Management Chapter 10s Homework The two basic factors in choosing between single and multiple sampling are the cost per sample and the cost per observation

Supplement to Chapter Ten – Acceptance Sampling

Templates: Acceptance Sampling (B)

Lecture Suggestions

(B) – includes Basic template

Example 2

See Instructions template for complete instructions.

Acceptance Sampling

Acceptance Sampling – Binomial Distribution Basic

<Back N = 500 n = 10 c = 1

Fraction defective = 0.1 Fraction defective = 0.15

Basic Template: You can simply copy the basic template below and paste into another worksheet.

^Top If you also copy the graphs you will have to fix the cell references in the graph

(right-click on the graph, click Select Data…, and Edit the Series values for each series).

Acceptance Sampling – Binomial Distribution

0.7361

0.6

0.7

0.8

0.9

1

Operating Characteristic Curve

0.0816

0.05

0.06

0.07

0.08

0.09

Average Outgoing Quality

Page 2

Acceptance Sampling

n = 10

c = 1

Fraction

Defective P(Accept) AOQ

0.000 1 0

0.050 0.9138616 0.0456931

0.350 0.0859544 0.0300841

0.400 0.0463574 0.018543

0.450 0.0232571 0.0104657

0.500 0.0107422 0.0053711

0.550 0.0045022 0.0024762

0.600 0.0016777 0.0010066

0.650 0.0005399 0.0003509

0.700 0.0001437 0.0001006

1.000 0 0

0.4

0.6

0.8

1

1.2

P(accept)

0.06

0.08

0.1

Page 3

0.100 0.7360989 0.0736099

0.150 0.5442998 0.081645

0.200 0.3758096 0.0751619

0.300 0.1493083 0.0447925

Acceptance Sampling

0 1

0.0000 1 -1.32E-16 1.87E-11 0.95

0.0275 0.970615 0.026692 9.1E-09 0.9

0.0825 0.802837 0.066234 4.2E-06 0.8

0.1375 0.59101 0.081264 0.000144 0.7

0.1925 0.398881 0.076785 0.001678 0.6

0.2200 0.318469 0.070063 0.004502 0.55

0.2475 0.249704 0.061802 0.010742 0.5

0.3025 0.145456 0.044001 0.046357 0.4

0.3575 0.078689 0.028131 0.149308 0.3

0.4125 0.039294 0.016209 0.37581 0.2

0.4400 0.026864 0.01182 0.5443 0.15

0.4675 0.017927 0.008381 0.736099 0.1

0.4950 0.011652 0.005768 0.913862 0.05

0.5225 0.007359 0.003845 1 0

0.1 0

0.1 0.736099

0.15 0 0

0.15 0.5443 0.081645

Lecture Suggestions – Supplement to Chapter 10

<Back

Example 1: Acceptance Sampling

1. Select the Example 1.

2. Enter the following data: N=5000, n=80, and c=2

3. The operating characteristic curve is on the left. Use the spinner button below the graph to

demonstrate the probability of acceptance for various levels of incoming fraction defectives. Also use

4. The average outgoing quality curve is on the right. Use the spinner button below the graph to

demonstrate AOQ for various levels of incoming fraction defective. You can find the maximum AOQ

Example 1

Acceptance Sampling – Binomial Distribution

<Back N = 5000 n = 80 c = 2

Fraction defective = 0.01 Fraction defective = 0.03

Note: Example 1 in text uses Poisson approximation to the Binomial.

0.9534

0

0.1

0.2

0.3

0.5

0.7

0.9

1

0.00 0.05 0.10 0.15 0.20

Fraction defective

Operating Characteristic Curve

0.0170

0

0.004

0.01

0.014

0.016

0.018

0.00 0.05 0.10 0.15 0.20

Fraction defective

Average Outgoing Quality

Page 6

Example 1

0 1

0.0000 1 -2.26E-17 9.4E-99 0.95

0.0075 0.977405 0.007331 2.57E-75 0.9

0.0225 0.731247 0.016453 6.15E-52 0.8

0.0375 0.418904 0.015709 2.57E-38 0.7

0.0525 0.202443 0.010628 1.06E-28 0.6

0.0600 0.134446 0.008067 8.71E-25 0.55

0.0675 0.08713 0.005881 2.68E-21 0.5

0.0825 0.034409 0.002839 2.61E-15 0.4

0.0975 0.01269 0.001237 2.5E-10 0.3

0.1050 0.007538 0.000791 3.83E-08 0.25

0.1125 0.004419 0.000497 3.86E-06 0.2

0.1275 0.001463 0.000187 0.010684 0.1

0.1425 0.000463 6.6E-05 1 0

0.1500 0.000256 3.84E-05

0.01 0

0.01 0.953447

0.03 0 0

0.03 0.568123 0.017044

Page 7

Example 2

Acceptance Sampling – Binomial Distribution

<Back N = 500 n = 10 c = 1

Fraction defective = 0.1 Fraction defective = 0.15

0.7361

0

0.1

0.2

0.4

0.7

0.8

1

0.00 0.20 0.40 0.60

P(accept)

Fraction defective

Operating Characteristic Curve

0

0.03

0.04

0.07

0.09

0.00 0.20 0.40 0.60

AOQ

Fraction defective

Average Outgoing Quality

Page 8

Example 2

0 1

0.0000 1 -1.32E-16 1.87E-11 0.95

0.0275 0.970615 0.026692 9.1E-09 0.9

0.0825 0.802837 0.066234 4.2E-06 0.8

0.1375 0.59101 0.081264 0.000144 0.7

0.1650 0.490348 0.080907 0.00054 0.65

0.1925 0.398881 0.076785 0.001678 0.6

0.2200 0.318469 0.070063 0.004502 0.55

0.2475 0.249704 0.061802 0.010742 0.5

0.3025 0.145456 0.044001 0.046357 0.4

0.3575 0.078689 0.028131 0.149308 0.3

0.4125 0.039294 0.016209 0.37581 0.2

0.4400 0.026864 0.01182 0.5443 0.15

0.4675 0.017927 0.008381 0.736099 0.1

0.4950 0.011652 0.005768 0.913862 0.05

0.5225 0.007359 0.003845 1 0

0.5500 0.004502 0.002476

Page 9

Solved Problem 2

Acceptance Sampling – Binomial Distribution

<Back N = 300 n = 5 c = 1

Fraction defective = 0.15 Fraction defective = 0.27

0.8352

0.6

0.7

0.8

0.9

1

Fraction defective

Operating Characteristic Curve

0.1595

0.12

0.14

0.16

0.18

Fraction defective

Average Outgoing Quality

Page 10

Solved Problem 2

0.1200 0.887549 0.106506 0.00672 0.8

0.1600 0.816509 0.130641 0.015625 0.75

0.2000 0.73728 0.147456 0.03078 0.7

0.3600 0.409364 0.147371 0.1875 0.5

0.4000 0.33696 0.134784 0.256218 0.45

0.4400 0.271432 0.11943 0.33696 0.4

0.5200 0.163499 0.08502 0.52822 0.3

0.6000 0.08704 0.052224 0.73728 0.2

0.6400 0.059794 0.038268 0.83521 0.15

0.6800 0.039007 0.026525 0.91854 0.1

0.7600 0.013404 0.010187 1 0

0.15 0

0.15 0.83521

0.27 0 0

0.27 0.590683 0.159485

Supplement to Chapter 10 – Problems 2-6 Note: This worksheet displays results only, you must copy the shaded

<Back area into the corresponding template to make additional calculations.

2. Acceptance Sampling – Binomial Distribution

N = 4000 n = 20 c = 1

3a. Acceptance Sampling – Binomial Distribution

N = 8000 n = 15 c = 0

3b-c. Acceptance Sampling – Binomial Distribution

N = 8000 n = 150 c = 0

4. Acceptance Sampling – Binomial Distribution

Note: AOQL is estimated from each of the following sampling plans.

4a.

N = 3000 n = 100 c = 0

N = 3000 n = 100 c = 1