1. Effects of Variability

2. Successive Units on Time Line t How variable is this system ? p. 5

3. Wise Men On Variability.. God does not play dice with the universe. – Albert Einstein Stop telling God what to do. – Niels Bohr

4. Understanding Variability Variability: Non-uniformity of a class of entities (departure from regular, predictable behavior) Associated with, but not identical to, Randomness (variability without explicitly analyzed cause) p. 5

5. Input : Unpredicted Volume swings Random arrivals (randomness is the rule, not the exception) Incoming quality Product Mix Resources : Breakdowns / Maintenance Operator absence Set-up times Tasks : Inherent variation Lack of SOPs Quality (scrap / rework) Routes : Variable routing Dedicated machines Buffer Processing Especially relevant in service operations (i.e. not just factories): emergency room air-line check in call center check-outs at cashier Variability: Where does it come from?

6. .. Wise Men On Variability All the evidence points to God being an inveterate gambler, Who throws the dice on every possible occasion! He not only plays dice with the Universe, but sometimes He throws them where they cannot be seen! – Stephen Hawking

7. Quantifying Variability

8. Factory Physics Notation.. t :Average of random variable (time - arrival, processing, departure etc.) σ 2 : Variance of random variable c 2 : SCV, Squared Coefficient of Variation, = σ 2 /t 2 m f : Mean Time Between Failures (MTBF) m r : Mean Time To Repair (MTTR) A : Availability of machine = m f / (m f + m r ) t s : Setup time N s : Number of units produced between setups p. 3

9. Variability Classes in Factory Physics Effective Process Times: HV, LV, and MV are all possible in effective process times LV: Actual Process times without outages MV: Effective Process times with short adjustments (e.g. Setups) HV: Effective Process times with long outages(e.g. Failures) 0.75 High variability (HV) Moderate variability (MV) Low variability (LV) 01.33 cece p. 5

10. Variability Formulae p. 5

11. Variability Formulae p. 5

12. Variability Effects Example of Breakdowns …

13. Situation II: Tortoise and Hare - Availability Hare X19: t 0 = 15 min  0 = 3.35 min c 0 2 =  0 2 /t 0 2 = 3.35 2 /15 2 = 0.05 m f = 12.4 hrs (744 min) m r = 4.133 hrs (248 min) c r = 1.0 Availability: Tortoise: t 0 = 15 min  0 = 3.35 min c 0 2 =  0 2 /t 0 2 = 3.35 2 /15 2 = 0.05 m f = 1.9 hrs (114 min) m r = 0.633 hrs (38 min) c r = 1.0 A = No difference between machines in terms of availability. Based on p. 2

14. Tortoise and Hare - Variability Hare X19: t e = c e 2 = Tortoise 2000 t e = c e 2 = Hare X19 is much more variable than Tortoise 2000!

15. Variability Effects Example of Setups …

16. Variability Effects: Setup Example... Data: Fast, inflexible machine – 2 hr setup every 10 jobs Slower, flexible machine – no setups Traditional Analysis? No difference!

17. ... Setup Example … Factory Physics Approach: Compare mean and variance Fast, inflexible machine – 2 hr setup every 10 jobs

18. … Setup Example … Slower, flexible machine – no setups but more variable processing Conclusion: Flexibility can reduce variability.

19. … Setup Example New Machine: Consider a third machine same as the first machine with setups, but with shorter, more frequent setups Analysis: Conclusion: Shorter, more frequent setups induce less variability.

20. Variability Effects Effect of Breakdowns: Hare or Tortoise? Not to scale

21. The Student Syndrome Deadline Degree of Effort Time on Project

23. Where Does Variability Come From ? Sources of Variability: setups and batching work-pace variation machine failures differential skill levels materials shortages engineering change orders yield loss customer orders rework product differentiation operator unavailability material handling