The machine shop in a bicycle manufacturing firm makes three gears that fit toge

Question

The machine shop in a bicycle manufacturing firm makes three gears that fit together to become part of the gear shift mechanism for the bicycle. Each part must be a specific diameter within specific tolerances. The three parts, when put together to slip into the rear wheel of the bike, must also meet an overall diameter within a specific tolerance.

Samples for the three parts were taken.

Bicycle Parts Co.

Sample Means and Standard Deviations

Part 1

Part 2

Part 3

1.74831

2.01144

1.25426

1.75740

2.00448

1.24775

1.75134

2.01492

1.24558

1.73316

2.00448

1.24992

1.75134

2.00448

1.23907

1.71498

2.00100

1.25860

1.75437

2.00796

1.25643

1.73619

2.00100

1.25209

1.73922

1.98708

1.25426

1.73619

1.99752

1.24341

1.74528

1.99752

1.25643

1.74831

2.00100

1.24775

1.76346

1.99404

1.24341

1.74528

2.00796

1.24558

1.76952

2.00448

1.23907

1.70892

2.00448

1.24124

1.75134

2.00100

1.24558

1.71195

1.99752

1.24992

1.74831

2.00100

1.25209

1.77861

2.00100

1.24992

1.75740

1.98708

1.24992

1.73619

1.99404

1.24558

1.74225

1.98708

1.24992

1.74528

1.98360

1.24775

1.73922

2.00100

1.24775

Calculate the mean and standard deviations for each part and compare them to the following specification limits:

Part     Nominal (inches) Tolerance (inches)

1        1.750 + 0.045

2        2.000 + 0.060

3 1.250 + 0.030

2. Will the production process permit an acceptable fit of Part 1 at least 99.73 percent of the time?

3. Will the production process permit an acceptable fit of Part 2 at least 99.73 percent of the time?

4. Will the production process permit an acceptable fit of Part 3 at least 99.73 percent of the time?

5. Will the production process permit an acceptable fit of all three part combined into a slot with a specification of 5 + 0.081 inches at least 99.73% of the time?

Bicycle Parts Co.

Sample Means and Standard Deviations

Part 1

Part 2

Part 3

1.74831

2.01144

1.25426

1.75740

2.00448

1.24775

1.75134

2.01492

1.24558

1.73316

2.00448

1.24992

1.75134

2.00448

1.23907

1.71498

2.00100

1.25860

1.75437

2.00796

1.25643

1.73619

2.00100

1.25209

1.73922

1.98708

1.25426

1.73619

1.99752

1.24341

1.74528

1.99752

1.25643

1.74831

2.00100

1.24775

1.76346

1.99404

1.24341

1.74528

2.00796

1.24558

1.76952

2.00448

1.23907

1.70892

2.00448

1.24124

1.75134

2.00100

1.24558

1.71195

1.99752

1.24992

1.74831

2.00100

1.25209

1.77861

2.00100

1.24992

1.75740

1.98708

1.24992

1.73619

1.99404

1.24558

1.74225

1.98708

1.24992

1.74528

1.98360

1.24775

1.73922

2.00100

1.24775

Explanation / Answer

Based on the sample testings:

The production of All the parts is permitted along with the part combining the three of them as the 99.73% value is within the tolerance value of the part manufactured.

Hope this helps.

Part 1 Part 2 Part 3 Total Part 1 Part 2 Part 3 Total 1.74831 2.01144 1.25426 5.01401 Mean 1.745 2.000 1.249 4.993 1.7574 2.00448 1.24775 5.00963 SD 0.016 0.008 0.005 0.018 1.75134 2.01492 1.24558 5.01184 1.73316 2.00448 1.24992 4.98756 99.73% 1.75134 2.00448 1.23907 4.99489 Lower Limit 1.696 1.977 1.233 4.939 1.71498 2.001 1.2586 4.97458 upper limit 1.793 2.023 1.264 5.047 1.75437 2.00796 1.25643 5.01876 1.73619 2.001 1.25209 4.98928 1.73922 1.98708 1.25426 4.98056 1.73619 1.99752 1.24341 4.97712 1.74528 1.99752 1.25643 4.99923 1.74831 2.001 1.24775 4.99706 1.76346 1.99404 1.24341 5.00091 1.74528 2.00796 1.24558 4.99882 1.76952 2.00448 1.23907 5.01307 1.70892 2.00448 1.24124 4.95464 1.75134 2.001 1.24558 4.99792 1.71195 1.99752 1.24992 4.95939 1.74831 2.001 1.25209 5.0014 1.77861 2.001 1.24992 5.02953 1.7574 1.98708 1.24992 4.9944 1.73619 1.99404 1.24558 4.97581 1.74225 1.98708 1.24992 4.97925 1.74528 1.9836 1.24775 4.97663 1.73922 2.001 1.24775 4.98797

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