Control Chart | X-Bar R-Chart | Types | Excel Template

What is a 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 as a 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 whether 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 non-manufacturing 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.

Use of Control Chart

• It is used to predict the performance of the manufacturing process
• Find out the special causes within the process
• Identify the trend of the process

History:

➝ 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 need to reduce the frequency of failures and repairs.
➝ By 1920, the engineers had already realized the importance of reducing variation in 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 Control Charts:

→ 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.

👉 Control Chart Excel Template Download

How do I create a 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.

Control Chart Formulas:

Step 2: Calculate the subgroup average:

→ In the second_step, we find the individual subgroup'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 averages.

Step 4: Calculate the subgroup Range (R):

→ In the fourth_step, we find the individual subgroup'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 ranges.

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.

→ 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.

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.

Control Chart Example:

➨ [A] Example of 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?

Advantages of Control Chart:

➝ Control_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 information about the behavior of the process.
➝ It helps in predicting operation performance.
➝ It makes it possible to implement substantial Quality Improvement.

👉 See Also:

➨ All Topics

➨ Lean Manufacturing

➨ ISO 9001:2015 & IATF 16949:2016

➨ 7 QC Tools

➨ MSA, FMEA, PPAP, APQP, SPC

➨ Six Sigma & Lean Six Sigma

➨ QA & QC Topics