Question

1. You are monitoring length of corn that your sister is selling at the farmer’s market. You have following data over 4 days. Draw 3 sigma level control charts (X-bar and R-chart). Calculate and show values for UCL, CL, and LCL using the table given below. Discuss your graphs. Is everything okay?

day 1	day 2	day 3	day 4
15	13	10	8
13	12	9	7
15	11	11	9

           

Factors for 3 Sigma level Sample Control Limit Factor          Control Limit Factor Size          for Sample Mean               for Sample Range n            A2                       D3                        D4 2            1.880                   0                          3.267 3            1.023                   0                          2.575 4            0.729                   0                          2.282 5            0.577                   0                          2.116 10          0.308                   0.223                   1.777 15          0.223                   0.348                   1.652 20          0.180                   0.414                   1.586 25          0.153                   0.459                   1.541

I need step by step on how to create the graphs. Thank you

Answer 1

day 1	day 2	day 3	day 4	Range
15	13	10	8	15-8=7
13	12	9	7	13-7=6
15	11	11	9	15-9=6

X double bar=133/12=11.08

R bar= (7+6+6)/3=6.33

For n=4, A2= 0.729  , D3=0, D4= 2.282

For X bar chart

CL= 133/12=11.08

UCL= X double bar+A2*R bar =11.08+0.729*6.33=15.69

LCL= X double bar-A2*R bar =11.08-0.729*6.33=6.47

Chart is as below=

For R Chart

CL=19/3=6.33

UCL= D4*R bar=2.282*6.33=14.45

LCL= D3*R bar=0*6.33=0

Chart is given below

As all the points of X bar and R charts are within the UCL and LCL values, thus the process is in control