Control Chart in 7 QC Tools

Control Chart in 7 QC Tools

➝ It is a statistical tool used to differentiate between process variation resulting from a common cause & special cause.
➝ The Control Chart in 7 QC Tools is a type of run chart used for studying the process variation over time.
→ This is classified as per recorded data is variable or attribute.
→ In our business, any process is going to vary, from raw material receipt to customer support.
→ Machines have wear, tear, and malfunction and tear after a long run.
→ Control charts measure variation and show it to you graphically and we can easily say that it is within an acceptable limit or not?
→ Many processes can be tracked by this graph like defects, production time, inventory on hand, cost per unit and other metrics.
→ Also, we can use this graph to measure nonmanufacturing processes like billing errors, missed appointments, customer support calls, bill payment dues, days between billing and payment, expenses, on-time delivery failure, unplanned absences, etc.


➝ It was invented by Dr. Walter A. Shewhart working for Bell Labs in the 1920s.
➝ So this is called "Shewhart Control Charts".
➝ The company's engineers had been seeking to improve the reliability of their telephony transmission systems.
➝ Because amplifiers and other equipment had to be buried underground, there was a stronger business needs to reduce the frequency of failures and repairs.
➝ By 1920, the engineers had already realized the importance of reducing variation in the manufacturing operation.

Principles of variation:

➝ Every process has variation.
➝ More the variation, the more loss to the Organization.
➝ Two types of causes are responsible for the variation.
     (1) Common cause
     (2) Special cause
➝ Action entirely depends on the type of cause identified.

[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 part 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...

Types of data:

→ There are two types - Attribute and Variable
     [1] Attribute:
     ⇢ Attribute data that can be counted or can give an answer in Go/No Go, OK/Not OK or Pass/Fail
     ⇢ e.g. aesthetic look of product ok or not ok
     [2] Variable:
     ⇢ Variable data can be measured.
     ⇢ e.g. Weight, Height, Length, Hardness, Diameter, Angle

Types of the Control Chart:

→ There are many types of control charts are available in Statistical Process Control.
→ The classification 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?
→ For better understanding refer below picture which is very easy to understand with the help of classification.

Types of the Control Chart

Steps for making Control Chart:

→ Here we take an example of the most common (X-Bar, R chart)
→ To understand this example we are taking variable data and subgroup size=5 as per the classification mentioned above
→ We can easily construct (X-Bar, R chart) in simple 8 steps which are mentioned below:
  1. Collect the data.
  2. Calculate the subgroup average.
  3. Determine the overall average.
  4. Calculate the range.
  5. Compute the average of the range.
  6. Calculate the control limit
  7. Plot the data in the graph.
  8. Interpret the Graph.

Step 1: Collect the data:

→ Record the readings and stratify it into subgroups as per our sampling plan and record it in the Check Sheet.

Step 2: Calculate the subgroup average:

→ In the second step, we find the individual sub group's average as per the formula mentioned in the picture.

Step 3: Determine the overall average X-double bar:

→ Here we find the overall average by using all sub group's individual average.

Step 1 2 3

Step 4: Calculate the subgroup Range (R):

→ In the fourth step, we find the individual sub group's range as per the mentioned formula.

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

→ Here we find out the average range of all individual subgroups range.

Step 4 5

Step 6: Calculate the control limit

→ In this step, we find the limit of the X-bar and R chart with the below-mentioned formula.

Step 6

→ Different Constants value are mentioned in below pictures which is very important for the Graph:
→ The source of this constant value is the AIAG-SPC  handbook.

Constants for the graph

Step 7: Plot of the data:

→ Vertical axis: X-Bar and R values.
→ Horizontal axis: subgroup number.
→ Draw the central line: X-double bar and R-bar
→ Draw all control limits UCL & LCL.
→ Plot the X-Bar and R values and join the points.
→ Write necessary items like the name of the operation, product, size of the subgroup, work conditions, shift, etc.

➨ [A] Example of X-Bar and R Chart:

X-Bar and R Chart

Step 8: Interpret the Graph:

[A] Process stability:

➝ Look at the pattern of variation.
➝ It should be random and not a systematic pattern.
➝ Look for the presence of special causes.
➝ For detailed information, go through these 8 rules of special cause identification.

[B] Process capability:

➝ Compare with specification and establish Process Capability e.g. are our processes capable enough to achieve customer's specifications?


➝ This chart gives information about the common causes and special causes.
➝ It also helps in determining whether the Process is capable or not & stable or not? so, we can get the information about the behavior of the process.
➝ It helps in predicting operation performance.
➝ It makes possible to implement substantial Quality Improvement.

👉 Also Read:
      2. Cause & Effect Diagram (Fishbone or Ishikawa)

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