a.
To find: The center line and control limits should be drawn on the s chart and
a.
Answer to Problem 31.53E
For the s chart, the center line is 0.0141, the lower control limit is 0, and the upper control limit is 0.0295.
For
Explanation of Solution
Given info:
The target diameter for ring is
Calculation:
s chart:
Center line for an s chart:
Upper control limits:
From Table 31.3: Control chart constants, the value of
Lower control limits:
From Table 31.3: Control chart constants, the value of
Thus, the center line is 0.0141, the lower control limit is 0, and the upper control limit is 0.0295.
Center line for a
Upper control limits:
Lower control limits:
Thus, the center line is 74, the lower control limit is 73.9799, and the upper control limit is 74.0201.
b.
To find: The center line and control limits should be drawn on the s chart and
To find: The center line and control limits should be drawn on the s chart and
b.
Answer to Problem 31.53E
The control limits are tabulated below:
Mean and SD | s chart | |||||
LCL | CL | UCL | LCL | CL | UCL | |
0 | 0.0138 | 0.0313 | 73.9225 | 73.945 | 73.9675 | |
0 | 0.0046 | 0.0104 | 73.9225 | 74 | 74.0075 |
The issues that might arise for the manufacturer of the engine when the two parts from the different manufacturers are assembled is the statistical control process does not provide required information about the data.
Explanation of Solution
Given info:
The target diameter for ring is
Calculation:
When
Center line for an s chart:
From Table 31.3: Control chart constants, the value of
Upper control limits:
From Table 31.3: Control chart constants, the value of
Lower control limits:
From Table 31.3: Control chart constants, the value of
Thus, the center line is 0.0138, the lower control limit is 0, and the upper control limit is 0.0313.
When
Center line for a
Upper control limits:
Lower control limits:
Thus, the center line is 73.945, the lower control limit is 73.9225, and the upper control limit is 73.9675.
When
Center line for an s chart:
From Table 31.3: Control chart constants, the value of
Upper control limits:
From Table 31.3: Control chart constants, the value of
Lower control limits:
From Table 31.3: Control chart constants, the value of
Thus, the center line is 0.0046, the lower control limit is 0, and the upper control limit is 0.0104.
When
Center line for a
Upper control limits:
Lower control limits:
Thus, the center line is 74, the lower control limit is 73.9225, and the upper control limit is 74.0075.
Justification:
For s chart, the control limits are wider when using
For
When changing the target value and sigma, the result of the process variation should be changed. Moreover, it is not necessarily capable of meeting the requirement of piston diameter and difficult to identifying the defective items. Thus, the statistical control process does not provide information about the data when the two parts from the different manufacturers are assembled.
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Chapter 31 Solutions
The Basic Practice of Statistics
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