Question

Temperature is used to measure the output of a production process. When the process is in control, the mean of the process is

*μ* = 128.5

and the standard deviation is

*σ* = 0.3.

(a)

Compute the upper and lower control limits if samples of size 6 are to be used. (Round your answers to two decimal places.)

UCL = LCL =

Construct the

*x*

chart for this process.

A graph shows three horizontal lines. The horizontal axis is labeled Sample Number and ranges from 0 to 10. The vertical axis is labeled Sample Mean x bar and ranges from 127.75 to 129.50. The bottom line is labeled LCL and intersects the vertical axis at about 128.02. The middle line intersects the vertical axis at 128.50. The top line is labeled UCL and intersects the vertical axis at about 128.98. The entire region between the LCL line and the UCL line is shaded.

A graph shows three horizontal lines. The horizontal axis is labeled Sample Number and ranges from 0 to 10. The vertical axis is labeled Sample Mean x bar and ranges from 127.75 to 129.50. The bottom line is labeled LCL and intersects the vertical axis at about 128.35. The middle line intersects the vertical axis at 128.50. The top line is labeled UCL and intersects the vertical axis at about 128.65. The entire region between the LCL line and the UCL line is shaded.

A graph shows three horizontal lines. The horizontal axis is labeled Sample Number and ranges from 0 to 10. The vertical axis is labeled Sample Mean x bar and ranges from 127.75 to 129.50. The bottom line is labeled LCL and intersects the vertical axis at about 128.24. The middle line intersects the vertical axis at 128.50. The top line is labeled UCL and intersects the vertical axis at about 128.76. The entire region between the LCL line and the UCL line is shaded.

A graph shows three horizontal lines. The horizontal axis is labeled Sample Number and ranges from 0 to 10. The vertical axis is labeled Sample Mean x bar and ranges from 127.75 to 129.50. The bottom line is labeled LCL and intersects the vertical axis at about 128.13. The middle line intersects the vertical axis at 128.50. The top line is labeled UCL and intersects the vertical axis at about 128.87. The entire region between the LCL line and the UCL line is shaded.

(b)

Consider a sample providing the following data.

128.8 | 128.2 | 129.1 | 128.7 | 128.4 | 129.2 |

Compute the mean for this sample. (Round your answer to two decimal places.)

*x*

=

Is the process in control for this sample?

Yes, the process is in control for the sample. No, the process is out of control for the sample.

(c)

Consider a sample providing the following data.

129.3 | 128.7 | 128.6 | 129.2 | 129.5 | 129.0 |

Compute the mean for this sample. (Round your answer to two decimal places.)

*x*

=

Is the process in control for this sample?

Yes, the process is in control for the sample. No, the process is out of control for the sample.

Answer #1

a.

*μ* = 128.5

and the standard deviation is

*σ* = 0.3

n= sample size 6

UCL = mean +3 Q/ sqrt n

= 128.5 + 3 * 0.3 /sqrt 6 = 128.8674

LCL = mean - 3 Q/ sqrt n

= 128.5 - 3 * 0. 3/ sqrt 6 = 128.1325

A process is said to be out-of control, if any of sample points fall beyond the control limits (below the LCLor above the UCL)

b.

(128.8+128.2+129.1+128.7+128.4+129.2)/6

= 128.83

Since in the above sample, one point (128.83) is below the UCL and
no point is above LCL ( 128.13), the process is said to be in
-control of sample

c.

(129.3 +128.7 +128.6 + 129.2 +129.5 + 129.0) / 6 =129.05

Since in the above sample, four points (129, 129.2, 129.3, 129.5) are above the UCL and nopoint is below LCL (128.13), the process is said to be out-of-control

x= 129.05

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