Lehrstuhl und Institut
für Arbeitswissenschaft
der RWTH Aachen
Industrial Engineering,
Ergonomics & Work Organisation
Unit 4
Work and Time Study I
winter term 2005/2006
Univ.-Prof. Dr.-Ing. Christopher Schlick
Structure: Work and Time Study
1
Work and Time Study - Basics
2
REFA - Stop Watch Time Study
3
Work Sampling method
4
MTM method
5
MTM method - Case Study
6
Conclusion
© IAW 2005/2006
Work and Time Study I
Work and Time Study II
2
Learning Targets Work and Time Study I
„
Being acquainted with the operational purpose of time
data
„
Being capable to distinguish between different REFA
types of activities and different REFA types of times
„
Being capable to distinguish between different methods
for the determination of time data
„
Understanding the REFA Stop Watch Time Study
method and the work sampling method
„
Being acquainted with possibilities and limitations in the
usage of these time measurement methods
© IAW 2005/2006
3
Structure: Work and Time Study
1
Work and Time Study - Basics
2
REFA - Stop Watch Time Study
3
Work Sampling method
4
MTM method
5
MTM method - Case Study
6
Conclusion
© IAW 2005/2006
Work and Time Study I
Work and Time Study II
4
Application of time data
Areas of Application
Purpose of time data:
Work planning
To select suitable processes, means, and methods
Pre-calculation
To determine estimated piece prices, budgets
Scheduling
To minimize delays, to calculate and monitor the delivery deadlines
Workplace and machine
occupation
To optimize the exploitation of capacity, to design workplaces and machines
Material delivery
To optimize the availability of materials and to plan the stock
Personnel planning
To plan employee capacity, work schedules and production programs
Cost accounting
To calculate the manufacturing costs and sell prices, to balance projects,
and departments, etc. (economic parameters)
Payment
© IAW 2005/2006
To determine piece-per-hour production rate, to set the wage per
unit and bonuses
5
Classifying Production Operations according to facilities,
work piece, or working person
In order to obtain information / data for the individual departments
of the organization, it is necessary to describe the various
procedures and processes in terms of time:
When production procedures and processes are classified according to…
•
the working person, the activities of one employee within a specific time
period are analyzed.
Work order time
•
the production facilities, the status of machines, equipment, etc. is
regarded.
Holding time
•
the product or work piece which is manufactured, the production
cycle of an assembly / product is described in terms of time.
Lead time
Different time
© IAW 2005/2006
types
6
Classification of procedures and processes
according to the production facilities
utilization
In use
Not in use
Production
facilities
BI
BL
B
Plant closed
BT
Interruption of
utilization
Main utilization
BH
Ancillary utilization
BN
Additional utilization
BZ
Interruption due to
the cycle
BA
Interruption due to
dysfunction
BS
Interruption due to
recreation
BE
Interruption due to
personal reasons
BP
BK
BR
BX
Not identifiable
© IAW 2005/2006
REFA 1997
7
Classification of procedures and processes
according to the production facilities
Main utilization
BH
... is the regular and direct utilization of the production facilities
according to the purpose (e.g. drilling with a drilling machine).
Ancillary utilization
BN
... is a regular and collateral utilization of the production facilities as a
preparation for the main utilization(e.g. exchanging drill).
Additional utilization
BZ
... Is the main and ancillary utilization of the production facilities,
whose occurrence and cycle is not to be pre-determined.
Interruption due to
the cycle
BA
Production facilities wait regularly for the activity of the working
person, for the changing of work pieces, or for the termination of
certain cycle sections with other production facilities.
Interruption due to
dysfunction
BS
... is additional waiting of the production facilities due to technical and
organizational dysfunctions.
Interruption due to
recreation
BE
The utilization of the production facilities is interrupted by the
recreation of the working person.
Interruption due to
personal reasons
BP
The utilization of the production facilities is interrupted by the
interruption of the working person due to personal reasons.
© IAW 2005/2006
REFA 1997
8
Classification of procedures and processes according
to the work piece
Modifying
Affecting
AE
Conveying
AF
Additional
modifying
AZ
Checking
Work piece
AP
A
Lying due to the
cycle
AA
Additional (miscellaneous) lying
AS
Lying
© IAW 2005/2006
Mounting
AL
Not identifiable
AX
REFA 1997
9
Classification of procedures and processes according
to the work piece
Affecting
AE
... is a modification of the form or state of work pieces.
... is the modification of work pieces concerning position
(handling) and location (transportation).
Conveying
AF
Additional
modifying
AZ
... is affecting and conveying, whose occurrence and cycle is not
to be pre-determined.
Checking
AP
... is the controlling of work pieces in the material flow.
Lying due to the
cycle
AA
... arises, if modifying and checking of the work pieces is
interrupted due to the cycle.
Additional (miscellaneous) lying
AS
... arises, if modifying and checking of work pieces is interrupted
due to dysfunctions.
Mounting
AL
... is the lying of work pieces in the storage areas.
© IAW 2005/2006
REFA 1997
10
Classification of procedures and processes according to
the working person
Activity
On duty
Off duty
Working
person
MI
ML
M
Plant closed
MT
Interruption of
activity
Main activity
MH
Ancillary activity
MN
Additional
activity
MZ
Interruption due to
the cycle
MA
Interruption
due to dysfunction
MS
Interruption due to
recreation
ME
Interruption due to
personal reasons
MP
MK
MR
MX
Not identifiable
© IAW 2005/2006
REFA 1997
11
Procedure Categorization based on the working person
Main activity:
planned activity, directly related to the task
processing the piece
assembling the parts
repairing the vehicle
© IAW 2005/2006
Ancillary activity:
planned activity, indirectly related to the task
clamping pieces
adjusting apparatus
unpacking and if applicable pre-assembling spare
parts
Additional activity:
unforeseeable activity
refinish a work piece
new calibration of assembly robot
repeated order of spare parts if delivery defective
12
Procedure Categorization Based on the the working
person
Interruption due to
the cycle
(Allowable delays):
Regular waiting period occurring when a machine or device needs time to
complete a procedure autonomously.
automatic tool changing from repository
awaiting drying after washing
Interruption due to
dysfunction
(Non-allowable delays)
Unscheduled waiting periods due to technical and organizational dysfunctions
waiting for a locksmith
electrical power outage
Interruption due to
recreation:
Interruption of an activity due to reduce fatigue
Interruption due to
personal reasons:
Interruption or delay of an activity due to personal reasons
smoking a cigarette
using the lavatory
delayed start of work
© IAW 2005/2006
13
Example: Classification of procedures & processes for
working person, production facilities, and work piece
No.
Process section
Working
person
Production Work
facilities
piece
1.
Clamping work piece in bench vice.
MN
BA
AF
2.
Drilling a hole into the work piece.
MH
BH
AE
3.
Controlling the cross section dimension of
the drilling hole by using a caliper gage.
MN
BA
AP
4.
Labeling work piece in terms of color.
MN
BA
AE
5.
Removing the shavings from bench vice and MN
work piece by using a hand brush.
BA
AA
6.
Dismantling the work piece from bench vice
and placing it in a box.
BA
AF
© IAW 2005/2006
MN
14
Classification Based on the working person’s activity
Type of time
Type of activity
Main activity
Σ t MH
Ancillary activity
Σ tMN
Additional activity
Σ tMZ
Interruption due to
the cycle
Σ tMA
Interruption due to
dysfunction
Σ tMS
Interruption due to
Recreation
Σ tME
Interruption due to
personal reasons
Σ tMP
© IAW 2005/2006
Time for activity t t
Basic time t g
Waiting time
tw
Recreation t
re
time
Objective
t
additional time s
Time per
te
unit
Additional
tv
time
Personal
t
additional time p
REFA 1997
15
Time classification for the work order time
Work order time T
(allowed time for the
working person)
Set-Up time
tr
Execution time
ta = m * te
Time per unit te
Basic time
trg
Recreation
time trer
Additional
time trv
Basic time
tg
Recreation
time ter
Additional
time tv
Further classification is possible
Time for
activity tt
© IAW 2005/2006
Waiting
time tw
objective
additional
time ts
personal
additional
time tp
REFA 1997
16
Methods for the determination of time data
Determining time
Analytical-experimental methods
(ACTUAL TIMES)
observation
self-report
• manual time
measurement
- stopwatch
- REFA procedures
• made by the worker
• work sampling
(time measurement
by means of
statistical analysis)
– ratio delay
– methods for time
measurement
– ...
• interview
techniques
– list of activities,
their duration, and
the frequency of
their occurrence
based on
equipment used
• with the aid of
devices (e. g.,
computer log-files)
Statistical time models
© IAW 2005/2006
Analytical-computational methods
(TARGETED TIMES)
comparison and
estimation
• Comparison of the
work procedures for
which the time
standards are to be
determined with
similar activities for
which time standards
have already been
set.
• The estimation is
based on standard
times for the procedure based on
historical records or
experience
(comparative
estimation).
compilation
• systems of
predetermined
times
- Methods Time
Measurements
(MTM)
- Work Factor (WF)
calculation of
work cycles
• based on
formulas (e.g.,
for turning)
• based on
nomographs
• standard times
- catalogue of
task times
- nomograph
Sequence-analytical time models
17
Structure: Work and Time Study
1
Work and Time Study - Basics
2
REFA - Stop Watch Time Study
3
Work Sampling method
4
MTM method
5
MTM method - Case Study
6
Conclusion
© IAW 2005/2006
Work and Time Study I
Work and Time Study II
18
Subject of the REFA Stop Watch Time Study method
A stop watch time study is the determination of allocated
times by measuring and analyzing actual times.
A stop watch time study consists of:
„ the description of the work system (procedure, working
method, working conditions),
„ the determination of allocation bases, influencing
variables, performance rates, and actual times for
individual process sections, and
„ the analysis of this data to determine targeted times
for certain process sections.
© IAW 2005/2006
19
REFA Standard Program Stop Watch Time Study (1)
1.
Determining the purpose of the stop
watch time study
2.
Preparing the stop watch time study
3.
Making a choice between progress-times
measurement and individual-times
measurement
7.
Is an automatic recording time
measuring device utilized?
yes
Accomplishing the time study
according to the type of the
time measurement device
no
© IAW 2005/2006
4.
Selecting the time measuring device
5.
Selecting the time study sheet as per
operational sequence
REFA 1997
20
REFA Standard Program Stop Watch Time Study (2)
cyclic operational sequence
6a Sampling and describing the
sequence in consideration of
the purpose of the stop watch
time study, determining
measuring points
6.
7.
yes
Are operational sequences
no
with regular recurrences
existent?
6b Taking in allocation bases and
influencing variables
6c Accomplishing the stop watch
time study
© IAW 2005/2006
Non-cyclic operational
sequence
Describing working
tasks, - procedures,methods and conditions
Accomplishing time
study:
Sampling and describing
the sequence in
consideration of the
purpose of the stop
watch time study;
determining measuring
points; taking in
allocation bases and
influencing variables;
measuring actual times
and appraising
performance rates
8. Analyzing stop watch
time study
21
Clamping in
next piece
Releasing
Unclamping and
Depositing piece
Releasing
Processing piece
Machine stopped
Clamping
in piece
Releasing
Process
sections
Measurement
REFA Standard Program Step 3
Ti1 = 30 HM
Ti2 = 30 HM
Determined
time per unit ti
(in HM)
0
Ti3 = 25 HM
30
0
Ti4 = 35 HM
30
0
25
0
F1
F2
F3
F4
30
60
85
120
Ti1 = 30 HM
Ti2 = 30 HM
Ti3 = 25 HM
Determined
progress time
F (in HM)
0
Calculated
time per unit ti
35
Ti4 = 35 HM
HM - 1/100 minutes (a hundredth minute)
© IAW 2005/2006
22
REFA Standard Program Step 7
Situation:
Workers differ in their performance rates.
Worker A assembles 12 components per hour.
Worker B assembles only 10 components per hour under the same conditions.
Problem: How can a performance standard be determined (targeted performance = 100%), that
can be used for production and operation scheduling and also be met by all workers?
Solution: Observation of the activities with regard to their intensity and effectiveness
Performance rate
(appearance)
© IAW 2005/2006
=
Intensity
is manifested by
• speed of movement
• physical exertion
Effectiveness:
is assessed in terms of
how
• rhythmically
• harmoniously and
• rapidly
work is performed
23
Structure: Work and Time Study
1
Work and Time Study - Basics
2
REFA - Stop Watch Time Study
3
Work Sampling method
4
MTM method
5
MTM method - Case Study
6
Conclusion
© IAW 2005/2006
Work and Time Study I
Work and Time Study II
24
The subject of work sampling
Work Sampling
(German: Multimoment)
multum (lat.) ~ much
momentum (lat.) ~ moment
Definition:
The work sampling study is a sampling method which
provides estimations for the relative frequency, as the case
may be for the duration of predominantly unsteady occurring
work processes, or for similar sizes with a
• arbitrary accuracy together with a
• statistical confidence (level of significance) α.
© IAW 2005/2006
25
Work sampling methods
Work sampling methods
(MM)
Work sampling
ratio delay (MMH)
Counted measurands
Absolute
percentage
frequency
rates
© IAW 2005/2006
11
12
1
10
2
9
3
8
4
7
6
5
Work sampling by
methods of time
measurement (MMZ)
Measured values
Minute-values
Hour-values
26
Principle of Work Sampling
Three work processes are distinguished, which are encoded in terms of color in white, grey, or black in the schedule.
The work processes’ as the case may be activities’ proportions of the labor time is to be determined.
Begin of tours
8h
First annotation
9h
10h
11h
12h
13h
14h
Last annotation
B
C
D
Lunch Break
Workstations
A
E
Number of
observations
of the incidents
End of tours
15h
16h
17h
t1
t2
t3
321
74
85
354
63
63
361
55
64
348
98
34
363
72
45
73
15
12
p̂ 1
p̂ 2
p̂ 3
min
T= 40 hours ≡ 100 %
Stop watch time study
Working time
Time
% proportions as
a result of the
time study
Work sampling study
n1
70
n2
p̂ 1 17,5
p̂ 2 12,5
p̂ 3
n3
N = 40 annotations ≡ 100 %
n3
5
=
N 40
Estimation of the probability according
to frequency observations
Source: Haller-Wedel (1969)
© IAW 2005/2006
27
REFA standard program work sampling
I
Determination of target
II
Determination of types of
action
III
Determination of tour plan
IV
Determination of necessary
amount of observations N‘
Accomplishment of further
observations
V
Determination of tour terms
Calculation of necessary amount of
observations N‘
VI
Accomplishment of N = 500
observations
no
yes
VII Interim analysis
© IAW 2005/2006
f < f‘?
VIII
Final analysis
REFA 1997
28
Approximation of the binomial distribution by normal
distribution
p (ni )
f ( x)
Probability
N→∞
Moivre-Laplacetheorem
1
2
3
4
5
6
0
Number of observations ni with
N annotations for p1=p2=0,5
Normal distribution
Probability density
Binomial distribution
-σ
μ
σ
x
Characteristics of the normal distribution
• The graph of the distribution proceeds bell-shaped and is axially symmetric regarding the expected value μ (average
value)
• Expected value μ, mode and median coincide
• The differences between the distributions are to be ascribed to two parameters, scilicet expected value (average value)
and standard deviation (dispersion):
Expected value μ : barycenter of the distribution
∞
μ = E( x) = ∫ x f ( x)dx
Standard deviation σ : dispersion about the barycenter
(kurtosis)
σ = E ( ( x − μ )2 )
−∞
© IAW 2005/2006
29
MMH – Probability of error
Starting from the barycenter μ of the normal distribution, approx. 68% of any cases are to be expected in the
interval [μ - σ ; μ - σ]. Due to the rapidly dispersing distribution, 95,5% of the cases are already covered in the
duplicate interval [μ - 2σ ; μ - 2σ] („Two Sigma“). The probability α, that observations are located outside the
Two-Sigma-Interval is only approx. 4,5%. The variable α is referred to as probability of error. Analogical, each
probability of error α corresponds to a certain sigma interval [ − z α / 2 σ ; z α / 2 σ ] . The value 1-α indicates the
area A below the bell-shaped curve in the sigma interval.
f ( x)
A=
zα / 2
∫
f ( x)dx
− zα / 2
Standardized normal
distribution with
μ=0 und σ=1
≡ 1−α
− zα / 2
-2σ
zα / 2
-σ
μ
σ
2σ
x
68 %
-1,96σ
© IAW 2005/2006
95,5 %
95 %
1,96σ
30
MMH – Basics of the estimation
• Within the MMH procedure, a probability of error α is required - typically 5% - which should not be
exceeded within the estimation of the proportion pi of the activity i in which we are interested, with
the accuracy fi..Consequently, the required interval is [pi –fi ; pi +fi ].
• Due to the probability of error α, it is possible to determine the corresponding sigma intervals
[ − z α / 2 σ ; z α / 2 σ ] by dint of the standardized normal distribution. As to be recognized on the
previous slide, i.e. the sigma interval for α=0,05 is approx. [-1,96σ ; 1,96σ].
• Moreover, it is to be considered that the estimated value of the proportion of the activity i in which
we are interested is not standard normal distributed, but shows the average value pˆ i and a
dispersion sˆi .
• Previous to the MMH data collection the relative activity proportions pˆ i have to be estimated
plausibly by the observer according to his experiences. If observations are already available (i.e.
N=500 in the REFA standard program), the probability simply will be estimated according to the
principle of maximum likelihood by the relative frequency:
pˆ i =
ni
N
• If no observations are available, the accuracy boundaries –fi as the case may be + fi will be used
instead of a subjective estimation. If data was collected, the following estimation according to the
principle of maximum likelihood would be utilized:
sˆi =
© IAW 2005/2006
pˆi (1− pˆi )
N
31
MMH - Main Formula
Finally, the MMH main formula can be affiliated. This is an interval estimation of the proportion pi of the activity i
with the required accuracy fi around the mean of the interval with a probability of error α ( P(true value of pi is
located in the interval) = 1-α ) ):
[ pˆ i − f i ; pˆ i + f i ]
The accuracy can easily be expressed as sigma interval:
f i = z α 2 sˆi m
it z α
with
2
= 1, 96 for
für α = 5%
The MMH main formula for the necessary sample size N with estimated activity proportions pˆ i , the required
accuracy fi and the probability of error α is:
sˆi =
Previous to the MMH observations:
N '=
© IAW 2005/2006
zα
2
2
pˆ i ′ (1 − pˆ i ′ )
f ′²
pˆ i (1 − pˆ i )
pˆ i (1 − pˆ i )
⇔ N =
N
sˆi 2
After the MMH observations:
N =
zα
2
2
pˆ i (1 − pˆ i )
f²
32
Example: MMH in large firms of the retail industry
Verkäufer
(alle
Sales clerk
(allMärkte)
markets)
Hauptprozess
"Interaktion
mitwith
demthe
Kunden"
Primary process
"Interaction
customer"
50,00
45,00
40,00
p [%]
35,00
30,00
25,00
20,00
15,00
10,00
5,00
0,00
8am-08.00
9am
09.00
9am09.00
10am
10.00
10am
11am
noon10.00
- - 11.00
- - 12.00
11am 12.00
noon
1pm
11.00
13.00
1pm -13.00
2pm
14.00
2pm -14.00
3pm
15.00
3pm -15.00
4pm
16.00
4pm -16.00
5pm
17.00
5pm -17.00
6pm
18.00
6pm -18.00
7pm
19.00
7pm -19.00
8pm
20.00
time
Uhrzeit
N=178
N=920
N=888
N=931
N=1094 N=1064 N=1238 N=1002 N=910
f= 3,4%
f=3,0%
f=3,1%
f=3,0%
f=2,7%
f=2,6%
f=2,4%
f=2,8%
N=905
N=601
N=482
f=3,1% f=3,1%
f=4,0%
f=4,3%
Observations in three markets, six days each
MMH as the basis of a related-to-need short-term manpower planning
© IAW 2005/2006
Hinrichsen, Peters, Schlick 2005
33
Work Sampling method: Advantages and Disadvantages
Advantages
„ Representative image of the actual state
„ Comprehension of a large amount of workstations is possible
„ Comparatively low expenditure of time in comparison to the stop
watch time study
„ No measuring instruments necessary
Disadvantages
„ Time-influencing variables and reasons for actual times are not
directly apparent from the results of the study
„ Annotations are based on non-recurring observations and thus
are not to be verified later on
„ Performance rates are not to be measured
„ Results are to be manipulated by observing persons
© IAW 2005/2006
34
Questions of learning success
9 What are the operational purposes of time data in companies?
9 How are the REFA activities basically structured?
9 Which types of activities can be distinguished regarding working persons,
production facilities and products?
9 How is the work order time (allowed time for the working person) structured?
9 Which methods for the determination of time data can be distinguished?
9 What are the basic characteristics of the REFA - Stop Watch Time Study?
9 How is the performance rate defined?
9 What are basic characteristics of a work sampling method?
© IAW 2005/2006
35
Lehrstuhl und Institut
für Arbeitswissenschaft
der RWTH Aachen
Industrial Engineering, Ergonomics
& Work Organisation
Exercise
Unit 4
Work and Time Study I
winter term 2005/2006
Univ.-Prof. Dr.-Ing. Christopher Schlick
Classes of operations
Task 1
An A bearing surface has to be milled on work pieces in a
limited-lot production. In order to improve the efficiency of
the production processes, Mr. Schulze from Industrial
Engineering carries out an analysis of the actual times of
the process.
To do so he observes the process and notes single
activities of the process. Help Mr. Schulze by matching
the activities of the production process in table 1 with the
corresponding classes of operations (MH, MN, MZ etc.).
(Use figure 1 as a help!)
© IAW 2005/2006
37
Figure 1
Principal
activity
Activity
On duty
Off duty
Working
person
MI
ML
M
Plant closed
MT
Interruption of
activity
MK
MR
Not identifiable
© IAW 2005/2006
MH
Ancillary
activity
MN
Additional
activity
MZ
Interruption inherent
to the cycle
MA
Interruption
due to dysfunction
MS
Interruption due to
recreation
(
ME
Interruption due to
personal reasons
MP
MX
38
Table 1
Nr.
Activities
1.
Read job order and graph
2.
Take cutter, clamp cutter and set milling machine
3.
Take work piece and clamp work piece
4.
Supervise milling and first cut
5.
Milling without supervision
6.
Unclamp work piece
7.
Check the surface quality of the work piece (planned
visual inspection)
Deposit work piece
8.
9.
10.
© IAW 2005/2006
Class of
Operation
Unscheduled changing of the cutter, because the
surface quality of the work piece has degraded due to
abrasion of the cutter
Foreman introduces a new colleague to the employee
at the milling machine
39
Time Classification based on the working person’s
behavior
Task 2
Calculate the job order time allowed for the manufacture of 300
pieces of steel protective caps. Thereby use the REFA Time
Classification based on the working person‘s behavior.
© IAW 2005/2006
40
Time Classification based on the working person’s
behavior
job
joborder
order
time
timeallowed
allowed
TT
time
timeallowed
allowed
tat ==mm* *tet
Set
Setup
uptime
time
trt
r
a
e
time
timeper
perunit
unit
tet
e
Set
Setup
upbasic
basictime
time
trg
trg
Set
Setup
up
recovery
recoverytime
time
trer
t
rer
Set
Setup
up
additional
additionaltime
time
trv
t
basic
time
basic
tgt time
g
rv
recovery
recovery
time
time
ter
ter
Additional
Additional
time
time
tvt
v
further classification possible
activity
activity
time
time
ttt
t
influencable
influencable
activity
activitytime
time
ttb
ttb
© IAW 2005/2006
waiting
waiting
time
time
twt
w
object-related
object-related
additional
additionaltime
time
tst
s
worker-related
worker-related
additional
additionaltime
time
tpt
p
non
- -influencable
non
influencable
activity
activitytime
time
ttu
ttu
41
Time Classification based on the working person‘s
behavior
Task:
Input:
Production of steel protective caps
Blank plates
Drawing -Nr. 026/417
Equipment:
800 t - drawing press
Batch size m:
300 pieces
Additional time rate zv:
7%
Recovery time ter:
0.015 min/piece
no set up recovery time and no set up additional time
Procedure for one work cycle (number of units 1) incl. set up the machine:
Nr.
Operations
1
2
3
4
5
6
7
8
Mount stamping tool in press
Test and control press
Grasp plate and transport it to press
Insert plate into die
Operate press with both hands, stamp
Remove protective cap from the die
Set protective cap down
Walk from transporting rig to pallet
8.00
1.30
0.10
0.05
0.15
0.08
0.06
0.06
9
Dismantle tool
5.00
© IAW 2005/2006
Targeted time
in min
42
Work Sampling
Task 3
In a work sampling study for the optimization of setup
time which is to be accomplished by Mr. Mueller, 45
injection molding machines should be included. How
many tours are necessary, if a probability of error of at
most 5% should form the basis of the result. Please act
on the assumption that a total deviation f‘ of 1.5% is not to
be exceeded.
Hint: Within the last measurement, the setup time had a
part of 15%.
The following is imperative:
3.84 ⋅ p '⋅ (100 − p ' )
N '=
f '²
© IAW 2005/2006
N´ = Total number of necessary annotations
p´ = Expectancy value as percentage
f´ = Desired spread as the case may be tolerated error
43