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.