# Chap 14 - Chapter 14 Statistical Methods for Quality...

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Unformatted text preview: Chapter 14 Statistical Methods for Quality Control Learning Objectives 1. Learn about the importance of quality control and how statistical methods can assist in the quality control process. 2. Learn about acceptance sampling procedures. 3. Know the difference between consumer’s risk and producer’s risk. 4. Be able to use the binomial probability distribution to develop acceptance sampling plans. 5. Know what is meant by multiple sampling plans. 6. Be able to construct quality control charts and understand how they are used for statistical process control. 7. Know the definitions of the following terms: producer's risk assignable causes consumer's risk common causes acceptance sampling control charts acceptable criterion upper control limit operating characteristic curve lower control limit 14 - 1 Chapter 14 Solutions: 1. a. For n = 4 UCL = μ + 3( σ / n ) = 12.5 + 3(.8 / 4 ) = 13.7 LCL = μ- 3( σ / n ) = 12.5 - 3(.8 / 4 ) = 11.3 b. For n = 8 UCL = μ + 3(.8 / 8 ) = 13.35 LCL = μ- 3(.8 / 8 ) = 11.65 For n = 16 UCL = μ + 3(.8 / 16 ) = 13.10 LCL = μ- 3(.8 / 16 ) = 11.90 c. UCL and LCL become closer together as n increases. If the process is in control, the larger samples should have less variance and should fall closer to 12.5. 2. a. μ = = 677 5 25 5 542 . ( ) . b. UCL = μ + 3( σ / n ) = 5.42 + 3(.5 / 5 ) = 6.09 LCL = μ- 3( σ / n ) = 5.42 - 3(.5 / 5 ) = 4.75 3. a. p = = 135 25 100 0 0540 ( ) . b. σ p p p n =- = = ( ) . ( . ) . 1 0 0540 0 9460 100 0 0226 c. UCL = p + 3 σ p = 0.0540 + 3(0.0226) = 0.1218 LCL = p- 3 σ p = 0.0540 -3(0.0226) = -0.0138 Use LCL = 4. R Chart: UCL = RD 4 = 1.6(1.864) = 2.98 LCL = RD 3 = 1.6(0.136) = 0.22 x Chart: UCL = x 2 A R + = 28.5 + 0.373(1.6) = 29.10 LCL = x 2 A R- = 28.5 - 0.373(1.6) = 27.90 5. a. UCL = μ + 3( σ / n ) = 128.5 + 3(.4 / 6 ) = 128.99 LCL = μ- 3( σ / n ) = 128.5 - 3(.4 / 6 ) = 128.01 14 - 2 Statistical Methods for Quality Control b. x x n i = = = Σ / . . 772 4 6 128 73 in control c. x x n i = = = Σ / . . 774 3 6 129 05 out of control 6. Process Mean = 2012 19 90 2 20 01 . . . + = UCL = μ + 3( σ / n ) = 20.01 + 3( σ / 5 ) = 20.12 Solve for σ : σ =- = ( . . ) . 2012 20 01 5 3 0 082 7. Sample Number Observations x i R i 1 31 42 28 33.67 14 2 26 18 35 26.33 17 3 25 30 34 29.67 9 4 17 25 21 21.00 8 5 38 29 35 34.00 9 6 41 42 36 39.67 6 7 21 17 29 22.33 12 8 32 26 28 28.67 6 9 41 34 33 36.00 8 10 29 17 30 25.33 13 11 26 31 40 32.33 14 12 23 19 25 22.33 6 13 17 24 32 24.33 15 14 43 35 17 31.67 26 15 18 25 29 24.0024....
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## This note was uploaded on 11/08/2011 for the course MAT/FIN 272 taught by Professor Burns during the Spring '11 term at Central Connecticut State University.

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Chap 14 - Chapter 14 Statistical Methods for Quality...

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