Question

please show all steps no excel

10 pts 10) in a complex assembly operation. It is found that the learning curve rate is 80%. The standard time of 35 minutes per assembly is reached after the 125th unit. Find: a) The time required for the very first unit. b) The time required for the 20th unit.

Answer 1

Learning curve is a theory that provides that the more a particular task is done over time, the effort and time to complete the task becomes lesser.

a. Time required for the very first unit

It is represented in the equation as Tn=T1nb

where,n = the unit number (1 for the first unit, 2 for the second unit, etc.)

T1 = the amount of time to produce the first unit, lets assume this as X

Tn = the amount of time to produce unit n = 3.5 minutes it took for 125th unit

b = the learning curve factor, calculated as In (p)/ln(2) = LN(0.8)/LN(2) = -0.22314/0.69315 = -0.32193 (this is found from the excel function =LN; this can also be found using 'LOG' excel function as =LOG(0.8,2)

Applying this in the equation,

3.5 = X * 125^-0.32193

3.5 = X*0.211323

X = 3.5/0.211323 = 16.56

Thus, the time required for the very first unit = 16.56 minutes

b. Time required for the 220th unit

Applying the same above equation, Tn=T1nb

where,n = the unit number = 220

T1 = the amount of time to produce the first unit = 16.56 minutes (as above)

b = the learning curve factor, calculated as In (p)/ln(2) = LN(0.8)/LN(2) = -0.22314/0.69315 = -0.32193 (this is found from the excel function =LN; this can also be found using 'LOG' excel function as =LOG(0.8,2)

Thus,

Tn = 16.56 * 220^-0.32193

Tn = 16.56*0.211323

Tn  = 2.92 minutes

Thus, the time required for the 220th unit = 2.92 minutes