## What is a Control Chart?

→ A Control Chart is a statistical tool.

→ It is used to study how a process changes over time.

→ It helps us to identify between process variation resulting from a common cause and a special cause.

→ The control chart is the most important tool among the 7 QC tools.

→ The Control Chart is widely used in the ** Lean Six Sigma Project** globally.

**Table of Contents:**

- What is a Control Chart?
- When to Use Control Chart?
- Why Use a Control Chart?
- Control Chart Uses
- History
- Key Components of Control Charts
- Principles of variation
- Classification of Control Charts
- Example of Control Chart
- Interpretation of the Control Chart
- Relation Between Process Stability and Capability
- Advantages of Control Chart
- Limitations of Control Chart
- Benefits of Control Chart
- Conclusion

## When to Use Control Chart?

- Monitoring ongoing production processes
- After implementing process changes
- Detecting variability and trends
- Quality control in manufacturing
- When establishing baselines
- Routine process monitoring

## Why to Use a Control Chart?

- Early detection of issues
- Distinguishing between common cause and special cause variation
- Monitoring process stability
- Supporting continuous improvement
- Enhanced quality control
- Resource optimization
- Employee engagement and empowerment

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## Control Chart Uses:

→ Control charts are versatile tools and those are used in various scenarios to monitor, control, and improve processes.

→ It is used to predict the performance of the manufacturing process.

→ Find out the special causes and common causes within the process.

→ Identify the trend of the process.

→ We can review process variation with time for the manufacturing and non-manufacturing processes with this chart.

**⏩Control Chart Use to Monitor Manufacturing Processes Such as:**

- Defects Rate,
- Production Time,
- Inventory on Hand,
- Cycle Time
- Cost per Unit, etc

**⏩Control Chart Use to Monitor Non-Manufacturing Processes Such as:**

- Billing Errors
- Missed Appointments,
- Customer Support Calls,
- Bill Payment Dues,
- Days Between Billing and Payment,
- Expenses,
- On-time Delivery Failure,
- Unplanned Absences, etc.

→ They are fundamental tools in Statistical Process Control (SPC).

→ And used to monitor the quality and variation of processes.

## History:

→ Control Chart was invented by Dr. Walter A. Shewhart working for Bell Labs in the 1920s.

→ So It is called *"Shewhart Charts"*.

→ It is also known as a process behavior chart.

→ In the 1920s, Shewhart worked on improving the reliability of the manufacturing process for telephone equipment.

→ The engineers had already realized the importance of reducing variation in manufacturing operations.

→ He introduced the idea that a process could be in statistical control or not in control.

→ Also, he has given the concept of common causes variation and special causes variation.

→ In 1931, Shewhart published a book, "Economic Control of Quality of Manufactured Product."

→ This book has set the foundation for modern quality control.

→ This concept was further developed and popularized worldwide by W. Edwards Deming.

## Key Components of Control Charts:

**⏩The key components of control charts are:**

- Center Line (CL)
- Control Limits
- Data Points
- Zones

#### 1. Center Line (CL):

→ The Center Line represents the average or mean of the process data.

#### 2. Control Limits:

→ Two types of control limits are (1) Upper Control Limit (UCL) and (2) Lower Control Limit (LCL).

→ Generally, control limits are set at ±3 standard deviations from the center line.

→ These limits help identify when the process is going out of control.

#### 3. Data Points:

→ Data points are the individual readings, records, measurements, or observations which are plotted on the chart.

→ Over a period plotting data points we can monitor the process.

#### 4. Zones:

→ Zones are the area between the control limits and the center line.

→ Zones are divided into two and that helps interpret the chart.

## Principles of variation:

→ All the processes have variations as per the 6M changes such as Man, Machine, Material, Method, Measurement, and Mother Nature (Environment) changes.

→ Machines have wear, tear, malfunction, etc.

→ Control Charts measure the variation of the process.

→ So we can easily interpret it after plotting into the graph.

→ Also, we can easily say whether the process variation is within an acceptable limit or not?

→ Now we learn about the principles of variation of any process.

→ Every process has variation.

→ The more variation, the more loss to the Organization.

→ The variation has a certain pattern.

→ After identifying the pattern we can take appropriate action to eliminate the cause of the variation.

→ So the actions depend on the types of pattern and cause identified.

→ This way we can reduce the loss of the business and improve our process.

**⏩Two types of causes are responsible for the variation that are:**

- Common cause
- Special cause

### 1. Common Cause:

→ "Common cause is fluctuation caused by unknown factors resulting in a steady but random distribution of output around the average of the data."

→ e.g. the rubbing effect of matting parts like gears, bearings, etc...

### 2. Special Cause:

→ "Special cause is caused by known factors that result in a non-random distribution of output"

→ e.g. machine breakdown, accident, etc...

## Classification of Control Charts:

→ There are many types of charts available in Statistical Process Control.

**⏩The most common types of control charts are:**

- X Bar & Range “R” Chart
- Standard Deviation “S” & Range “R” Chart
- I-MR Chart
- “u” Chart
- “c” Chart
- “p” Chart
- “np” Chart

**⏩The classification of these charts depends on the below parameters:**

- Nature of recorded data type such as variable or attribute
- The number of samples is available in each subgroup or we can say subgroup size
- Focus on defects (occurrence) or defectives (pieces or units)
- The subgroup size is equal or not?

→ The main two types of charts are variable and attribute charts.

→ Classification of the Control Chart is mentioned below.

→ For better understanding refer below picture.

## Example of Control Chart:

→ In this example, we will learn how to make a control chart.

→ Now we will take an example of the most common (X-Bar, R chart).

→ We will learn step by step, with one example of the manufacturing process variation.

→ For this example we are taking variable data and subgroup size=5 as per the classification mentioned above.

→ We can easily make (X-Bar, R chart) as explained below.

### How to Make a Control Chart?

→ We can easily make this with 7 simple steps.

**⏩Seven steps for making a control chart are:**

- Collect the data
- Calculate the subgroup average
- Determine the overall average
- Calculate the range
- Compute the average of the range
- Calculate the control limit
- Plotting of data in graph

#### Step 1: Collect the Data:

→ The first step is to collect data from the manufacturing process.

→ Record the readings and stratify it into subgroups as per our sampling plan.

→ In our example the subgroup size is 5.

→ So we will take 5 samples at a time during data collection.

#### Step 2: Calculate the Subgroup Average:

→ Now after data collection, we need to calculate the average of the subgroup.

→ So we will find the individual subgroup's average as per the formula mentioned in the below picture.

→ We need to apply a simple average formula.

#### Step 3: Determine the Overall Average X-double Bar:

→ So after finding the individual subgroup's average, now we need to find out the overall average of all subgroups.

→ Refer to the below-mentioned formula of the overall average.

#### Step 4: Calculate the Subgroup Range (R):

→ In the fourth step, we will find the individual subgroup's range.

→ Range is the simple difference between the highest and lowest numbers.

→ For calculating the subgroup range we will use the range formula.

#### Step 5: Calculate the Average Range (R-bar):

→ Now after finding the range, we need to find the average of the range.

→ So in the fifth step, we will find the average of the range.

→ For this we will use a simple average formula.

#### Step 6: Calculate the Control Limit:

→ Till now, we have calculated the various parameters based on the data collected and formulas.

→ Now in the sixth step, we will find the control limit of the X-bar and R-chart.

→ As per the below formulas, we will find out the control limits of the X-bar and R chart.

→ Different constant values are mentioned below pictures which are very important for the Graph.

→ The constants depend on the subgroup size.

→ As the subgroup size changes the constant value also changes.

→ The source of this constant value is the AIAG-SPC handbook.

#### Step 7: Plotting of Data in Graph:

→ Plot the vertical axis as X-Bar and R values and the horizontal axis as subgroup numbers.

→ Draw the central line as an X-double bar and R-bar.

→ Draw all control limits UCL & LCL as calculated in the previous step.

→ Plot the X-bar and R values and join the points.

→ Write necessary items like the name of the operation, process, product, size of the subgroup, work conditions, shift, etc.

→ Refer to the below picture for an example of a control chart for your better understanding.

## Interpretation of the Control Chart:

→ With the help of the control chart we can identify the special cause variation and common cause variation of the process.

→ Based on that we can take action and eliminate special causes and reduce the variation at the minimum level.

→ If all data points fall within the UCL and LCL, then the process is in control.

→ If one or more data points fall outside the UCL or LCL, then it indicates a special cause.

→ A run of seven or more points consistently above or below the center line suggests a systematic shift in the process.

→ A series of points that show a consistent upward or downward trend indicates a potential issue.

→ Study our article where we have explained ** The Eight Rules of Control Chart Interpretation** with examples, patterns, and trends.

## Relation Between Process Stability and Capability:

→ Process Stability and Process Capability are the most important concepts in interpretation.

→ Below we have explained both concepts.

### Process Stability:

→ Process Stability refers to the consistency of the process to stay within the Control Limits.

→ If the process distribution remains consistent over time then we can say that the process is stable or in control.

→ If the Outputs are spread outside the limits, then we can say that the process is unstable or out of control.

### Process Capability:

→ Process Capability is a measure of the ability of the process to meet customer specifications.

→ It is the measure that tells how good each individual output is.

→ An estimation of the ppm is a method to measure process capability.

→ PPM means defective parts per million.

→ Process Capability analysis uses measures like Cp, Cpk, Pp, and Ppk to determine the process capability.

## Advantages of Control Chart:

→ It gives information about the common causes and special causes.

→ This chart also helps in determining whether the process is capable or not & stable or not?

→ It helps in predicting operation performance.

→ It makes it possible to implement substantial Quality Improvement.

## Benefits of Control Chart:

- Early detection of problems
- Process improvement
- It ensures consistent quality by monitoring process performance over time
- It is very useful for decision-making.
- Continuous Improvement tool
- Quality improvement and cost reduction
- Enhanced customer satisfaction
- Improve plant efficiency and effectiveness

## Limitations of Control Chart:

- Control charts frequently assume that the data follows a normal distribution
- Measurement errors can affect on interpretation
- The effectiveness of control charts depends on the accuracy of the data collected
- Time and resource-intensive

## Conclusion:

→ Control charts are a fundamental tool in quality control and process management.

→ It helps in monitoring, controlling, and improving processes.

→ Control charts can detect variations and trends.

→ This ability helps organizations in different ways such as: (1) maintaining process stability, (2) enhancing product quality, (3) driving continuous improvement, etc.

→ Apart from the above benefits, they have some limitations as well.

→ We can easily reduce the limitation of the control chart by integrating it with other quality management practices.

→ The organizations can get benefits by using control charts such as: (1) achieving greater process control, (2) higher quality products, and services, (3) overall operational excellence, etc.

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