The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the ma

Question

The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation, with the following results. Tread wear measurements are in hundredths of an inch. Sample Tread Wear 1 31 42 28 2 26 18 35 3 25 30 34 4 17 25 21 5 38 29 35 6 41 42 36 7 21 17 29 8 32 26 28 9 41 34 33 10 29 17 30 11 26 31 40 12 23 19 25 13 17 24 32 14 43 35 17 15 18 25 29 16 30 42 31 17 28 36 32 18 40 29 31 19 18 29 28 20 22 34 26 Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the R chart. Compute the upper and lower control limits for the R chart. (Round your answers to two decimal places.) UCL = LCL =

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Acacia 3 years 2021-08-17T17:01:07+00:00 1 Answers 0 views 0

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    2021-08-17T17:02:44+00:00

    Answer:

    LCL = 4.72

    UCL = 18.08

    Step-by-step explanation:

    Sample size, n = 20

    Sample _ tread wear, x __ Range

    1 ______ 33.67 ___ 14

    2______ 26.33 ___ 17

    3 _____ 29.67 ____ 9

    4 ______ 21 ______ 8

    5 ______ 34 ______ 9

    6 ______ 39.67 ___ 6

    7 ______ 22.33 ___ 12

    8 ______ 28.67 ___ 6

    9 ______ 36 ______8

    10 _____ 25.33 ___ 13

    11 _____ 32.33 ____14

    12 _____ 22.33 ___ 6

    13 _____ 24.33 ___ 15

    14 _____ 31.67 ___ 26

    15 _____ 24 _____ 11

    16 ____ 34.33 ____ 12

    17 ____ 32 _______ 8

    18 ____ 33.33 ____ 11

    19 ____ 25 _______11

    20 ___ 27.33 _____12

    Sample mean, xbar = Σx / n = 29.167

    Rbar = ΣR/ n = 11.4

    The R chart control limit is given by :

    Rbar(1 – 3(d3/d2))

    From the R chart :

    d3 = 0.729 ; d2 = 3.735

    Hence,

    LCL = 11.4(1 – 3(0.729/3.735))

    LCL = 11.4(0.4144578) =

    LCL = 4.72481892 = 4.72

    UCL = 11.4(1 – 3(0.729/3.735))

    UCL = 11.4(1.5855421)

    UCL = 18.075180 = 18.08

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