Statistical Quality Control: The Mean Chart - Kickoffall Info Hub

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Thursday, October 31, 2019

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



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