Mathematics: Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results:Hour Xbar R Hour Xbar R Hour Xbar R Hour Xbar R1 3.15 0.76 7 3.15 0.53 13 3.21 0.80 19 3.31 1.662 3.10 1.13 8 2.65 1.08 14 2.83 1.31 20 2.99 1.143 3.12 1.48 9 2.92 0.76 15 3.12 1.01 21 2.65 1.034 3.49 1.31 10 2.85 1.28 16 2.74 0.55 22 3.28 0.415 3.17 1.22 11 2.93 1.17 17 2.86 1.43 23 2.94 1.636 2.86 0.37 12 3.07 0.35 18 2.84 1.34 24 2.54 0.92Based on the sampling

what you have is rightStep-by-step explanation:...

Sampling 4 pieces of precision-cut wire (to be used

hellp138

29.01.2022

(A)

Control Limits, X-bar Chart

LCL UCL Mean

3.739 2.240 2.990

(B)

Control Limits, R Chart

LCL UCL Mean

0 2.345 1.028

Step-by-step explanation:

(A)

X Chart:

From the data provided, the parameters computed are as follows:

Mean, X = 2.990,

Range, R = 1.028,

For Number of samples, n = 4, Values of A₂ are given in the Factors table for calculating control limits,

n A2 D3 D4

4 0.729 0 2.282

Compute the Upper Control Limit and Lower Control Limit for the x-chart as follows:

$\text{UCL}_{X} = X + A_{2} \times R = 2.990 + 0.729 \times 1.028 = 3.739\\\\LCL_{X} = X - A_{2} \times R = 2.990 - 0.729 \times 1.028 = 2.240$

Control Limits, X-bar Chart

LCL UCL Mean

3.739 2.240 2.990

Since, all the points are within the UCLₓ and LCLₓ control Limits, the process is said to be in control.

(B)

R Chart:

Compute the Upper Control Limit and Lower Control Limit for the R-chart as follows:

$UCL_{R} = D_{4} \times R = 2.282 \times 1.028 = 2.345\\\\LCL_{R} = D_{3}\times R = 0 \times 1.028 = 0$

Control Limits, R Chart

LCL UCL Mean

0 2.345 1.028

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