BASIC PRACTICE OF STATISTICS+LAUNCHPAD
BASIC PRACTICE OF STATISTICS+LAUNCHPAD
8th Edition
ISBN: 9781319053093
Author: Moore
Publisher: MAC HIGHER
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Chapter 31, Problem 31.53E

a.

To determine

To find: The center line and control limits should be drawn on the s chart and x¯ chart.

a.

Expert Solution
Check Mark

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 x¯ chart, the center line is 74, the lower control limit is 73.9799, and the upper control limit is 74.0201.

Explanation of Solution

Given info:

The target diameter for ring is μ=74millimeters and σ=0.015millimeter .

Calculation:

s chart:

Center line for an s chart:

CL=c4σ=0.9400(0.015)=0.0141

Upper control limits:

From Table 31.3: Control chart constants, the value of B6 corresponding with the sample size n=5 is 1.964.

UCL=B6σ=1.964(0.015)=0.0295

Lower control limits:

From Table 31.3: Control chart constants, the value of B5 corresponding with the sample size n=5 is 0.

LCL=B5σ^=0(0.015)=0

Thus, the center line is 0.0141, the lower control limit is 0, and the upper control limit is 0.0295.

x¯ chart:

Center line for a x¯ chart:

CL=μ=74

Upper control limits:

UCL=μ+3σn=74+30.0155=74+0.0201=74.0201

Lower control limits:

LCL=μ3σn=7430.0155=740.0201=73.9799

Thus, the center line is 74, the lower control limit is 73.9799, and the upper control limit is 74.0201.

b.

To determine

To find: The center line and control limits should be drawn on the s chart and x¯ chart when μ=73.945mm and σ=0.015mm .

To find: The center line and control limits should be drawn on the s chart and x¯ chart when μ=74mm and σ=0.005mm .

b.

Expert Solution
Check Mark

Answer to Problem 31.53E

The control limits are tabulated below:

Mean and SD s chart x¯ chart
LCL CL UCL LCL CL UCL
μ=73.945mm and σ=0.015mm 0 0.0138 0.0313 73.9225 73.945 73.9675
μ=74mm and σ=0.005mm 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 μ=73.945mm and σ=0.015mm .

Calculation:

When μ=73.945mm and σ=0.015mm , the control limits for s chart is as follows:

Center line for an s chart:

From Table 31.3: Control chart constants, the value of c4 corresponding with the sample size n=4 is 0.9213.

CL=c4σ=0.9213(0.015)=0.0138

Upper control limits:

From Table 31.3: Control chart constants, the value of B6 corresponding with the sample size n=4 is 2.088.

UCL=B6σ=2.088(0.015)=0.0313

Lower control limits:

From Table 31.3: Control chart constants, the value of B5 corresponding with the sample size n=4 is 0.

LCL=B5σ^=0(0.015)=0

Thus, the center line is 0.0138, the lower control limit is 0, and the upper control limit is 0.0313.

When μ=73.945mm and σ=0.015mm , the control limits for x¯ chart is as follows:

Center line for a x¯ chart:

CL=μ=73.945

Upper control limits:

UCL=μ+3σn=73.945+30.0154=73.945+0.0225=73.9675

Lower control limits:

LCL=μ3σn=73.94530.0154=73.9450.0225=73.9225

Thus, the center line is 73.945, the lower control limit is 73.9225, and the upper control limit is 73.9675.

When μ=74mm and σ=0.005mm , the control limits for s chart is as follows:

Center line for an s chart:

From Table 31.3: Control chart constants, the value of c4 corresponding with the sample size n=4 is 0.9213.

CL=c4σ=0.9213(0.005)=0.0046

Upper control limits:

From Table 31.3: Control chart constants, the value of B6 corresponding with the sample size n=4 is 2.088.

UCL=B6σ=2.088(0.005)=0.0104

Lower control limits:

From Table 31.3: Control chart constants, the value of B5 corresponding with the sample size n=4 is 0.

LCL=B5σ^=0(0.005)=0

Thus, the center line is 0.0046, the lower control limit is 0, and the upper control limit is 0.0104.

When μ=74mm and σ=0.005mm , the control limits for x¯ chart is as follows:

Center line for a x¯ chart:

CL=μ=74

Upper control limits:

UCL=μ+3σn=74+30.0054=74+0.0075=74.0075

Lower control limits:

LCL=μ3σn=7430.0054=740.0075=73.9925

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 μ=73.945mm and σ=0.015mm .

For x¯ chart, the control limits are wider when using μ=74mm and σ=0.005mm .

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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