1. Introduction to Transfer Lines Active Learning – Module 1
Dr. Cesar Malave
Texas A & M University

2. Background Material
Any Manufacturing systems book has a chapter that covers the introduction about the transfer lines and general serial systems.
Suggested Books:
Chapter 3(Sections 3.1 and 3.2) of Modeling and Analysis of Manufacturing Systems, by Ronald G.Askin and Charles R.Stanridge, John Wiley & Sons, Inc, 1993.
Chapter 3 of Manufacturing Systems Engineering, by Stanley B.Gershwin, Prentice Hall, 1994.

3. Lecture Objectives
At the end of the lecture, every student should be able to
Understand and analyze about serial production systems that are subject to machine failures and random processing times
Evaluate the effectiveness (availability) of a transfer line given
Failure rates for the work stations
Repair rates for the work stations

4. Time Management Readiness Assessment Test (RAT) - 5 minutes
Introduction minutes
Lecture on Paced Lines without buffers minutes
Spot Exercise - 5 minutes
Team Exercise - 5 minutes
Homework Discussion minutes
Conclusion minutes
Total Lecture Time minutes

5. Readiness Assessment Test (RAT)
Solve the following problem on probability:
Six red discs, numbered from 1 to 6, and 4 green discs, numbered from 7 to 10, are placed in box A. Ten blue discs, numbered from 1 to 10, are placed in box B. Two discs are drawn from Box A and two discs are drawn from Box B. The four discs are drawn at random and without replacement.
Find the probability that the discs drawn are:
one red disc, one green disc and two blue discs with all four discs odd numbered.

6. Solution
Probability: The total number of occurrences of a selection/event "a", divided by the total number of occurrences (a) plus the number of failures of those occurrences "b" (i.e.. total possible outcomes)
Hence, probability is given by P = a /(a+b)
The problem can be solved the following way:
Probability = P (red-odd)*P (green-odd)*P (blue-odd)*P (blue-odd) +
P (green-odd)*P (red-odd)*P (blue-odd)*P (blue-odd)
= ( 3/10 * 2/9 * 5/10 * 4/9 ) + ( 2/10 * 3/9 * 5/10 * 4/9 )
= 4/135

7. Introduction
Transfer Line: A set of serial, automatic machine and/or inspection stations linked by a common material transfer and control system.
Buffers: Means for protecting workstations from failures elsewhere in the line, thereby improving station utilization.

8. Introduction (Contd..) Sample transfer line with intermediate buffers1 2 3 1 # #
Workstation #
Buffer #
Sample transfer line with intermediate buffers
Reasons for a station to be non-functional
Station failure
Total line failure
Station blocked
Station starved Wo

9. Introduction (Contd..) Classification of Failures
Time Dependent Failures
Occur with a chronological frequency
Time between failures is measured in units like hours
E.g.: Daily Maintenance
Operation Dependent Failures
Occur while the system is running
Time between failures is measured in cycles
E.g.: Tool Wear

10. Introduction (contd..) downtime) (uptime ) uptime ( + = E
Effectiveness (Availability) of a line can be defined as:
E (uptime): Productive cycle time ( expected value )
E (uptime + downtime): Total cycle time ( expected )
downtime)
(uptime )
uptime ( + = E

11. Paced Lines without Buffers
Operation Dependent Failures: Assumptions
Mean time to failure(MTTF) follows a geometric distribution with failure rate and the density function is given by = ( )
Mean cycles to failure(MCTF) is 1/
The number of cycles for repair at station is geometric with mean 1/bi cycles.
Assume bi = b, i = 1,2,…M

12. Assumptions (contd..)
All uptime and downtime random variables are independent.
Idle stations do not fail.
Failures occur at the end of the cycle, they do not destroy the product.
A maximum of one station can fail on any cycle.

13. Deeper insight into the assumptions:
Geometric distribution(GD) application in transfer lines.
Every workstation will have two states – failure and working
Probability that a station has failed = and working = 1 -
Probability that the station fails at the 1st cycle is
Probability that the station fails at the 2nd cycle = ( )
Probability that the station fails at the 3rd cycle = ( )2
Probability that the station fails at the t th cycle = ( )t-1
GD assumption allows the use of discrete time and discrete state Markow chain model to solve the above.
At most one station failure assumption allows us to ignore the 2nd order terms.
Idle station failure distinguishes between the two types of failures.

14. Model Analysis:
Probability that the transfer line (M stations) first fails at the end of the tth cycle :
Let us define
Hence the above probability equation becomes
P(T = t) = b(1 - b)t-1
M station line behaves like a single station but with failure parameter b replacing ai ..

15. Model Analysis (contd..):
By expanding the terms in b and noting that ai being small, higher order terms approach zero and hence b
Effectiveness of a line can be calculated as the ratio of the expected productive cycles between failures(uptime) divide by expected total cycles between failures(uptime + downtime).
where b-1 is the mean number of cycles for repair to a station.

16. Spot Exercise
Find the line availability for a three-station line in the respective cases 1 and 2: Also analyze the variation in the results obtained.
The first, second and third stations average a failure every 10, 20 and 30 cycles respectively. Average repair time is 2 cycles.
The first, second and third stations average a failure every 5, 10 and 15 seconds respectively. Average repair time is 2 seconds.

17. Solution Case 1: and b = ½ Case 2:
Analysis: Effectiveness has been reduced from 0.75 to 0.71 because stations 1 and 2 continue the aging process while idle as a result of a failure at the other station

18. Time Dependent Failures: Assumptions
Time to failure for station i is exponential with rate parameter ai
Repair times are exponential with parameter bi
For an operating time of t,
Expected number of failures for a station i : ait
Expected repair time : ait/bi
Effectiveness of a station i is given by :
As stations are independent,
E = E1*E2*E3*…

19. Team Exercise
Repairmen can fix a failed workstation in 10 minutes on an average. Cycle time is 20 seconds. Stations seem to operate 250 cycles on average before failing. Estimate the daily (8-hour shift) production for a six-station line. What is the average daily workload of the operator. ( problem 3.16 – Askin & Stanridge)

20. Solution Given: Average Repair time = 10 min, Cycle time C = 20sec
αi = 1/250, b-1 = 30
(a) Estimate the output for 8 hours = 8*60*3 = 1440 cycles
E = [1 + b-1Σ αi ]-1 = [1 + 30(0.024)]-1 = 0.581
Units/shift = * 1440 = 837
(b) Average daily workload of the repairmen
The % of time repairmen are busy = (1 – E) * 100
= 41.9 % of shift
= 3.35 hrs

21. Homework
A 15 stage transfer line is being considered. Stations 1 through 10 should have the same reliability. Each station is expected to operate approximately 1000 cycles between failures. The last 5 stations are expected to break down about once every 600 cycles. Repair times will vary but should average about the equivalent of 12 cycles in duration. Estimate the availability of the line.

22. Conclusion
Transfer Lines : Serial production systems that are very costly and subjected to random failures
Failures are of two types – Time Dependent and Operation Dependent
They can affect the entire line or just a single station
Reliability models help in estimating system effectiveness when buffers are not used