# Control chart |Types| x̅ and R chart

**What is control chart**

The control chart is the fundamental tool of __s____tatistical 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 __s____tatistical 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**

Where:

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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