IE 1055 2025 Homework 3 Due Jan 25 2017 1 Problem 2 25 from the text This problem was on the last assignment Assume that part A must pass through machines 1 and 2 to be completed For example machine 1 drills a hole and machine 2 puts a taper in the hole made at machine 1 Similarly part B must pass through both machines 3 and 4 to be completed Please note that on problem 2 25 that the desired output 06 means the output of station 6 and that input 11 to machine 1 is a typo and means the input to machine 1 it ought to read input to machine 1 20 pts a Determine an equation for the required input for both machines 1 and 3 not just machine 1 as stated in the problem b Determine the required input for both machines 1 and 3 if the following scrap percentages apply d1 10 d2 05 d3 05 d4 02 d5 04 d6 01 c If the desired output of parts at station 6 is 70 parts per hour determine the input rate of parts required at stations 1 and 3 for the problem variations described in parts b and c of this problem d How does the answer to part b change if 75 of the defects at machine 1 and 99 of the defects at machine 5 can be reworked Give both a qualitative and quantitative answer the quantitative answer will relate I1 to O6 for example but will not be a number such as start with 100 parts because no numeric value is specified for O6 Answer 20 pts a Part A M 1 M 2 P1 Part B M 3 P2 M 4 P3 M 5 M 6 P5 Part C P6 P4 If O6 is the desired output for part C then the required inputs I1 to machine 1 and I3 to machine 3 are O6 I1 1 P1 1 P2 1 P5 1 P6 O6 I3 1 P3 1 P4 1 P5 1 P6 THIS SOLUTION MAY ONLY BE USED FOR IE 1055 2025 SPRING 2017 b Part A Part B 0 90 0 95 M 1 M 2 0 96 0 99 0 95 0 98 M 5 M 6 M 3 M 4 Part C Given p1 0 10 p2 0 05 p3 0 05 p4 0 02 p5 0 04 p6 0 01 If O6 is the desired output for part C then the required inputs I1 to machine 1 and I3 to machine 3 are O6 I1 1 p1 1 p 2 1 p5 1 p 6 O6 1 0 10 1 0 05 1 0 04 1 0 01 O 6 1 230 O6 0 813 O6 I3 1 p3 1 p 4 1 p5 1 p 6 O6 1 0 05 1 0 02 1 0 04 1 0 01 O 6 1 130O6 0 885 c If the desired output for part C is 70 then the required inputs to machine 1 and 3 are O6 I1 1 p1 1 p 2 1 p5 1 p 6 70 1 0 10 1 0 05 1 0 04 1 0 01 86 14 87 THIS SOLUTION MAY ONLY BE USED FOR IE 1055 2025 SPRING 2017 O6 I3 1 p3 1 p 4 1 p5 1 p 6 70 1 0 05 1 0 02 1 0 04 1 0 01 79 1 80 Note that we need to round up to the next greatest integer in order to insure that we meet the required throughput d Part A 0 90 0 95 M 1 M 2 0 96 0 99 0 95 0 98 M 5 M 6 M 3 M 4 q1 Part B Part C q5 Given q1 0 75 q5 0 99 If O6 is the desired output for part C then the required inputs I1 to machine 1 and I3 to machine 3 are O6 1 q1 p1 1 q5 p5 I1 1 p1 1 p 2 1 p5 1 p 6 O 1 0 10 0 75 1 0 04 6 1 0 10 1 0 05 1 0 04 1 0 888 O6 1 092O6 0 813 O6 1 q5 p5 I3 1 p3 1 p4 1 p5 1 p6 O6 1 0 04 0 99 1 0 05 1 0 02 1 0 04 1 0 01 0 960 O6 1 085O6 0 885 THIS SOLUTION MAY ONLY BE USED FOR IE 1055 2025 SPRING 2017 2 2 23 except change the quantity required to 300 non defective parts 10 pts Answer 10 pts S 15 min H 8hrs shift 60min hr 480 min shift E 15min 20min 0 75 Q 300 375 1 0 2 units R 7 8 0 875 F 15min unit 375 units shift 17 86 0 75 480min shift 7 8 18 Machines You could also choose to use an S value of 20 and then drop E from the denominator 3 Rework problem 2 23 still change the quantity required to 300 non defective parts if one half of the defective items can be reworked Assume that the reworked items also have an 80 probability of being non defective and that the parts can be reworked indefinitely thus the reworked parts have the same probability of being good as the new parts do these assumptions are similar to what we assumed in the class discussion How does your answer compare to the answer for problem 2 23 from problem 2 Discuss any implications 10 pts Answer 10 pts The equipment fraction does not change because the processing rate is still 375 units The reason is that with rework the number of parts to start with should be I O 1 qp 1 p but the processing rate I PR 1 qp O 1 qp O 1 p 375 1 p 1 qp since the last expression is exactly what we had before It is important to note that now there is less scrap and therefore the input rate would be lower too 4 You work for SteelPro a fabrication company that specializes in machining specialty alloys One of your best customers is Bombardier Transportation Bombardier has asked you to fill an order for 20 of their part 107 Bombardier will pay you 500 for each good part 107 but will only accept exactly 20 good ones no more no less The raw materials required to make a 107 cost 150 Unfortunately you have yield loss issues related to manufacturing the 107 Assume that the 107s are produced independently of each other with the probability of an individual 107 being good being equal to 0 85 Defective 107s can be scrapped for 50 There is also the technical challenge that the way you THIS SOLUTION MAY ONLY BE USED FOR IE 1055 2025 SPRING 2017 process the 107s is that you machine the entire batch whatever batch size you choose and then you heat treat and further process them and only after the heat treating and further processing do the defects become detectable Thus you must determine the batch size to …