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 done, the control limits for 3-sigma x overbarx chart are (round all intermediate calculations to three decimal places before proceeding with furthercalculations):Upper Control Limit (UCL Subscript x overbarUCLx) = ?Lower Control Limit (LCL Subscript x overbarLCLx) = ?Based on the x overbarx-chart, the wire cutting process has beenIN CONTROL or OUT OF CONTROL?The control limits for the 3-sigma R-chart are (round all intermediate calculations to three decimal places before proceeding with further calculations):Upper Control Limit (UCL Subscript Upper RUCLR) = ?Lower Control Limit (LCL Subscript Upper RLCLR) = ?

(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:

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:

Control Limits, R Chart

 LCL        UCL        Mean

  0        2.345       1.028

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )