ANALYTICAL MODELS OF LEARNING CURVES WITH

VARIABLEPROCESSING TIME

M.S.P,MUTHUKUMARANAGE

E/11/267 1

New labour

INTRODUCTION

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INTRODUCTION

New or unskilled operators cannot achieved acceptable speed at first time.

The operator will require less and less time to complete the similar task as time goes on.

This is the basic concept of learning curves.

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INTRODUCTION

The concept of learning curve was reported by wright in 1936.Wright developed a mathematically representation of learning curve

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LEARNING RATE (¢)

The operator’s performance will improve at a constant rate each time the output doubles.

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MATHEMATICALLY REPRESENTATIONLearning curve has mathematically representation.The basic model is log linear model.The equation of the log linear model

Y=KX ^n Y- direct labour hours required to produce xth unit. K- direct labour hours to produce first unit. X- cumilative unit numbers N- learning index

N= log ¢ / log 2

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OTHER MODELS

1. The plateau model

2. The stanford-b model

3. The dejong model

4. The S model

Above all models are the different form of log linear model.

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2

3

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Cumulative unit numberDi

rect

labo

ur h

ours

per

un

it

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OBJECTIVES

Calculate the time to complete a given batch of items exactly for

1. One machine system

Start Buffer Activity End

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• 2. Two machine system (2M1B)

Develop equations to find variability of processing time and average processing time.

Start Activity Buffer Activity End

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CALCULATION Single machine processing time to complete 1000 parts by using log

linear model when

Processing time is deterministic.

Cumulative Unit Number

Dire

ct la

bor h

ours

10

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Processing time has exponential distribution.

1 2 3 4 5Cumulative Unit Number

Dire

ct la

bor h

ours K

K3n

K4n K5n

K2n

Mean = K*Xn

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Exponential distribution

Mean=1/λ

Hypo-exponential distribution

λ(i)

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CALCULATION

Considering hypo exponential distribution

Mean time for produce 1000 parts =1587 hr

Variance =3062 hr0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

0.000X

Dens

ity

1479

0.025

1695

0.025

1587

Distribution PlotNormal, Mean=1587, StDev=55.33

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Results Using Other Models

Model Name Equation Mean Variance

Stanford-B model

Y(x)=Y1(X+B)-b

1559.857 2813.13

Dejong’s model

Y(x)=Y1[M+(1-M)X-b]2428.25 6336.51

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Work To Be Done

Develop above calculations for two machine one buffer system (2M1B)

1.With Infinite buffer size

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Infinite 16

2. With finite buffer size(by increasing one by one)

Start Activity Buffer Size= 1 Activity End

Start Activity Buffer size=2 Activity End

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THANK YOU

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