SYSEN536 HW3

xlsx

School

Pennsylvania State University, World Campus *

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Course

536

Subject

Industrial Engineering

Date

Feb 20, 2024

Type

xlsx

Pages

19

Uploaded by CountSeaLionMaster1018

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Problem 1 P(A and B) 12% 29% P(A) 41% P(B) 65% 35% P(B|A) 29.27% P(A|B) 18.46% 17.1% P(A and B ) P( B ) P( A | B )
Part a Beta for the exponential distribution PE(T<=15|Beta)=0.5 Beta Mean #NAME? b) PN(Y <=25 | μ, σ) = 0.25 PN(Y <=125 | μ, σ) = 0.75 Mean μ #NAME? 74.13 c) Pr(Y <= 15 |Min, MostLikely, Max)= 0.15, 15 Pr(Y <= 50 |Min, MostLikely, Max)= 0.50 50 The parameters μ and σ for a normal distribution St. Deviation σ Find the Min, Most Likely, and Max for the triangular distribution given: Pr(Y <= 15 |Min, MostLikely, Max)= 0.15,
Pr(Y > 95 |Min, MostLikely, Max)= 0.05. 95 Mean Estimation 53.33 Mean 48.19 d) Find the parameter value a1 and a2 for the Beta Distribution PB(Q<=0.3|a1,a2)=0.05 PB(Q<=0.5|a1,a2)=0.25 Alpha 1 3.674952 Alpha 2 2.169143 Mean #NAME?
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a) No. of defective No.of Boxes 0 68 1 27 2 3 3 2 AIC Poisson 164.8122 BIC Poisson = 167.3 The Poisson is the best fitting as both AIC and BIC fittings. The m roughly amounting to 12 bulbs i
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b) No of Defective No of Boxes 0 68 1 27 2 5 There is a 0.02 difference in mean compared to the part A The number of defective bulbs p events occurring in a fixed inter the Poisson distribution can be
c) The choice of distribution depends on the specific characteristics of the data and the objectives of the quality-control program. If the assembly line process is such that the occurrence of defective bulbs follows a Poisson-like pattern (i.e., random and independent events occurring at a constant rate), then the Poisson distribution may be appropriate.
s it has the lowest vaules in mean is 0.39 defective bulbs in a box
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per box can be viewed as rval (each box produced), and a reasonable choice.
New Supplier Breakage rate Current Supplier 468 6.40% 444 474 5.20% 449 474 5.20% 443 479 4.20% 440 482 3.60% 439 478 4.40% 448 467 6.60% 441 469 6.20% 434 484 3.20% 427 470 6.00% 446 463 7.40% 452 468 6.40% 442 450 444 433 441 436 429 Minimum 463 3.20% 427 Maximum 484 7.40% 452 PartA 1)
2) 3) New Supplier Current Supplier Mean 473 441 5% 464 429 95% 481 453 Part B Cost per Shell New Supplier $ (0.0528812) Current Supplier $ (0.0538696) #NAME? ($25.00) Decision Taco New Shell Supplier
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-0.052881154280763 #NAME? ($23.75) 2) 3) Using the EVM the optimal strategy is to switch to the justified through the reduced cost per taco proportion taco shells. Taco Current Shell Supplier -0.0555 -0.055 -0.0545 -0.054 -0.0535 -0.053 -0.0525 -0.052 -0.0515 0% 20% 40% 60% 80% 100% Cumulative Probabilities for Decision Tree Choice Comparison for Node 'Decision' New Curre Cumulative Probability PrecisionTree Course Versio P enn State University PrecisionTree Course Versio P enn State University PrecisionTree Course Versio P enn State University PrecisionTree Course Versio P enn State University PrecisionTree Course Versio P enn State University
Breakage rate 11.20% 10.20% 11.40% 12.00% 12.20% 10.40% 11.80% 13.20% 14.60% 10.80% 9.60% 11.60% 10.00% 11.20% 13.40% 11.80% 12.80% 14.20% 9.60% 14.60%
18.5% 18.5% 464 -0.053879310344828 Chance -0.052881154280763 63.0% 63.0% 473 -0.052854122621565 18.5% 18.5% 481 -0.051975051975052 5th percentile Mean / 50th percentile 95th percentile
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18.5% 0.0% 429 -0.055361305361305 Chance -0.053869640293481 63.0% 0.0% 441 -0.053854875283447 18.5% 0.0% 453 -0.05242825607064 e new supplier. This can be nal to the number of broken 5th percentile Mean / 50th percentile 95th percentile e 'Taco' Shell Supplier ent Shell Supplier on on on on on
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PrecisionTree RiskProfile - Cumulative Chart Chart Data New Shell Supplier Current Shell Supplier Value Probability Value Probability #1 Infinity 0.0000% Infinity 0.0000% #2 -0.0538793103 0.0000% -0.0553613054 0.0000% #3 -0.0538793103 18.5000% -0.0553613054 18.5000% #4 -0.0528541226 18.5000% -0.0538548753 18.5000% #5 -0.0528541226 81.5000% -0.0538548753 81.5000% #6 -0.051975052 81.5000% -0.0524282561 81.5000% #7 -0.051975052 100.0000% -0.0524282561 100.0000% #8 Infinity 100.0000% Infinity 100.0000% Performed By: vineet balla Date: Tuesday, January 30, 2024 10:29:15 AM Model: Decision Tree 'Taco' in [SYSEN536 HW3.xlsx]Problem4 Analysis: Choice Comparison for Node 'Decision' (D95) -0.0555 -0.055 -0.0545 -0.054 -0.0535 -0.053 -0.0525 -0.052 -0.0515 0% 20% 40% 60% 80% 100% Cumulative Probabilities for Decision Tree 'Taco' Choice Comparison for Node 'Decision' New Shell Supplier Current Shell Supplier Cumulative Probability PrecisionTree Course Version P enn State University PrecisionTree Course Version P enn State University PrecisionTree Course Version P enn State University PrecisionTree Course Version P enn State University PrecisionTree Course Version P enn State University

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