工厂物理学Chapter_8_1.pdf

APIC Dr David Ben Arieh 1 Basics of Variability Part I Chapter 8 Advanced Production and Inventory Control Dr David Ben Arieh APIC Dr David Ben Arieh 2 But Before we begin Homework Chapter 7 Problem 7 APIC Dr David Ben Arieh 3 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Variability Basics God does not play dice with the universe Albert Einstein Stop telling God what to do Niels Bohr APIC Dr David Ben Arieh 4 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Variability Makesa Difference Little s Law TH WIP CT so same throughput can be obtained with large WIP long CT or small WIP short CT The difference Variability Penny Fab One achieves full TH 0 5 j hr at WIP W0 4 jobs if it behaves like Best Case but requires WIP 27 jobs to achieve 95 of capacity if it behaves like the Practical Worst Case Why Variability APIC Dr David Ben Arieh 5 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Tortise and Hare Example Two machines subject to same workload 69 jobs day 2 875 jobs hr Capacity of 4 jobs hour subject to unpredictable outages availability 75 Hare X19 long but infrequent outages Tortoise 2000 short but more frequent outages Performance Hare X19 is substantially worse on all measures than Tortoise 2000 Why Variability APIC Dr David Ben Arieh 6 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Variability Views Variability Any departure from uniformity Random versus controllable variation Examples Randomness Essential reality Artifact of incomplete knowledge Management implications Robust policy is key APIC Dr David Ben Arieh 7 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Probabilistic Intuition Uses of Intuition driving a car throwing a ball mastering the stock market First Moment Effects Throughput increases with machine speed Throughput increases with availability Inventory increases with lot size Our intuition is good for first moments g APIC Dr David Ben Arieh 8 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Second Moment Effects Which is more variable processing times of parts or batches Which are more disruptive long infrequent failures or short frequent ones Where should you place a machine with high variability at the beginning or end of the line Our intuition is less secure for second moments Misinterpretation e g regression to the mean Probabilistic Intuition cont APIC Dr David Ben Arieh 9 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Variability Definition Variability is anything that causes the system to depart from regular predictable behavior Sources of Variability setups workpace variation machine failures differential skill levels materials shortages engineering change orders yield loss customer orders rework product differentiation operator unavailability material handling APIC Dr David Ben Arieh 10 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Measuring Process Variability CV variationoft coefficien timeprocess ofdeviation standard job a of timeprocessmean t c t Note we often use the squared coefficient of variation SCV ce2 The primary random variable is effective process time te APIC Dr David Ben Arieh 11 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Variability Classesin Factory Physics Effective Process Times actual process times are generally LV effective process times include setups failure outages etc HV LV and MV are all possible in effective process times Relation to Performance Cases For balanced systems MV Practical Worst Case LV between Best Case and Practical Worst Case HV between Practical Worst Case and Worst Case 0 75 High variability HV Moderate variability MV Low variability LV 01 33 ce APIC Dr David Ben Arieh 12 Low and Moderate Variability Distributions APIC Dr David Ben Arieh 13 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Measuring Process Variability Example Trial Machine 1 Machine 2 Machine 3 1 22 5 5 2 25 6 6 3 23 5 5 4 26 35 35 5 24 7 7 6 28 45 45 7 21 6 6 8 30 6 6 9 24 5 5 10 28 4 4 11 27 7 7 12 25 50 500 13 24 6 6 14 23 6 6 15 22 5 5 te 25 1 13 2 43 2 se 2 5 15 9 127 0 ce 0 1 1 2 2 9 Class LV MV HV APIC Dr David Ben Arieh 14 High Variability of Process Times APIC Dr David Ben Arieh 15 Causes of Variability Natural variability Preemptive outages breakdowns Non preemptive outages setups Operator availability Recycle APIC Dr David Ben Arieh 16 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Natural Variability Definition variability without explicitly analyzed cause Sources operator pace material fluctuations product type if not explicitly considered product quality Observation natural process variability is usually in the LV category timeprocess natural therepresent and where oo o o o t t c APIC Dr David Ben Arieh 17 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Preemptive Outages Down Time Mean Effects Definitions esrepair tim ofty variabiliof coefficent repair tomean time failure tomean time parts hr e g rate capacity base 1 ty variabilioft coefficien timeprocess base timeprocess base 0 0 0 0 rrr r f mc m m t r c t APIC Dr David Ben Arieh 18 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Down Time Mean Effects cont Availability Fraction of time machine is up Effective mean processing time and rate rf f mm m A Att Ar t m A t m r e oe e 0 0 APIC Dr David Ben Arieh 19 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Totoise and Hare Example Availability Hare X19 t0 15 min 0 3 35 min c0 0 t0 3 35 15 0 05 mf 12 4 hrs 744 min mr 4 133 hrs 248 min cr 1 0 Availability Tortoise t0 15 min 0 3 35 min c0 0 t0 3 35 15 0 05 mf 1 9 hrs 114 min mr 0 633 hrs 38 min cr 1 0 A A No difference between machines in terms of availability 75 0 38114 114 rf f mm m 75 0 248744 744 rf f mm m APIC Dr David Ben Arieh 20 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Down Time Variability Effects Effective Variability Conclusions Failures inflate mean variance and CV of effective process time Mean te increases proportionally with 1 A SCV ce2 increases proportionally with mr SCV ce2 increases proportionally in cr2 For constant availability A long infrequent outages increase SCV more than short frequent ones 0 22 0 2 2 2 0 22 2 0 2 0 1 1 1 t m AAcc t c mA tAm A Att r r e e e r rr e e Variability depends on repair times in addition to availability APIC Dr David Ben Arieh 21 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Tortoise and Hare Example Variability Hare X19 te ce2 Tortoise 2000 te ce2 Hare X19 is much more variable than Tortoise 2000 min 20 75 0 15 0 A t bilityhigh varia 25 6 15 248 75 01 75 0 11 05 0 1 1 2 0 22 0 t m AAcc r r min 20 75 0 15 0 A t ty variabilimoderate 0 1 15 38 75 01 75 0 11 05 0 1 1 2 0 22 0 t m AAcc r r APIC Dr David Ben Arieh 22 Non preemptive Outages Examples for non preemptive outages Ordinary capacity calculations do not analyze the impact of non preemptive outages Slow machine with short setups vs a fast machine with long setups same capacity Compare a fast machine 1 hour job that requires 2 hour setup every four parts on average to a slow machine 1 5 hour job with no setups equal capacity parts hour 3 2 hours 6 parts 4 e r APIC Dr David Ben Arieh 23 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Non preemptive Outages Setups Mean and Variability Effects Analysis Note we assume that the probability of doing a setup after any part is equal 2 2 2 2 2 2 2 0 2 0 1 e e e s s s s s e s s e s s s t c t N N N N t tt t c timesetup of dev std duration setup average setupsbetween jobs no average s s s t N APIC Dr David Ben Arieh 24 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Setups Mean and Variability Effects cont Observations Setups increase mean and variance of processing times Variability reduction is one benefit of flexible machines However the interaction is complex APIC Dr David Ben Arieh 25 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Setup Example Data Fast inflexible machine 2 hr setup every 10 jobs Slower flexible machine no setups but higher variability Traditional Analysis No difference jobs hr 8333 0 10 21 1 1 hrs 2 110 21 hrs 2 jobs setup 10 25 0hr 1 0 0 ee sse s s o tr Nttt t N ct jobs hr 833 02 1 1 1 50 hrs 1 2 0 0 tr ct e o APIC Dr David Ben Arieh 26 Wallace J Hopp Mark L Spearman 1996 2000 http www factory Setup Example cont Factory Physics Approach Compare mean and variance Fast inflexible machine 2 hr setup every 10 jobs 31 0 4475 0 1 jobs hr 8333 0 10 21 1 1 hrs 2 110 21 2 2 2 22 0 2 0 e s s s s se ee sse c N N N c t tr Nttt 0625 0 hrs 2 jobs setup 10 0625 0 hr 1 2 2 0 0 s s s c t N c t APIC