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ID: 357763 • Letter: S
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SHOW ALL WORK FOR THE QUESTIONS ASKED! WHEN IT SAYS CREATE A CHART, DO CREATE A CHART! AND WHEN IT SAYS TO EXPLAIN AN ANSWER, EXPLAIN THAT ANSWER! ANSWER ALL THE QUESTIONS ASKED IN GREAT DETAIL!
You're managing a packaging department at an Amazon fulfillment center and you use two complex machines to form the boxes, apply the tape and the shipping label. You have one skilled operator who knows how to operate the machines but recently has had health problems that have caused her to miss work 10% of the time. Machine 1 has a .97 reliability and machine 2 has a .90 reliability.
1. What is the current reliability of the system, including the operator?
2. You are part of a Kaizen team that is considering either scrapping machine 2 and replacing it with a machine that has a reliability of .97 at a cost of $5,000 or training another operator to fill in when the first operator at a cost of $5100. The prospective trainee has an excellent attendance record and has only missed 4 out of 250 work days in the past year. Management estimates that profits will increase by $7,000 per year if the line operated at 100% of capacity. If management wants to pay off its investment in the first year, determine the expected net profit for each alternative and recommend the most profitable to management.
Explanation / Answer
1) The current reliability depends on the operator. The question says he is unavailbale 10% of the time. Hence the reliability of system will be 0.9*0.97*0.9 = 0.786
2) Option 1: When machine 2 is replaced with a machine with reliability of 0.97 at $5000 investment
Expected profit at 100% capacity= $7000
Capacity with option 1: Reliability of current operator * Reliability of machine 1 * Reliability of new machine 2
= 0.9 * 0.97*0.97 = =0.8468
EARNINGS at 84.68% capacity = $7000*0.8468 = $5927.67
Additional investment in machine 2 = $ 5000
Net profit = $927.67
Option 2: When another operator is trained at $ 5100 to fill in when first operator is absent
Capacity with option 2: ( Capacity of first operator + Additional capacity due to new operator)* reliability of machine 1* reliabilty of machine 2
= ( 0.9 + 0.1*246/250)*0.97*0.9 = 0.8716
EARNINGS at 87.16% capacity = $7000*0.8716 = $6101.22
Net profit with option 2= $ 6101.22 - $ 5100 = $ 1001.22
The management should go with training another operator to achieve more profits
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