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

    9

    4

    8

    9

    15

    13

    7

    5

    9

    10

    14

    13

    16

    6

    12

    11

    10

    10

    13

    7

    16

    10

    14

    9

    12

    8

    14

    9

    10

    14

    13

    9

    9

    10

    13

    12

    10

    10

    15

    16

    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

    13

    10

    14

    12

    17

    9

    11

    12

    10

    14

    18

    15

    12

    10

    11

    13

    19

    14

    16

    9

    12

    10

    20

    13

    10

    12

    15

    9

    Determine the trial central line and control limits for the X and R (24 points).

    UCLX=

    CLX=

    LCLX=

    UCLR=

    CLR=

    LCLR=

Solutions

Expert Solution

The control limits are:

Sample size 5
Number of samples 20
Mean Range
Upper Control Limit, UCL 15.47 13.00
Center 11.92 6.15
Lower Control Limit, LCL 8.37 0.00

The calculations are:

Subgroup Number X1 X2 X3 X4 X5 Xbar R
1 12 10 13 15 12 12.4 5
2 10 7 16 14 8 11 9
3 11 12 10 16 9 11.6 7
4 8 9 15 13 7 10.4 8
5 9 10 14 13 16 12.4 7
6 12 11 10 10 13 11.2 3
7 16 10 14 9 12 12.2 7
8 14 9 10 14 13 12 5
9 9 10 13 12 10 10.8 4
10 15 16 10 13 12 13.2 6
11 10 12 14 16 11 12.6 6
12 16 13 9 11 8 11.4 8
13 16 11 13 15 10 13 6
14 15 13 10 12 9 11.8 6
15 12 14 8 16 11 12.2 8
16 15 13 10 14 12 12.8 5
17 9 11 12 10 14 11.2 5
18 15 12 10 11 13 12.2 5
19 14 16 9 12 10 12.2 7
20 13 10 12 15 9 11.8 6
Average 11.92 6.15
A2 0.577
A3 1.427
D3 0
D4 0.114
Sample size 5
Number of samples 20
Mean Range
Upper Control Limit, UCL 15.47 13.00
Center 11.92 6.15
Lower Control Limit, LCL 8.37 0.00

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