one question on work system - learning curve

ch19-learning_curves1.ppt

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Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Curves

Sections:

Learning Curve Theory

Why the Learning Curve Occurs

Determining the Learning Rate

Factors Affecting the Learning Curve

Learning Curve Applications

Time Standards Versus the Learning Curve

Chapter 19

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Curve Phenomenon

Reduction in cycle time that occurs in a repetitive work activity as the number of cycles increases

An important topic in time study
When a worker accomplishes a task over and over, the time required for each successive cycle decreases as he or she learns the task
At first the learning effect is rapid, and the cycle time decreases significantly
As more and more cycles are completed, the cycle time reduction becomes less and less

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Curve Theory

According to theory, there is a constant learning rate that applies to a given repetitive task
Learning rate = the proportion by which the dependent variable (e.g., task time) is multiplied every time the number of task cycles doubles
Rate of improvement is the proportion by which the dependent variable is reduced every time the number of units doubles IR = 1-LR
Example: If T1 = 10 hr and LR = 80%, then

T2 = 0.80(10) = 8.0 hr,

T4 = 0.80(8.0) = 6.4 hr

T8 = 0.80(6.4) = 5.12 hr

and so on

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Curve for LR = 80%

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Log-Linear Model

When learning curve time data are plotted on log-log coordinates, the plot yields a straight line with slope m

y = kxm

where y = dependent variable(usually the time or cost of a task cycle or work unit), k = constant representing the value of the dependent variable for the first work cycle, x = number of work units completed, and m = slope

m = and LR = 2m

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Same Learning Curve in Log-Log Plot

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Two Widely Used Log-Linear Models

Crawford Model

Dependent variable is unit time TN

Wright Model

Dependent variable is cumulative average time

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Crawford Model

Most widely used learning curve model in industry today

Example: T1 = 10 hr, LR = 80%, how long will it take to complete the 20th work unit?

m = ln(0.80)/ln 2 = -0.32193

T20 = 10(20)-0.32193 = 3.81 hr

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Crawford Model

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Cumulative average time

Cumulative average time between two values of N

Cumulative Total Time for Crawford Model

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes. Given this information, (a) what is the percent learning rate and (b) what is the total cumulative time to produce all 17 welded assemblies? Use the Crawford learning curve model.
Solution: (a) Given T7 = 45 min and T7+10 = T17 = 30 min
T7 = T1(7)m = 45
T17 = T1(17)m = 30
T1 = 45/7m = 30/17m
45/30 = 7m/17m = (7/17)m
1.5 = (0.41177)m
ln 1.5 = m ln 0.41177
0.40547 = -0.8873 m m = -0.45696
LR = 2-0.45696 = 0.7285 = 72.9%
(b) T1 = 45/7-0.45696 = 109.5 hr
E(TT17) = 109.5{(17.51-0.45696 – 0.51-0.45696)/(1-0.45696)}
E(TT17) = 109.5{(4.7317- 0.6863)/0.54304} = 815.7 min = 13.595 hr

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Wright Model

First learning curve model to be published
Based on cumulative average time per unit

= T1Nm

Total cumulative time:

TTN = N

or TTN = T1Nm+1

Unit time:

TN = TTN - TTN-1

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Advantage of Log-Linear Model

In some cases, a log-linear model turns out not to be the best model to use and several alternatives to log-linear formula are explored. The trouble with other alternative learning curve equation is that they have more complex forms and require valuation of more parameters than the log-linear model

Log-linear model Consists of only two parameters:

The time associated with the first unit

The slope m, from which can be derived the learning rate LR

Conversely, if LR is known, the slope m can be deduced

Determine the Learning Rate

Read Example 19.6 page 493
The unit time for the first unit of production is 72 hr and the total cumulative time for 50 units is 2,347 hr. Determine the learning rate for (a) the Crawford learning curve model and (b) the Wright learning curve model.

(b) Wright model: 2,347 = 72(50)m+1
32.5972 = (50)m+1
(m+1) ln 50 = ln 32.597
3.912 m + 3.912 = 3.484
3.912 m = -0.428 m = -0.1094
LR = 2-0.1094 = 0.927 = 92.7%

(a) Crawford model: E(TT50) = 2,347 = 72{(50.5m+1 – 0.5m+1)/(m+1)}
2,347/72 = 32.5972 = (50.5m+1 – 0.5m+1)/(m+1)
Trial and error solution required.
Try m = -0.30
32.5972 = (50.50.7 – 0.50.7)/(0.7) = 21.36
Try m = -0.20
32.5972 = (50.50.8 – 0.50.8)/(0.8) = 28.09
Try m = -0.15
32.5972 = (50.50.85 – 0.50.85)/(0.85) = 32.34
Try m = -0.14
32.5972 = (50.50.86 – 0.50.86)/(0.86) = 33.27
Interpolating, (32.597 – 32.34)/(33.27 – 32.34) = 0.276
Try m = -0.15 – 0.276(0.01) = -0.147
32.5972 = (50.50.853 – 0.50.853)/(0.853) = 32.61 (Close enough)
LR = 2-0.147 = 0.903 = 90.3%

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Comparison of Crawford and Wright

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Why the Learning Curve Occurs

Contributions of the worker

Worker becomes familiar with the task - the worker learns the task
Worker makes fewer mistakes as the task is repeated
Hand and body motions become more efficient, and there is a rhythm and pattern developed
Minor adjustments in workplace layout to reduce distances
Fewer delays that interrupt the operation

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Why the Learning Curve Occurs

Contributions of the larger organization

Methods improvements by the IE Department
Fine-tuning of machinery and tooling
Development of special tooling
Technological improvements
Product design improvements
Improved quality of starting materials
Better scheduling
Improved logistical support
Better motivation of workers

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Contributions to the Learning Curve

Contributions to learning by the worker and the organization

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Typical Learning Rates (Crawford)

Type of work LR, %

Assembly 84-85

Prototype assembly 65

Clerical ops 75-85

Inspection 86

Machining 90

Welding 85-90

Industry LR, %

Aerospace 85

Complex machines 75-85

Construction 70-90

Electronics mfg 90-95

Machine shop 90-95

Shipbuilding 80-85

Determining the Learning Rate

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

A metal fabrication shop would like to know what the learning rate is for a certain section of the plant that makes welded assemblies. In one case study, a total of four assemblies were completed. Records were kept for units 1 and 4, and the times were 60 hours and 48.6 hours, respectively. Unfortunately, the times for units 2 and 3 were lost. Use the Crawford learning curve model to determine the learning rate indicated by the data?
Solution: Two solutions:

(1) Note the doubling effect:

48.6 = 60(LR)(LR) = 60(LR)2
LR2 = 48.6/60 = 0.81
LR = = 0.90 = 90%

(2) Use the log-linear equation:

T4 = T1(N)m
48.6 = 60(4)m
0.81 = 4m
m ln 4 = ln 0.81
1.3863 m = -0.21072 m = -0.152
LR = 2-0.152 = 0.90 = 90%

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Worker-Machine Systems

Learning in a work-machine system will be a composite of the learning rates of the two components of the system

LRw-m = pw LRw + pm LRm

where pw = proportion of cycle time controlled by worker, and pm = proportion of cycle time controlled by machine

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Interruptions in the Learning Curve

Learning curve effect tends to be disrupted by interruptions in production
Possible reasons for interruptions:
Batch production, in which there are extended periods between repeat orders
Labor strikes
Vacations
Raw material shortages

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Loss due to Interruption

Assumptions
If the duration of the interruption exceeds 12 months, then resuming production after the break would be the same as starting over for the first time
If the duration of the interruption is less than one month, therefor no effect on remission.

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Loss due to Interruption

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Other Factors Affecting Learning

Product complexity
More opportunities for learning - higher T1 and lower LR
Preproduction planning
Fewer opportunities for learning - lower T1 and higher LR
Labor turnover - slower learning (higher LR)
Plateau model - learning curve consists of two phases:

Start-up - log-linear model applies

Steady state - no further improvement

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Plateau Learning Curve Model

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Why the Plateau Model Occurs

In a worker-machine system, worker is finally limited by the speed of the machine
No incentives for workers to make further improvements
Management is unwilling or unable to invest in newer production technologies that would sustain the learning curve
Management does not believe that learning can continue indefinitely, and this becomes a self-fulfilling prophecy

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Learning Curve Applications

Accident prevention

Capacity planning

Cost accounting

Cost estimating

Cost reduction

Contract administration

Failure analysis

Labor requirements estimation

Make-or-buy decisions

Methods analysis

New product introduction

Pricing negotiations

Pricing strategies

Product design changes

Productivity analysis

Quality control

Reliability analysis

Safety

Vendor selection

Wage incentives

Warranty maintenance

Worker performance analysis

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Time Standards vs. Learning Curve

Apparent contradiction:
A time standard is a constant value that is defined under the following conditions:
Standard method
Standard work units
Performed by a trained average worker
Task is performed at 100% performance
But the learning curve predicts that the actual time for the work cycle will decrease over time

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

How to Reconcile the Contradiction

Although the standard time is a constant, the actual cycle time for a manual task is a variable
The time varies from one cycle to the next
One of the reasons why the cycle time varies is because the worker learns the task
The cycle time is gradually reduced as the number of repetitions increases, as predicted by learning curve theory
As long as there are no changes in methods or work unit, it seems fair to give credit to the worker for reductions in cycle time due to improvements in skill, effort, pace, etc.

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

Standard Reference Quantity (SRQ)

In batch production, it can be argued that the quantity of the production run should influence the value of the time standard
Surely a worker must be given an opportunity to learn a task before he or she is measured against the time standard
SRQ = the discrete quantity of production (e.g., 10, 100, 1000 units) for which the standard time for the task is applicable
If the actual quantity of production is different from the SRQ, then an adjustment in the time standard is appropriate

Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

SRQ Adjustment Ratio

(

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