Question

The following data has been collected by a competitor of a space launch vehicle company engaged in successful first stage booster section refurbishment operations, however not all the data is available. The data available indicates the 5th refurbished 1st stage booster required 35 workdays to be ready for another flight. Data from other related manufacturing operations in the launch vehicle industry supports the use of a 90% to 95% learning curve. The competitor firm is interested in calculating the time for the 1st and 10th refurbished first stage booster section of the reusable launch vehicle. Compute the values for the 1st and the 10th first stage booster refurbishment times, first assuming a 90% learning curve, and again assuming a 95% learning curve as follows: a) First list given information and unknowns and identify the relevant variables to be used in this analysis. Then show the theoretical formula used

Answer 1

Variables:
`\(T_1\)`(1st booster time),
`\(T_5\)` (5th booster time = 35 days),
`\(n\)`(batch size),
`\(x\)` (cumulative units),
`\(r\)` (learning curve ratio),
`\(T_(10)\)` (10th booster time). Theoretical formula:
`\(T_n = T_1 * (x)^(\log_r(n))\).`

Let's define the variables based on the information provided:

Given information:

-
`\( T_1 \)` : Time required for the 1st refurbished first stage booster (unknown)

-
`\( T_5 \)` : Time required for the 5th refurbished first stage booster = 35 workdays

-
`\( n \)` : Batch size = 5 (as data is available for the 5th refurbished unit)

-
`\( x \)` : Cumulative production units completed (unknown)

-
`\( r \)` : Learning curve ratio

-
`\( T_(10) \)` : Time required for the 10th refurbished first stage booster (unknown)

Learning curve formula:
`\[ T_n = T_1 * (x)^(\log_r(n)) \]`

Now, let's substitute the given values and the unknowns into the formula:
`\[ 35 = T_1 * (5)^(\log_r(5)) \]`

This formula is used to calculate the time for the 5th refurbished first stage booster. To solve for
`\( T_1 \)`, you would need to rearrange the equation and solve for
`\( T_1 \).`

Now, the learning curve ratio
`(\( r \))` is given as 90% and 95%, so you will use these ratios to calculate
`\( T_(10) \)` based on the cumulative production units completed
`(\( x \)).`

The theoretical formula for calculating
`\( T_(10) \) is:\[ T_(10) = T_1 * (10)^(\log_r(10)) \]`

Now, you can use this formula twice, once with a 90% learning curve ratio and once with a 95% learning curve ratio, to calculate the theoretical time for the 10th refurbished first stage booster in each case.