example of a process that involves testing repetitive weekly builds:

The target is to complete the weekly build by the end of the day on Friday. However, observations show that sometimes the build gets delayed by 1 or 2 days, while on other occasions, it finishes a day early. To determine the acceptable range of variation mathematically, we can use a control chart. The control chart helps us establish control limits that define the acceptable range of variation. In this case, the process owner may accept a variation of up to one day early or one day late. By analyzing the data collected over 30 weeks on the control chart, we can assess whether the process output falls within the established acceptable limits. If any of the weekly builds deviate beyond the control limits, it indicates a need for corrective action to address the underlying issues in the process.

Week	Build Slippage in days
Week 1	2
Week 2	3
Week 3	0
Week 4	-1
Week 5	-2
Week 6	3
Week 7	0
Week 8	4
Week 9	-1
Week 10	19
Week 11	2
Week 12	3
Week 13	4
Week 14	1
Week 15	-1
Week 16	-2
Week 17	-3
Week 18	1
Week 19	2
Week 20	-4
Week 21	-17
Week 22	1
Week 23	1
Week 24	2
Week 25	3
Week 26	0
Week 27	0
Week 28	1
Week 29	2
Week 30	-1

Now we need to calculate the 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

To summarize the calculation of control limits for the given example:

• The average slippage of the build for 30 weeks is 0.73 days.
• The standard deviation is calculated to be 5.132273364, representing the amount of variation from the average.
• Multiplying the standard deviation by 3 gives the three-sigma value of 15.39682009.
• The upper control limit is obtained by adding the three-sigma value (15.39682009) to the average slippage (0.73), resulting in an upper control limit of 16.13.
• The lower control limit is obtained by subtracting the three-sigma value (15.39682009) from the average slippage (0.73), resulting in a lower control limit of -14.66.
• These control limits provide a range within which the slippage of the build is considered acceptable. Any data points falling outside these control limits may indicate the need for corrective action.

 Following is summary information for calculations for the given an example:

• Three Sigma (3 Sigma) is equal to 15.39682009.
• The average mean of slippage in days is 0.73 days.
• The upper control limit is 16.13.
• The lower control limit is -14.66.

These values help establish the control limits for the process and provide a reference range for determining if the slippage in build time is within acceptable limits.

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

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

In this chart, there are two data points (two weeks) that are beyond the control limits, and we need to do further investigation. As mentioned earlier, the control limit helps us determine whether corrective action is required. When data points are beyond the control limit, it shows that variability is not natural.

Analysis of standard deviation and control chart –

To aid in this investigation, additional tools such as the Cause and Effect diagram and Pareto Analysis can be utilized. A brainstorming tool can also be employed in conjunction with these tools.  After conducting a thorough root cause analysis and implementing corrective actions, it is essential to redraw the control chart. This allows us to track the progress and assess whether the variation is decreasing over time.

A crucial aspect to address is the presence of the special cause, here in the above example represented by the two weeks with data points exceeding the control limits. The collaborative approach helps identify and gain insight into the specific events or circumstances that occurred during those two weeks, ultimately leading to the identification of the root causes behind the observed variation.

Analyzing Process Performance and Variability: The Use of Control Charts in the PMP Context

1. In Quality Planning: By analyzing control chart data process improvement plans can be developed, quality policies can be refined, and appropriate metrics can be defined to measure process performance. Historical control chart records play a vital role in the development of these process improvement plans, quality management plans, and quality metrics.
2. In Controlling Quality:  Control Chart helps to determine whether a repetitive process is generating results within an acceptable range and exhibiting random behavior. If the process deviates from these criteria, further investigation is conducted to identify and eliminate any special cause variations.
3. Application in Agile: Agile teams can use control charts to monitor and analyze process performance, identify variations, and facilitate discussions on potential improvements. Conducting this investigation can be incorporated into the Iteration Retrospective. The objective of the retrospective would be to identify actionable steps that can be taken to regain control over the process. The retrospective serves as a platform to evaluate the data, discuss potential improvements, and define strategies for enhancing the process going forward

To obtain further information about the control chart, please check out the video provided below:

To summarize, control charts are essential quality tools used for both quality planning and control. They provide a visual representation of data over time and help determine if a process is stable, generating results within acceptable limits and exhibiting random variation. By identifying special cause variations, control charts facilitate the implementation of corrective actions. I hope this blog has provided you with the information you were seeking regarding the usage and significance of control charts. If you have any further questions, feel free to ask in the comments below.

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