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 = 123.5

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 122.75 to 124.50. The bottom line is labeled LCL and intersects the vertical axis at about 123.13. The middle line intersects the vertical axis at 123.50. The top line is labeled UCL and intersects the vertical axis at about 123.87. 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 122.75 to 124.50. The bottom line is labeled LCL and intersects the vertical axis at about 123.35. The middle line intersects the vertical axis at 123.50. The top line is labeled UCL and intersects the vertical axis at about 123.65. 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 122.75 to 124.50. The bottom line is labeled LCL and intersects the vertical axis at about 123.02. The middle line intersects the vertical axis at 123.50. The top line is labeled UCL and intersects the vertical axis at about 123.98. 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 122.75 to 124.50. The bottom line is labeled LCL and intersects the vertical axis at about 123.24. The middle line intersects the vertical axis at 123.50. The top line is labeled UCL and intersects the vertical axis at about 123.76. The entire region between the LCL line and the UCL line is shaded.

(b)

Consider a sample providing the following data.

123.8

123.2

124.1

123.7

123.4

124.2

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.

124.3

123.7

123.6

124.2

124.5

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

UCL - M + 3x Zn ANSWER a) Central line M=123.55-0.3, n=6 123.5+ 3 x 0.3 V6 = 123.5 +0.367 =123.867 LIL - M - 3x/ou - 123.5 - 3x o 0.3 VG =123.5 -0.367 = 193.133 LCLEM-3XSE mean (M) SE=s/on Ul=4+3XSE 123. 133 123.867 0.1225 123.5 b IT 123.733 since 123.733 lies in the inlerval (LeL UCL) So Prolese is under control DT 124.883 since 124.883 dole hot lies in the intcoval (22L, Ue) = (123.133 1123 .867) So Process is not under control CS Scanned with CamScanner