Statistical Process Improvement 

Answer to "Analyze Data" for Xbar Chart Assignment


Answer to Q1

The control chart looks like the following:

It is based on the following data:

 

Time Period Ratings of 1st Subject Ratings of 2nd Subject Ratings of 3rd Subject Ratings of 4th Subject Observed average Upper Control Limit Lower Control Limit Standard deviation of the period
1 80 84 82 80 81.5 79.24 75.26 1.01
2 70 72 74 70 71.5 79.24 75.26 1.01
3 76 78 76 78 77 79.24 75.26 1.01
4 80 78 78 80 79 79.24 75.26 1.01
               
Grand average 77.25            
Standard deviation  4.06            

These data were calculated using the following formula:

Answer to Question 2

The control chart looks like the following Figure:

This chart is based on the following data:

Time period Visit number Rating Satisfied? Consecutive dissatisfied patients UCL    
1 1 80 Yes 0 2.33 Count satisfied 12
1 2 84 Yes 0 2.33
1 3 82 Yes 0 2.33 Count satisfied 4
1 4 80 Yes 0 2.33
2 5 70 No 1 2.33 R 0.33
2 6 72 No 2 2.33
2 7 74 No 3 2.33 UCL 2.33
2 8 70 No 4 2.33
3 9 76 Yes 0 2.33    
3 10 78 Yes 0 2.33    
3 11 76 Yes 0 2.33    
3 12 78 Yes 0 2.33    
4 13 80 Yes 0 2.33    
4 14 78 Yes 0 2.33    
4 15 78 Yes 0 2.33    
4 16 80 Yes 0 2.33    

The formulas used to calculate these data are provided below:

Answer to Question 3

The control chart of the answer looks like the following Figure:

The chart is based on the following data:

Difference between observed and expected
July August September  
$96.90 ($102.13) $70.91    
$80.38 ($116.58) $69.65    
$81.33 $65.08 $73.33    
$66.59 ($32.14) $76.40    
$52.32 $73.62 $51.83    
$58.38 ($21.34) $68.78    
$66.31 $12.05 $78.22    
$79.87 ($115.92) $97.67    
$85.78   $76.78    
$71.44        
Standard deviation $63.48    
Grand expected avg $363.66    
Month Average Standard deviation of time period T-value Upper Control Limit Lower Control Limit
July $409.74 $20.08 1.81 $400.00 $327.33
August $396.07 $22.44 1.89 $406.08 $321.24
September $413.16 $21.16 1.91 $404.17 $323.16
    2.01    
         

 

The data are calculated using the following formulas:

 

 

 


Copyright © 2007. Revised 05/03/15. Farrokh Alemi, Ph.D.