Question

A furniture maker has an order for 93 identical tables. If the furniture maker estimates his learning curve at 78% and can reach steady production of 9 hours per table on the 6th table, how long should it take to make all the tables? Express your answer in hours to the nearest whole hour

Answer 1

We know the learning curve is 86% and time taken to produce 6th table is 9hours.

To find the total number of hours taken to make first 5 tables, we will have to back calculation.

Wright's Cumulative Average Model

In Wright's Model, the learning curve function is defined as follows:

Y = aX^b

where:
Y = the cumulative average time per unit.
X = the learning rate
a = time required to produce the first unit.
b = slope of the function when plotted on log-log paper.
   = log of the cumulative number of units produced/log of 2.

Let's say it takes him 100 hours to make first table then average hour and time calculation in below table. But we know it took him 9hours to produce 6th table. So using ratio and proportion

Learning Curve	86%
Number of tables	Average hours	Time (hours per table)	Actual time
1	100.00	100.00	16.66
2	86.00	72.00	12.00
3	78.74	64.21	10.70
4	73.96	59.63	9.94
5	70.45	56.43	9.40
6	67.71	54.01	9.00
Total			67.70

Number of tables	Average hours	Time (hours per table)	Actual time
1	100	=+Q5	=+S6*R5/R6
2	=Q$5*(Q$3)^(LN(P6)/LN(2))	=A6*Q6-SUM($R$5:R5)	=+S7*R6/R7
3	=Q$5*(Q$3)^(LN(P7)/LN(2))	=A7*Q7-SUM($R$5:R6)	=+S8*R7/R8
4	=Q$5*(Q$3)^(LN(P8)/LN(2))	=A8*Q8-SUM($R$5:R7)	=+S9*R8/R9
5	=Q$5*(Q$3)^(LN(P9)/LN(2))	=A9*Q9-SUM($R$5:R8)	=+S10*R9/R10
6	=Q$5*(Q$3)^(LN(P10)/LN(2))	=A10*Q10-SUM($R$5:R9)	9
Total			=+SUM(S5:S10)

So total time taken to make 74 tables = 67.70+9*68

= 613hours