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Fujiyama Electronics

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Chapter 14 – Problem 14

Problem Statement

Fujiyama Electronics, Inc. has been having difficulties with circuit boards purchased from an outside supplier. Unacceptable variability occurs between two drilled holes that are supposed to be 5 cm apart on the circuit boards. Thirty samples of 4 boards each were taken from shipments from the supplier as shown in the data from the worksheet Prob. 14-14, listed below.
a. Construct [pic] and R charts for these data.
b. If the supplier’s plant quality manager admitted that they were experiencing quality problems for shipments 18, 19, and 21, how would that affect your control chart? Show this adjustment on revised [pic] and R charts for these data.

Data

|1 |4.92 |4.26 |4.94 |4.29 |
|2 |4.65 |5.54 |5.00 |5.42 |
|3 |5.77 |5.26 |4.76 |4.79 |
|4 |6.25 |4.88 |5.66 |4.44 |
|5 |5.27 |5.41 |6.02 |4.91 |
|6 |5.22 |5.38 |5.08 |4.65 |
|7 |5.47 |4.68 |4.56 |4.70 |
|8 |5.71 |4.54 |4.17 |4.87 |
|9 |5.24 |5.58 |4.72 |5.41 |
|10 |4.42 |5.18 |4.79 |4.73 |
|11 |5.14 |4.26 |4.71 |5.48 |
|12 |4.92 |5.78 |5.50 |5.05 |
|13 |5.79 |3.83 |4.30 |4.78 |
|14 |4.92 |4.80 |4.75 |5.59 |
|15 |5.68 |5.74 |4.65 |5.20 |
|16 |5.43 |4.81 |5.27 |4.96 |
|17 |4.79 |6.04 |4.47 |5.18 |
|18 |4.43 |5.08 |3.69 |6.43 |
|19 |6.35 |5.95 |6.29 |5.89 |
|20 |5.03 |4.66 |5.25 |4.46 |
|21 |6.32 |6.09 |5.57 |5.91 |
|22 |4.30 |5.47 |4.27 |4.34 |
|23 |6.07 |4.97 |5.51 |5.02 |
|24 |5.11 |4.90 |5.91 |4.66 |
|25 |4.50 |5.24 |4.86 |4.35 |
|26 |4.91 |4.79 |5.74 |5.03 |
|27 |4.65 |4.71 |4.81 |5.32 |
|28 |4.70 |5.50 |6.04 |4.30 |
|29 |5.87 |5.30 |5.78 |5.07 |
|30 |4.41 |4.75 |4.95 |5.11 |

c. Ten more observations were taken, as shown in the second table below.
Using the revised [pic] and R charts from part (b), comment on what the chart shows after extending it with the new data.

|31 |4.92 |5.54 |5.00 |5.42 |
|32 |4.65 |5.14 |4.26 |4.71 |
|33 |5.78 |5.50 |5.05 |4.79 |
|34 |5.95 |3.83 |4.30 |4.44 |
|35 |4.92 |4.80 |4.75 |5.59 |
|36 |5.68 |5.74 |4.65 |4.65 |
|37 |4.78 |5.79 |5.20 |4.70 |
|38 |4.43 |4.81 |5.27 |4.87 |
|39 |6.04 |4.47 |5.18 |5.41 |
|40 |4.96 |5.18 |5.48 |4.73 |

Analysis

See computations and control charts below. (See spreadsheets P14-14AXR.xls, P14-14BXR.xls, and P14-14CXR.xls in the instructor’s manual for details.)

a) Center Lines, CL[pic] : [pic] = 5.100; CLR : [pic] = 1.083 Control limits for the [pic]- chart are:

[pic] ± A2 [pic] = 5.100 ± 0.729 (1.083) = 4.310 to 5.890

For the R-chart: UCLR = D4 [pic] = 2.282 (1.083) = 2.471 LCLR = D3 [pic] = 0

[pic] ± A2 [pic] = 5.037 ± 0.729 (1.057) = 4.266 to 5.808

For the R-chart: UCLR = D4 [pic] = 2.282 (1.057) = 2.412 LCLR = D3 [pic] = 0

The [pic] and R-charts, below, now show that the process is in control.

b) We can see from the above [pic]- chart that Samples 19 and 21 are out of control and from the R-chart, above, that sample 18 is out of control on its range. We must search for, and eliminate assignable causes and re-calculate the following control limits and related charts after dropping these 3 points:

New Center Lines: Center Lines, CL[pic] : [pic] = 5.037; CLR : [pic] = 1.057 Control limits for the [pic]- chart are:

[pic] ± A2 [pic] = 5.037 ± 0.729 (1.057) = 4.266 to 5.808

For the R-chart: UCLR = D4 [pic] = 2.282 (1.057) = 2.412 LCLR = D3 [pic] = 0

[pic]

[pic]

The additional data shows that the process is still operating within control limits. See the "composite" control charts below.

[pic]

[pic]

Conclusions

• Using 30 samples, with the calculated control limits, the preliminary [pic] and R-charts showed that the process was out of control. • Assignable causes were investigated and three points were removed. Both the [pic] and R- charts were then in control. • The additional 10 samples show that the process is still operating within control limits. See the "composite" control charts above.

Recommendations

The report to management would include the analysis presented above. It should also include the recommendations that he/she:

• Monitor the process, to ensure that assignable causes mentioned above, don’t recur. If they are obviously due to non-recurring factors, the process should remain in control. If it is felt that control limits are still realistic, continue to monitor the process without changing them.

• Perform a process capability study to determine areas for improvement.…...

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