Statistical Quality Control: The Mean Chart

The Mean chart is used to monitor the mean of a normally distributed variables simultaneously when samples are collected at regular intervals from a business or industrial process. It is often used to monitor the variables.  

Problem 1:

Draw a Mean Chart based on the data given below:

Solution:

1. Central Line

                  

Group 1 = 20+22+25+24/4  = 22.75

Group 2 = 18+ 23+ 20 + 26/4 = 21.75

Group 3 = 24+ 25+ 22+ 20/4 = 22.75

Group 4 = 23+21+ 26+24/4 = 23.5

Group 5 = 24+25+24+21/4 = 23.5

22.75 + 22.75+21.75+23.5+23.5/ 5 (Number of Groups)

Central Line =    = 22.85

2. Upper Control Limit (UCL)

Where,   
X  = 22.85,

A₂ = 0.73       (constant value for sample size 4; refer ‘Annexure A: Factors for Constructing Control Charts)

R = ∑ R÷K

       R = Highest – Lowest                                                       

       K = Number of groups = 5

                                     

R = H – L

Group 1 = 25-20=5

Group 2 = 26-18= 8

Group 3 =25-20 = 5

Group 4 = 26-21= 5

Group 5 = 25-21 = 4

5+8+5+5+4=27

 =  27/5 = 5.4

UCL= 22.85+0.73×5.4

= 22.85+3.94

           = 26.792

Lower Control Limit (LCL)

= 22.85 – 3.94

=18.91

Draw control chart:

Upper Control Limit= 26.792

Central Line               = 22.85

Lower Control Limit= 18.91

Annexure: 
Factors for Constructing Control Charts