Chapter 7.S, Problem 8P

a)

Summary Introduction

To determine: The duration needed to finish last unit.

Introduction: Learning curve is referred as the cost curve, experience curve, efficiency curve or productivity curve. The leaving curve gives information about the cost, efficiency, productivity and performance of an organization.

Answer to Problem 8P

The duration needed to finish last unit is 11.35 hours.

Explanation of Solution

Given information:

$\begin{array}{c}{\text{T}}_5=\text{14}\text{.5}\text{hours}\\ \text{Total}\text{units}=\text{25}\\ \text{Learning}\text{curve}=90\text{\%}\end{array}$

Formula:

${\displaystyle \sum {\text{T}}_{\text{n}}}={\text{T}}_{\text{1}}\times \text{Unit}\text{factor}$

Calculation of duration needed to finish last unit:

Time to complete last unit can be calculate by computing the time of completion of first unit and then computing the time to complete last unit.

Estimation of time to complete first unit:

At 90% learning curve, the unit factor for 1 unit is 0.783 (using learning curve coefficient table)

$\begin{array}{c}{\text{T}}_5={\text{T}}_{\text{1}}\text{×0}\text{.783}\\ \text{600}={\text{T}}_{\text{1}}\times \text{0}\text{.783}\\ {\text{T}}_{\text{1}}=\frac{14.5}{0.783}\\ =\text{18}\text{.52}\text{hours}\end{array}$

The time for completing the first unit is calculated by dividing 14.5 with the unit factors 0.783 which yields 18.52 hours.

Estimation of time to last unit:

At 90% learning curve, the unit factor for 25 units are 0.613 (using learning curve coefficient table)

$\begin{array}{c}{\text{T}}_{25}={\text{T}}_1\times \text{Time}\text{factor}\\ =18.52\times 0.613\\ =\text{11}\text{.35}\text{hours}\end{array}$

The time for completing last unit (25^th units) is calculated by multiplying 18.52 with the unit factors 0.613 which yields 11.35 hours.

Hence, the duration needed to finish last unit is 11.35 hours.

b)

Summary Introduction

To determine: The duration needed to finish tenth unit.

Introduction: Learning curve is referred as the cost curve, experience curve, efficiency curve or productivity curve. The leaving curve gives information about the cost, efficiency, productivity and performance of an organization.

Answer to Problem 8P

The duration needed to finish tenth unit is 13.06 hours.

Explanation of Solution

Given information:

$\begin{array}{c}{\text{T}}_5=\text{14}\text{.5}\text{hours}\\ \text{Total}\text{units}=\text{25}\\ \text{Learning}\text{curve}=90\text{\%}\end{array}$

Formula:

${\displaystyle \sum {\text{T}}_{\text{n}}}={\text{T}}_{\text{1}}\times \text{Unit}\text{factor}$

Estimation of duration needed to finish tenth unit:

At 90% learning curve, the unit factor for tenth unit is 0.705.

$\begin{array}{c}{\text{T}}_{\text{n}}={\text{T}}_1\times \text{Unit}\text{factor}\\ =18.52\times 0.705\\ =13.06\text{hours}\end{array}$

The time for completing tenth units is calculated by multiplying 18.52 with 0.705 which yields 13.06 hours.

Hence, the duration needed to finish tenth unit is 13.06 hours.

c)

Summary Introduction

To estimate: The average time per unit for 25 units.

Introduction: Learning curve is referred as the cost curve, experience curve, efficiency curve or productivity curve. The leaving curve gives information about the cost, efficiency, productivity and performance of an organization.

Answer to Problem 8P

The average time per unit for 25 units is 13.12 hours.

Explanation of Solution

Given information:

$\begin{array}{c}{\text{T}}_5=\text{14}\text{.5}\text{hours}\\ \text{Total}\text{units}=\text{25}\\ \text{Learning}\text{curve}=90\text{\%}\end{array}$

Formula:

${\displaystyle \sum {\text{T}}_{\text{n}}}={\text{T}}_{\text{1}}\times \text{Unit}\text{factor}$

Calculation of average time per unit for 25 units:

The average time per unit for 25 units is calculated by computing the duration for all 25 units and taking average for the durations.

Estimation of time to complete 25 units:

At 90% learning curve, the unit factor for 25 units is 17.713.

$\begin{array}{c}{\text{T}}_{1-25}={\text{T}}_1\times \text{Time}\text{factor}\\ =18.52\times 17.713\\ =\text{328}\text{.04}\text{hours}\end{array}$

The duration for 25 units is calculated by multiplying 18.52 with 17.713 which yields 328.04 hours.

Estimation of average time of 25 units:

$\begin{array}{c}\text{Average}\text{time}=\frac{328.04}{25}\\ =13.12\text{hours}\end{array}$

The average time for 25 units is calculated by dividing 328.04 with 25 which gives 13.12 hours.

Hence, the average time per unit for 25 units is 13.12 hours.