Beth Zion Hospital has received initial certification from the state of Californ

Question

Beth Zion Hospital has received initial certification from the state of California to become a vernter for liverstransplants. The hospital, however, must complete its first 18 transplants under great scrutiny and at no cost to the patients. The very first transplant, just completed, required 30 hours. On the basis of research at the hospital, Beth Zion estimates that it will have an 80% learning curve. Estimate the time it will take to complete:

a) the 5th liver transplant

b) all of the first 5 transplants

c) the 18th transplant

d) all 18 transplants

Please show all work, thank you!

Explanation / Answer

According to the Wright's learning curve theory Y = a(X^b) where: Y = the cumulative average time (or cost) per unit (for n number of Units) X = the cumulative number of units produced (i. e. n Units) a = time (or cost) required to produce the first unit. b = slope of the function when plotted on log-log paper.    = log of the learning rate/log of 2. - Here in this question we have to find the time to complete X Transplants , where X is X= 4 Transplants X= 5 Transplants X= 17 Transplants X= 18 Transplants - Time required to proudce the 1st Unit is 116 Hrs a= 30 Hrs The Hospital expects that it will have 80% Learning Curve. Assuming that the company would experience the same learning curve Cumulative time (Y) taken for X nos of transplant is as per below calculations b= Log(80%)/Log(2) b= 0.67807 = 1-0.32193 Y = a(X^b) 77 Hrs When X = 4 Transplants Y = a(X^b) 89 Hrs When X = 5 Transplants Y = a(X^b) 205 Hrs When X = 17 Transplants Y = a(X^b) 213 Hrs When X = 18 Transplants From the above calculations, a) The time taken by the 5th Transplant = cumulative time for 1st 5 transplant - cumulative time taken for 1st 4 Transplants 13 Hrs b) Time taken for the 1st 5 Transplants = 89 Hrs c) The time taken by the 18th Transplant = cumulative time for 1st 18 transplant - cumulative time taken for 1st 17 Transplants 8 Hrs d) Time taken for the 1st 18 Transplants = 213 Hrs

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