Question

In: Statistics and Probability

The net weight (in oz.) of a dry bleach product is to be monitored by X...

  1. The net weight (in oz.) of a dry bleach product is to be monitored by X and R and X and S control charts using a sample size of n = 5. Data for 20 preliminary samples are shown below.

Subgroup Number

X1

X2

X3

X4

X5

1

12

10

13

15

12

2

10

7

16

14

8

3

11

12

10

16

14

4

8

11

15

13

7

5

9

10

14

13

16

6

12

11

10

14

13

7

16

10

14

9

12

8

14

9

10

14

13

9

9

10

13

12

10

10

15

8

10

13

12

11

10

12

14

16

11

12

16

13

9

11

8

13

16

11

13

15

10

14

15

13

10

12

9

15

12

14

8

16

11

16

15

4

10

14

12

17

9

11

12

10

14

18

15

12

10

11

13

19

14

16

9

12

10

20

13

5

12

15

8

Determine the trial central line and control limits for the X and R.

UCLX=

CLX=

LCLX=

UCLR=

CLR=

LCLR=

Solutions

Expert Solution

Ans : From the data first we calculate and

Let X : Quality Variable under Study

k= random sample each of size n are available on variable X

Ri : Sample range of ith random sample

= max(xij) - min(Xij)  

  

Now we calculate using following table :

No. X1 X2 X3 X4 X5 Ri Xi-bar
1 12 10 13 15 12 5 12.4
2 10 7 16 14 8 9 11
3 11 12 10 16 14 6 12.6
4 8 11 15 13 7 8 10.8
5 9 10 14 13 16 7 12.4
6 12 11 10 14 13 4 12
7 16 10 14 9 12 7 12.2
8 14 9 10 14 13 5 12
9 9 10 13 12 10 4 10.8
10 15 8 10 13 12 7 11.6
11 10 12 14 16 11 6 12.6
12 16 13 9 11 8 8 11.4
13 16 11 13 15 10 6 13
14 15 13 10 12 9 6 11.8
15 12 14 8 16 11 8 12.2
16 15 4 10 14 12 11 11
17 9 11 12 10 14 5 11.2
18 15 12 10 11 13 5 12.2
19 14 16 9 12 10 7 12.2
20 13 5 12 15 8 10 10.6

= 134/20

= 6.7

= 236/20

= 11.8

Control limits for R - chart

Upper Control Limit

UCLR = D4 *

where D4 is calculate from statistical constants for control chart for n=5

UCLR = 2.155 * 6.7

UCLR =14.1705

Central Line

CLR =

CLR = 6.7

Lower Control Limit

LCLR = D3 *

= 0 * 67

LCLR = 0

Control limits for - chart

Upper Control Limit

UCL = + A2 *

where A2 is calculate from statistical constants for control chart for n=5

UCL = 11.8 + 0.577*6.7

UCL =15.665

Central Line

CL =

CL= 11.8

Lower Control Limit

LCL = - A2 *

= 11.8 -0.577*6.7

LCL = 7.9341

Final Answer :

central line and control limits for the and R

UCL =15.665

CL= 11.8

LCL = 7.9341

R chart :

UCLR =14.1705

CLR = 6.7

LCLR = 0


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