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1
Worker-Machine Systems
 Worker operates a powered equipment
 Examples:
Machinist operating a milling machine
Construction worker operating a backhoe ‫حفار‬
Truck driver driving an 18-wheel tractor-trailer ‫جرار‬
‫ومقطورة‬
Worker crew operating a rolling mill ‫ماكينة‬
‫درفلة‬
Clerical worker entering data into a PC
2
Relative Strengths
Humans
 Sense unexpected stimuli

‫متوقعه‬ ‫الغير‬ ‫بالمؤثرات‬ ‫الشعور‬
 Solve problems
 Adapt to change
 Generalize from observations
 Learn from experience
 Make decisions on incomplete data
Machines
 Perform repetitive operations
consistently
 Store large amounts of information
 Retrieve data from memory reliably
 Perform multiple tasks at the same
time
 Apply high forces and power
 Perform computations very quickly
 Make routine decisions quickly
3
Relative Strengths
 In a worker-machine system the worker and
the machine both contribute their own
strengths and capabilities
 The result is synergistic ‫التآزرية‬
 Types of worker-machine systems:
 Types of powered machinery used in the system
 Numbers of workers and machines in the system
 Level of operator attention required to run the
machinery
4
Types of Powered Equipment
 Powered machinery: A source of power other
than human (or animal) strength is used to
operate that tool (or machine).
1.Portable power tools
 Light enough in weight so that they can be easily carried
2.Mobile powered equipment
 Heavy pieces of equipment but transportable
3.Stationary powered machines
 Perfom functions in a stationary location
5
Classification of Powered
Machinery
Cars, buses, trucks, airplanes
Tractor, bulldozers, backhoes, forklifts
Electric power generators
Ovens, cash register
PCs, photocopiers, telephones
Turning, drilling, milling
Portable power drills, chain saws,
electric hedge trimmers
6
Numbers of Workers and Machines
One worker and One machine
 Taxicab driver and taxi
One worker and Multiple machines
 A worker operating several machines
7
Numbers of Workers and Machines
Multiple workers and One machine
 A crew on a ship
Multiple workers and Multiple machines
 Emergency repair crew responding to
machine breakdowns in a factory
8
Level of Operator Attention
 Full-time attention
 Welders performing arc welding
 Part-time attention during each work cycle
 Worker loading and unloading a production machine on
semi-automatic cycle
9
Level of Operator Attention
 Periodic attention with regular servicing
 Worker loading a machine every 20 cycles
 Periodic attention with random servicing
 Firefighters responding to alarms
 Maintenance worker repairing machines
10
Good Work Design for Machine-Worker
Systems
1. Design the controls of the machine to be logical and easy to
operate for the worker.
2. Design the work sequence so that as much of the worker’s
task as possible can be accomplished while the machine is
operating.
3. Minimize the idle times of both the worker and the machine.
4. Design the task and the machine to be safe for the worker.
5. If the system is a multiple worker or/and multiple machine
system, optimize the number of workers or machines in the
system according to a specified objective.
11
Cycle Time Analysis
 Two categories of worker-machine systems in terms of cycle time
analysis
 Cases:
1. Systems in which the machine time depends on operator
control
 A typist typing a list of names on a typewriter
 Carpenter using power saw to cut lumber
 A construction worker operating a backhoe
 Cycle time analysis is same as for manual work cycle
2. Systems in which machine time is constant and independent
of operator control
 Operator loading semi-automatic production machine
 Our focus is on this 2nd type
 Two types:
12
Case 2.a: Cycle Times with No Overlap
Between Worker and Machine
 Worker elements and machine elements are sequential
 There is no overlap in work elements between the
worker and the machine
 While worker is busy, machine is idle
 While machine is busy, worker is idle
 Normal time for cycle
Tn = Tnw + Tm,
where
Tnw = Normal time for the worker-controlled portion of the
cycle time, min
Tm = Machine cycle time (assumed to be constant)
13
Case 2.a: Cycle Times with No Overlap
Between Worker and Machine
 Standard time for cycle
Tstd = Tnw (1 + Apfd) + Tm (1 + Am)
where
Am = Machine allowance factor
 Am=30%: Workers love that since efficiencies are
overestimated
 Am=0%: Workers hate that since efficiencies are
underestimated
 Am= Apfd
14
Example 2.8: Effect of machine
allowance on standard time
 Given: The work cycle consists of several
manual work elements (operator controlled)
and one machine element performed under
semiautomatic control. The manual work
elements: a normal time of 1 min and the
semiautomatic machine cycle time is 2 min.
Apfd=15%.
 Determine: the standard time using
(a) Am =0,
(b) Am=30%.
15
Example 2.8: Solution
 The normal time for the work cycle: Tn=1.0+2.0=3.0 min
(a) Tstd = Tnw (1 + Apfd) + Tm (1 + Am)
Tstd=1.0(1+0.15)+2.0=3.15 min
Workers
(b) Tstd = Tnw (1 + Apfd) + Tm (1 + Am)
Tstd=1.0(1+0.15)+2.0(1+0.30) =3.75 min
Workers
16
Example 2.9: Effect of machine
allowance on worker efficiency
 Given: Standard times in the previous example (Example 2.8).
 Determine: The worker efficiencies if 150 units are produced in
an 8-hour shift.
 Solution:
(a) Hstd = Q Tstd
Hstd=150(3.15)=472.5min=7.875hr
Ew = Hstd / Hsh
Ew=7.875/8.0=0.984= 98.4%
(b) Hstd = Q Tstd
Hstd=150(3.75)=562.5min=9.375hr
Ew = Hstd / Hsh
Ew=9.375/8.0=1.172= 117.2%
17
Case 2.b: Internal Work Elements
 Some worker elements are performed while
machine is working
 Internal work elements performed simultaneously
with machine cycle
 External work elements performed sequentially with
machine cycle
 Desirable to design the work cycle with
internal rather than external work elements
 If it is possible, include operator work elements
that are performed while machine is running.
18
Normal Time and Standard Time
 Normal time
Tn = Tnw + Max{Tnwi , Tm}
 Standard time
Tstd = Tnw (1 + Apfd) +Max{Tnwi (1 + Apfd) , Tm (1 + Am)}
 Actual cycle time
Tc = Tnw / Pw + Max{Tnwi /Pw , Tm}
where
Tnw = normal time for the worker’s external elements, min
Tnwi = normal time for the worker’s internal elements, min
Tm = machine cycle time, min
19
Example 2.10: Internal vs external work
elements in cycle time analysis
0.75
0.73
Total
(idle)
0.15
Worker transports finished part and deposits into tote pan
6
(idle)
0.10
Worker unloads finished part from machine
5
0.75
(idle)
Machine semiautomatic cycle
4
(idle)
0.12
Worker loads part into machine and engages machine
semiautomatic cycle
3
(idle)
0.23
Worker picks up raw workpart and transports to machine
2
(idle)
0.13
Worker walks to tote pan containing raw stock
1
Machine
Time
(min)
Worker
Time
(min)
Work Element Description
Seq.
Tc=0.73+0.75=1.48 min
20
0.75
0.73
Total
(operating)
0.15+
0.13+
0.23=
0.51
Worker transports finished part and deposits it into tote
pan, walks to tote pan containing raw stock, and picks up
raw workpart and transports it to machine. (This element
is internal to the machine semiautomatic cycle.)
4
0.75
(idle)
Machine semiautomatic cycle
3
(idle)
0.12
Worker loads part into machine and engages
semiautomatic machine cycle
2
(idle)
0.10
Worker unloads finished part from machine
1
Machine
Time
(min)
Worker
Time
(min)
Work Element Description
Seq.
Tc=0.10+0.12+0.75=0.97 min
Example 2.10: Internal vs external work
elements in cycle time analysis
21
Example 2.10: Internal vs external work
elements in cycle time analysis
 The cycle time is reduced from 1.48 min to 0.97 min.
 % cycle time reduction=(CTcurrent-CTimproved)/CTcurrent
=(1.48-0.97)/1.48=34%
 Rcurrent=1/1.48 min=0.68 units per min
 Rimproved=1/0.97 min=1.03 units per min
 % increase in R=(Rimproved-Rcurrent)/Rcurrent
=(1.03-0.68)/0.68=53%
22
Automated Work Systems
 Automation is the technology by which a
process or procedure is accomplished without
human assistance
 Implemented using a program of instructions
combined with a control system that executes
the instructions
 Power is required to drive the process and
operate the control system
23
Automated Work Systems
Automated robotic
spot welding cell
(photo courtesy of Ford
Motor Company)
24
Levels of Automated Systems
 There is not always a clear distinction between worker-machine
systems and automated systems, because many worker-
machine systems operate with some degree of automation.
1. Semiautomated machine
 Performs a portion of the work cycle under some form of
program control
 Human worker tends the machine for the rest of the cycle by
loading unloading etc.
 Operator must be present every cycle
 Same characteristics with worker-machine system
 e.g.,an automated lathe requires a worker to unload parts at
every cycle, although changing tools may not be required at
every cycle
25
Levels of Automated Systems
1. Fully automated machine
 Operates for extended periods of time with no human
attention (longer than one work cycle, e.g. every
hundredth cycle ‫كل‬
‫مائة‬
‫دورة‬ )
 e.g., periodically the molded parts at a molding
machine must be collected.
26
Determining worker and machine
Requirements
 How many workers/machines are required to
achieve the organization’s work objectives?
 If too few workers are assigned to perform a
given amount of work
 The work cannot be completed on time, customer
service will suffer.
 If too many workers are assigned to perform
a given amount of work
 The payroll costs are higher than needed, and
productivity will suffer.
27
Determining worker and machine
Requirements
• Workload (WL): Total hours required to
complete a given amount of work or to produce a
given number of work units scheduled during the
period
 Available time (AT): The number of hours (in the
same period) available from one worker or
worker-machine system
28
Case 3.1: When Setup is not a Factor
Workload
WL=QTc
where
WL = workload scheduled for a given period, hr,
Q = quantity to be produced during the period. pc/period,
Tc = work cycle time required per work unit, hr/pc. (Tc =Tstd)
If the workload includes multiple part or product styles that are
produced by the same work system:
where
Qj =quantity of part or product style j, pc,
Tcj =cycle time of part or product style j, hr/pc.
j cj
j
WL Q T
 
29
 Number of workers and number of machines
required:
W = WL / AT, or n = WL / AT
where
w = number of workers,
n = number of workstations,
AT = available time of one worker in the
period, hr / period / worker
Case 1: When Setup is not a Factor
30
Example 2.11: Determining Worker
requirements
 Given: 800 shafts must be produced in the
lathe section of a machine shop in particular
week. Each shaft is identical and Tstd=11.5min.
All the lathes are identical. There are 40 hours
of available time on each lathe.
 Determine: Number of lathes and lathe
operators must be devoted during that week.
31
Example 2.11: Solution
 Workload:
WL=800(11.5 min)=9200 min=153.33hr
Machine (and worker) requirements
w =n =153.3/40=3.83 (round up)
=4 lathe operators and lathes
32
Factors that affect the workload
1. Learning effect: As learning occurs in repetitive
manual work, worker efficiency increases, cycle
time decreases so that the workload is reduced.
2. Worker efficiency: Worker may perform either
above or below standard performance.
Ew = Workload actually completed
Workload completed at standard performance
 Worker efficiency greater than 1.00 reduces the
workload.
33
Factors that affect the workload
Defect rate: Fraction of parts produced that are defective.
A defect rate greater than zero increases the quantity of
work units that must be processed to yield the desired
quantity. So workload increases with defect rate.
The relationship between the starting quantity and the final
quantity produced:
Q =Q0 (1-q)
where
Q= quantity of good units made in the process,
Q0 =original or starting quantity; q=fraction defect rate.
The combined effect of worker efficiency and defect rate is
given by
WL=(QTstd) / (Ew(1-q))
34
Availability
 A common measure of reliability for equipment
 Defined as the proportion of time the equipment is
available to run relative to the total time it could be used.
 Available time increases as availability increases
AT=Hsh A
where
AT =available time, hr/worker,
Hsh=shift hours during the period, hr,
A =availability, expressed as a decimal fraction.
35
Example 2.12: Effect of worker efficiency
defect rate, and availability
 Given: Previous example. Anticipated
availability of the lathes 95%. Expected worker
efficiency during production=110%. The
fraction defect rate=3%.
 Determine: Number of lathes required.
36
Example 2.12: Solution
 Total workload
WL=(QTstd) / (Ew(1-q))
WL =( 800 (11.5/60) ) / ( 1.10 (1-0.03) ) = 143.7 hr
Available time
AT=Hsh A
AT=40(0.95)=38hr/machine
n=WL/AT
n=143.7/38=3.78 lathes (and lathe operators)
=4 lathes (and lathe operators)

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03.ppt

  • 1. 1 Worker-Machine Systems  Worker operates a powered equipment  Examples: Machinist operating a milling machine Construction worker operating a backhoe ‫حفار‬ Truck driver driving an 18-wheel tractor-trailer ‫جرار‬ ‫ومقطورة‬ Worker crew operating a rolling mill ‫ماكينة‬ ‫درفلة‬ Clerical worker entering data into a PC
  • 2. 2 Relative Strengths Humans  Sense unexpected stimuli  ‫متوقعه‬ ‫الغير‬ ‫بالمؤثرات‬ ‫الشعور‬  Solve problems  Adapt to change  Generalize from observations  Learn from experience  Make decisions on incomplete data Machines  Perform repetitive operations consistently  Store large amounts of information  Retrieve data from memory reliably  Perform multiple tasks at the same time  Apply high forces and power  Perform computations very quickly  Make routine decisions quickly
  • 3. 3 Relative Strengths  In a worker-machine system the worker and the machine both contribute their own strengths and capabilities  The result is synergistic ‫التآزرية‬  Types of worker-machine systems:  Types of powered machinery used in the system  Numbers of workers and machines in the system  Level of operator attention required to run the machinery
  • 4. 4 Types of Powered Equipment  Powered machinery: A source of power other than human (or animal) strength is used to operate that tool (or machine). 1.Portable power tools  Light enough in weight so that they can be easily carried 2.Mobile powered equipment  Heavy pieces of equipment but transportable 3.Stationary powered machines  Perfom functions in a stationary location
  • 5. 5 Classification of Powered Machinery Cars, buses, trucks, airplanes Tractor, bulldozers, backhoes, forklifts Electric power generators Ovens, cash register PCs, photocopiers, telephones Turning, drilling, milling Portable power drills, chain saws, electric hedge trimmers
  • 6. 6 Numbers of Workers and Machines One worker and One machine  Taxicab driver and taxi One worker and Multiple machines  A worker operating several machines
  • 7. 7 Numbers of Workers and Machines Multiple workers and One machine  A crew on a ship Multiple workers and Multiple machines  Emergency repair crew responding to machine breakdowns in a factory
  • 8. 8 Level of Operator Attention  Full-time attention  Welders performing arc welding  Part-time attention during each work cycle  Worker loading and unloading a production machine on semi-automatic cycle
  • 9. 9 Level of Operator Attention  Periodic attention with regular servicing  Worker loading a machine every 20 cycles  Periodic attention with random servicing  Firefighters responding to alarms  Maintenance worker repairing machines
  • 10. 10 Good Work Design for Machine-Worker Systems 1. Design the controls of the machine to be logical and easy to operate for the worker. 2. Design the work sequence so that as much of the worker’s task as possible can be accomplished while the machine is operating. 3. Minimize the idle times of both the worker and the machine. 4. Design the task and the machine to be safe for the worker. 5. If the system is a multiple worker or/and multiple machine system, optimize the number of workers or machines in the system according to a specified objective.
  • 11. 11 Cycle Time Analysis  Two categories of worker-machine systems in terms of cycle time analysis  Cases: 1. Systems in which the machine time depends on operator control  A typist typing a list of names on a typewriter  Carpenter using power saw to cut lumber  A construction worker operating a backhoe  Cycle time analysis is same as for manual work cycle 2. Systems in which machine time is constant and independent of operator control  Operator loading semi-automatic production machine  Our focus is on this 2nd type  Two types:
  • 12. 12 Case 2.a: Cycle Times with No Overlap Between Worker and Machine  Worker elements and machine elements are sequential  There is no overlap in work elements between the worker and the machine  While worker is busy, machine is idle  While machine is busy, worker is idle  Normal time for cycle Tn = Tnw + Tm, where Tnw = Normal time for the worker-controlled portion of the cycle time, min Tm = Machine cycle time (assumed to be constant)
  • 13. 13 Case 2.a: Cycle Times with No Overlap Between Worker and Machine  Standard time for cycle Tstd = Tnw (1 + Apfd) + Tm (1 + Am) where Am = Machine allowance factor  Am=30%: Workers love that since efficiencies are overestimated  Am=0%: Workers hate that since efficiencies are underestimated  Am= Apfd
  • 14. 14 Example 2.8: Effect of machine allowance on standard time  Given: The work cycle consists of several manual work elements (operator controlled) and one machine element performed under semiautomatic control. The manual work elements: a normal time of 1 min and the semiautomatic machine cycle time is 2 min. Apfd=15%.  Determine: the standard time using (a) Am =0, (b) Am=30%.
  • 15. 15 Example 2.8: Solution  The normal time for the work cycle: Tn=1.0+2.0=3.0 min (a) Tstd = Tnw (1 + Apfd) + Tm (1 + Am) Tstd=1.0(1+0.15)+2.0=3.15 min Workers (b) Tstd = Tnw (1 + Apfd) + Tm (1 + Am) Tstd=1.0(1+0.15)+2.0(1+0.30) =3.75 min Workers
  • 16. 16 Example 2.9: Effect of machine allowance on worker efficiency  Given: Standard times in the previous example (Example 2.8).  Determine: The worker efficiencies if 150 units are produced in an 8-hour shift.  Solution: (a) Hstd = Q Tstd Hstd=150(3.15)=472.5min=7.875hr Ew = Hstd / Hsh Ew=7.875/8.0=0.984= 98.4% (b) Hstd = Q Tstd Hstd=150(3.75)=562.5min=9.375hr Ew = Hstd / Hsh Ew=9.375/8.0=1.172= 117.2%
  • 17. 17 Case 2.b: Internal Work Elements  Some worker elements are performed while machine is working  Internal work elements performed simultaneously with machine cycle  External work elements performed sequentially with machine cycle  Desirable to design the work cycle with internal rather than external work elements  If it is possible, include operator work elements that are performed while machine is running.
  • 18. 18 Normal Time and Standard Time  Normal time Tn = Tnw + Max{Tnwi , Tm}  Standard time Tstd = Tnw (1 + Apfd) +Max{Tnwi (1 + Apfd) , Tm (1 + Am)}  Actual cycle time Tc = Tnw / Pw + Max{Tnwi /Pw , Tm} where Tnw = normal time for the worker’s external elements, min Tnwi = normal time for the worker’s internal elements, min Tm = machine cycle time, min
  • 19. 19 Example 2.10: Internal vs external work elements in cycle time analysis 0.75 0.73 Total (idle) 0.15 Worker transports finished part and deposits into tote pan 6 (idle) 0.10 Worker unloads finished part from machine 5 0.75 (idle) Machine semiautomatic cycle 4 (idle) 0.12 Worker loads part into machine and engages machine semiautomatic cycle 3 (idle) 0.23 Worker picks up raw workpart and transports to machine 2 (idle) 0.13 Worker walks to tote pan containing raw stock 1 Machine Time (min) Worker Time (min) Work Element Description Seq. Tc=0.73+0.75=1.48 min
  • 20. 20 0.75 0.73 Total (operating) 0.15+ 0.13+ 0.23= 0.51 Worker transports finished part and deposits it into tote pan, walks to tote pan containing raw stock, and picks up raw workpart and transports it to machine. (This element is internal to the machine semiautomatic cycle.) 4 0.75 (idle) Machine semiautomatic cycle 3 (idle) 0.12 Worker loads part into machine and engages semiautomatic machine cycle 2 (idle) 0.10 Worker unloads finished part from machine 1 Machine Time (min) Worker Time (min) Work Element Description Seq. Tc=0.10+0.12+0.75=0.97 min Example 2.10: Internal vs external work elements in cycle time analysis
  • 21. 21 Example 2.10: Internal vs external work elements in cycle time analysis  The cycle time is reduced from 1.48 min to 0.97 min.  % cycle time reduction=(CTcurrent-CTimproved)/CTcurrent =(1.48-0.97)/1.48=34%  Rcurrent=1/1.48 min=0.68 units per min  Rimproved=1/0.97 min=1.03 units per min  % increase in R=(Rimproved-Rcurrent)/Rcurrent =(1.03-0.68)/0.68=53%
  • 22. 22 Automated Work Systems  Automation is the technology by which a process or procedure is accomplished without human assistance  Implemented using a program of instructions combined with a control system that executes the instructions  Power is required to drive the process and operate the control system
  • 23. 23 Automated Work Systems Automated robotic spot welding cell (photo courtesy of Ford Motor Company)
  • 24. 24 Levels of Automated Systems  There is not always a clear distinction between worker-machine systems and automated systems, because many worker- machine systems operate with some degree of automation. 1. Semiautomated machine  Performs a portion of the work cycle under some form of program control  Human worker tends the machine for the rest of the cycle by loading unloading etc.  Operator must be present every cycle  Same characteristics with worker-machine system  e.g.,an automated lathe requires a worker to unload parts at every cycle, although changing tools may not be required at every cycle
  • 25. 25 Levels of Automated Systems 1. Fully automated machine  Operates for extended periods of time with no human attention (longer than one work cycle, e.g. every hundredth cycle ‫كل‬ ‫مائة‬ ‫دورة‬ )  e.g., periodically the molded parts at a molding machine must be collected.
  • 26. 26 Determining worker and machine Requirements  How many workers/machines are required to achieve the organization’s work objectives?  If too few workers are assigned to perform a given amount of work  The work cannot be completed on time, customer service will suffer.  If too many workers are assigned to perform a given amount of work  The payroll costs are higher than needed, and productivity will suffer.
  • 27. 27 Determining worker and machine Requirements • Workload (WL): Total hours required to complete a given amount of work or to produce a given number of work units scheduled during the period  Available time (AT): The number of hours (in the same period) available from one worker or worker-machine system
  • 28. 28 Case 3.1: When Setup is not a Factor Workload WL=QTc where WL = workload scheduled for a given period, hr, Q = quantity to be produced during the period. pc/period, Tc = work cycle time required per work unit, hr/pc. (Tc =Tstd) If the workload includes multiple part or product styles that are produced by the same work system: where Qj =quantity of part or product style j, pc, Tcj =cycle time of part or product style j, hr/pc. j cj j WL Q T  
  • 29. 29  Number of workers and number of machines required: W = WL / AT, or n = WL / AT where w = number of workers, n = number of workstations, AT = available time of one worker in the period, hr / period / worker Case 1: When Setup is not a Factor
  • 30. 30 Example 2.11: Determining Worker requirements  Given: 800 shafts must be produced in the lathe section of a machine shop in particular week. Each shaft is identical and Tstd=11.5min. All the lathes are identical. There are 40 hours of available time on each lathe.  Determine: Number of lathes and lathe operators must be devoted during that week.
  • 31. 31 Example 2.11: Solution  Workload: WL=800(11.5 min)=9200 min=153.33hr Machine (and worker) requirements w =n =153.3/40=3.83 (round up) =4 lathe operators and lathes
  • 32. 32 Factors that affect the workload 1. Learning effect: As learning occurs in repetitive manual work, worker efficiency increases, cycle time decreases so that the workload is reduced. 2. Worker efficiency: Worker may perform either above or below standard performance. Ew = Workload actually completed Workload completed at standard performance  Worker efficiency greater than 1.00 reduces the workload.
  • 33. 33 Factors that affect the workload Defect rate: Fraction of parts produced that are defective. A defect rate greater than zero increases the quantity of work units that must be processed to yield the desired quantity. So workload increases with defect rate. The relationship between the starting quantity and the final quantity produced: Q =Q0 (1-q) where Q= quantity of good units made in the process, Q0 =original or starting quantity; q=fraction defect rate. The combined effect of worker efficiency and defect rate is given by WL=(QTstd) / (Ew(1-q))
  • 34. 34 Availability  A common measure of reliability for equipment  Defined as the proportion of time the equipment is available to run relative to the total time it could be used.  Available time increases as availability increases AT=Hsh A where AT =available time, hr/worker, Hsh=shift hours during the period, hr, A =availability, expressed as a decimal fraction.
  • 35. 35 Example 2.12: Effect of worker efficiency defect rate, and availability  Given: Previous example. Anticipated availability of the lathes 95%. Expected worker efficiency during production=110%. The fraction defect rate=3%.  Determine: Number of lathes required.
  • 36. 36 Example 2.12: Solution  Total workload WL=(QTstd) / (Ew(1-q)) WL =( 800 (11.5/60) ) / ( 1.10 (1-0.03) ) = 143.7 hr Available time AT=Hsh A AT=40(0.95)=38hr/machine n=WL/AT n=143.7/38=3.78 lathes (and lathe operators) =4 lathes (and lathe operators)