Control chart |Types| x̅ and R chart

What is control chart

The control chart is the fundamental tool of statistical process control, as it indicates the range of variability that is built into a system (known as common cause variation).

It helps to determine whether or not a process is operating consistently or if a special cause has occurred to change the process mean or variance.

The control chart have a centre line that represents the average value of the quality characteristic corresponding to the in-control state.Two other horizontal lines, called the upper control limit (UCL) and the lower control limit (LCL).

→Control Chart in 7QC tool is a type of run chart used for studying the process variation.

Use of control chart

  • To find, is there any change in location of process average.

  • To find,is there any change in the spread of the process.

  • To find, is there any change in shape.

History of control chart

The control chart was invented by Walter A. Shewhart working for Bell Labs in the 1920 so this is called Shewhart control charts.

What is Variability?

variability is define as the net result of many factors , which are constantly affecting the process

Cause of variability:

1-Common cause

Common cause are those cause which randomly affect the system, they are always present and built in to the process it self. this is also called as "inherent cause".

2-Special Cause

Special cause are those cause which represent non-random variation in process , which can be identified to a particular cause.

special variation might be caused by one or more of the following

  • Man-Setup (Speed, Feeding), accuracy, training, Experience etc.

  • Machine- Accuracy, Calibration, wear etc.

  • Material- Different material , mixing accuracy etc.

  • Measurement- Repeatability, Precision, accuracy, calibration etc.

  • Environment- Temperature , humidity etc.

Types of data

There are basically two type of data

1-Attribute data

These types of data are often referred to as discrete data.There are two kinds of attributes data:yes/no type of data and counting data.

2-Variable data

A quality characteristic that is measured on a numerical scale is called a variable. Examples

include dimensions such as length or width, temperature, and volume

Types of control chart

there are many type of control chart available in statistical process control, depend nature of data eg. attribute or variable, defect or defective and number or sample

Control chart for variable

The x̅ and R control charts are widely used to monitor the mean and variability of variables

Step to Make x̅ ,R Chart

  • Collect the data

  • Calcuate the average of sub group

  • Calculate the over all average

  • Calculate the range

  • Calculate the average of range

  • Calculate the control limit

  • data plot in graph

x̅ ,R Control Chart Formula


  • X is the individual value

  • n is the sample size

  • X bar is the average of reading in a sample

  • R is the Range (the difference between largest and smallest value in each sample)

  • R bar is the average of all the ranges.

  • UCL is Upper control limit

  • LCL is Lower control limit

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