X bar Chart and R Chart

X-bar Chart & R chart 

The X-bar chart is a type of control chart that is used to monitor/measure the arithmetic means of succeeding samples of constant size (n). It is used to measure characteristics of a continuous scale, such as temperature, thickness, weight etc.

Example

The below table gives the measurement of axles of bicycle wheels. Find whether process is in control or not.

(Hint: It is given as measurement from which we came to know it’s an X bar chart and R chart. We need to find mean and range to measure any quantity.)

Sample	Value of sample	X bar	Range
1	139,140,145,144	142	6
2	140,142,142,139	140.75	3
3	142,136,143,141	140.5	7
4	136,137,142,142	139.25	6
5	145,146,146,146	145.75	1
6	146,148,149,144	146.75	5
7	148,145,146,146	146.25	3
8	145,146,147,144	145.5	3
9	140,139,141,138	139.5	3
10	140,140,139,139	139.5	1
11	141,137,142,139	139.75	5
12	139,140,144,138	140.25	6

X bar= 142.125, R bar= 4.083

X-bar chart

UCL=145.11

LCL=139.15

R chart

UCL=9.31

LCL=0 (if LCL is negative, it should be considered as zero)

The below are control charts of X bar and R-chart.

There are four responses outside the control so, the process should be stopped and cause should be identified.

The R-chart all responses are within the control. Hence, the whole process is in control.

X-bar Chart

 

R Chart