om session2
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Om advanced sessionTRANSCRIPT
Variability BasicsOperations Management - WS 2014/2015
Univ.Prof. Werner Jammernegg / Dr. Emel Arikan, M.Sc.
W. Jammernegg: Variability Basics 1 – 46
Overview
1. Process Variability
2. Quality Control: Statistical process control
3. Quality Improvement: Process capability
W. Jammernegg: Variability Basics 2 – 46
Variability
DefinitionVariability is anything that causes the system to depart from regular, predictablebehavior.
Sources of Variability
I setupsI machine failuresI materials shortagesI yield lossI reworkI operator unavailability
I workpace variationI differential skill levelsI engineering change ordersI customer ordersI product differentiationI material handling
W. Jammernegg: Variability Basics 3 – 46
Process Variability
Overview
1. Process Variability
2. Quality Control: Statistical process control
3. Quality Improvement: Process capability
W. Jammernegg: Variability Basics 4 – 46
Process Variability
Measuring Process Variability
coefficient of variation of effective process times (CVe)
ce = σete
σe . . . standard deviation of process timete . . . mean process time of a job
Note: we often use the "‘squared coefficient of variation"’ (SCV), c2e
W. Jammernegg: Variability Basics 5 – 46
Process Variability
Variability Classes
Effective Process TimesI actual process times are generally LVI effective process times include setups, failure outages, etc.I HV, LV, and MV are all possible in effective process times
Relation to Performance Cases: For balanced systemsI MV - Practical Worst CaseI LV - between Best Case and Practical Worst CaseI HV - between Practical Worst Case and Worst Case
W. Jammernegg: Variability Basics 6 – 46
Process Variability
Measuring Process Variablity - Example
W. Jammernegg: Variability Basics 7 – 46
Process Variability
Causes of Variability
Natural VariabilityVariability without explicitly analyzed cause
Preemptive Outages (Breakdowns)Variability due to outages right in the middle of a job (e.g. due to power outages,operators being called away on emergencies, running out of consumables)
Nonpreemptive OutagesVariability due to outages for which we have some control as to exactly when theyoccur (e.g. due to setups, replacement of tools, shift changes)
ReworkVariability due to quality problems
W. Jammernegg: Variability Basics 8 – 46
Process Variability
Natural Variability
DefinitionVariability without explicitly analyzed cause
SourcesI operator paceI material fluctuationsI product type (if not explicitly considered)I product quality
ObservationNatural process variability is usually in the LV category
W. Jammernegg: Variability Basics 9 – 46
Process Variability
Variability from Preemptive Outages (Breakdowns)
Definitionst0 = base mean process timeσ0 = base standard deviation of process timec0 = base process coefficient of variability (σ0/t0)r0 = 1
t0 = base capacity (rate, e.g. parts/hr)
mf = mean time to failuremr = mean time to repaircr = coefficient of variability of repair times (σr/mr )
W. Jammernegg: Variability Basics 10 – 46
Process Variability
Variability from Preemptive Outages (cont.)
Availability - Fraction of time machine is up
A = mfmf +mr
Effective Processing Time and Ratere = A ∗ r0
te = t0/A
W. Jammernegg: Variability Basics 11 – 46
Process Variability
Example: Tortoise and Hare
Two machinesI subject to same workload: 69 jobs/day (2.875 jobs/hr)I subject to unpredictable outages (availability = 75%)
Hare X19I long, but infrequent outages
Tortoise 2000I short, but more frequent outages
PerformanceHare X19 is substantially worse on all measures than Tortoise 2000. Why?Variability!
W. Jammernegg: Variability Basics 12 – 46
Process Variability
Example: Tortoise and Hare (cont.)
Hare X19t0 = 15minσ0 = 3.33minc0 = σ0/t0 = 3.33/15 = 0.22mf = 12.4hrs(744min)mr = 4.133hrs(248min)cr = 1.0
Tortoiset0 = 15minσ0 = 3.33minc0 = σ0/t0 = 3.33/15 = 0.22mf = 1.9hrs(114min)mr = 0.633hrs(38min)cr = 1.0
AvailabilityA = A =
W. Jammernegg: Variability Basics 13 – 46
Process Variability
Variability from Preemptive Outages (cont.)
Effective Variabilityte = t0/A
σ2e = ( σ0A )2 + (m2
r +σ2r )(1−A)t0Amr
c2e = σ2e
t2e= c20 + (1 + c2r )A(1− A) mr
t0
Note: Variability depends on repair times in addition to availability!
ConclusionsI Failures inflate mean, variance, and CV of effective process timeI Mean (te) increases proportionally with 1/AI SCV (c2e ) increases proportionally with mr
I SCV (c2e ) increases proportionally with c2rI For constant availability (A), long infrequent outages increase SCV more
than short frequent onesW. Jammernegg: Variability Basics 14 – 46
Process Variability
Example: Tortoise and Hare (cont.)
Hare X19te =
c2e =
Tortoise 2000te =
c2e =
W. Jammernegg: Variability Basics 15 – 46
Process Variability
Variability from Non-Preemptive Outages (Setups)
DefinitionsNs = number of parts (or jobs) between setupsts = mean duration of setup timescs = CV of setup times (σs/ts)
Effective Variabilityte = t0 + ts
Ns
σ2e = σ20 + σ2s
Ns+ Ns −1
N2s
t2s
c2e = σ2e
t2e
W. Jammernegg: Variability Basics 16 – 46
Process Variability
Variability from Rework
Definitionsp = probability that a given part is defective
Effective Variabilityte = E [Te ] = t0
1−p
σ2e = Var(Te) = σ20
1−p + pt20(1−p)2
c2e = σ2e
t2e= (1−p)σ2
0+pt20t20
= c20 + p(1− c20 )
W. Jammernegg: Variability Basics 17 – 46
Process Variability
Quality and the Supply Chain
Effect of Variability on Purchasing Lead Times
Single Component SystemsI Required Service: 95% service levelI Consequences: supplier 1 has 14 days and supplier 2 has 23 days lead time
W. Jammernegg: Variability Basics 18 – 46
Process Variability
Quality and the Supply Chain (cont.)
Effect of Variability on Purchasing Lead Times
Multiple Component SystemsI Required Service: 10 component assembly
I each component with 95% service level: p = 0.95 → p10 = (0.95)10 = 0.5987I 95% service on the assembly: p10 = 0.95 → p = 0.951/10 = 0.9949
I Consequences: supplier 1 has 16.3 days and supplier 2 has 33.6 days lead time
W. Jammernegg: Variability Basics 19 – 46
Process Variability
Other Process Variability Inflators
SourcesI operator unavailabilityI recycleI batchingI material unavailabilityI et cetera, et cetera, et cetera
EffectsI inflate te
I inflate ce
ConsequencesEffective process variability can be LV, MV, or HV.
W. Jammernegg: Variability Basics 20 – 46
Process Variability
Total Productive Maintenance (TPM)
cf. Nakajima S (1988) Introduction to TPM: Total Productive Maintenance. Productivity Press, Inc.
W. Jammernegg: Variability Basics 21 – 46
Process Variability
Overall Equipment Effectiveness (OEE)
cf. Nakajima S (1988) Introduction to TPM: Total Productive Maintenance. Productivity Press, Inc.
W. Jammernegg: Variability Basics 22 – 46
Quality Control: Statistical process control
Overview
1. Process Variability
2. Quality Control: Statistical process control
3. Quality Improvement: Process capability
W. Jammernegg: Variability Basics 23 – 46
Quality Control: Statistical process control
Quality Control
Sample testing
I Acceptance sampling
I Sampling inspection(acceptance sampling, sampling inspection)
I OK/defect detection(qualitative attributes)(sampling by ATTRIBUTES)
W. Jammernegg: Variability Basics 24 – 46
Quality Control: Statistical process control
Acceptance check (Approval check)
Incoming goods inspection, Finished goods inspection
I Initial situation: A defective product primary damages the image of theproducer and only secondary affects the supplier
I Consequence: Sampling inspections with inspection plans(e.g. Standards with MIL STD 105 D)
I Best practice: Define the Acceptable Quality Level AQL and the rejectionlevel LTPD (Lot Tolerance Percent Defective)
W. Jammernegg: Variability Basics 25 – 46
Quality Control: Statistical process control
I AQL is defined as the accepted defect rate of a shipment by the customer
I LTPD is the defect rate of a shipment with inadequate quality
I AQL and LTPD are mainly used for the calculation of the required lot size
I Dynamical sampling plans: Change the lot size according to the history of thesupplier and the delivered products:
I Full inspection – Sampling inspection – Skip Lot
W. Jammernegg: Variability Basics 26 – 46
Quality Control: Statistical process control
SPC (Statistical Process Control)
Process Control: Monitoring of the production process:
I Quality control chart (Control chart)I Samples are taken at fixed time intervalsI Given sample size
I Control chart for important KPIs of the process parameterI Mean, variance, range,...
I SHEWHART–CHARTS (Classical control charts)I The decision (e.g. Stop production) will be taken according to ONE KPI.
W. Jammernegg: Variability Basics 27 – 46
Quality Control: Statistical process control
Statistical process control: Control–chart
I Process parameters are tracedI Mean valueI Percentage of defects
I Differentiation:I Common causes for variation
(within the control limits)I Classifiable reasons for
variation (out of the controllimits)
I Measurement of the processperformance:What is the natural variation ofthe process while it is undercontrol?
W. Jammernegg: Variability Basics 28 – 46
Quality Control: Statistical process control
Control chart
W. Jammernegg: Variability Basics 29 – 46
Quality Control: Statistical process control
Classical control chart: Mean-chart(X̄ -chart)
UCL = ¯̄x + 3σ√n
LCL = ¯̄x − 3σ√n
UWL = ¯̄x + 2σ√n
LWL = ¯̄x − 2σ√n
UCL Upper Control LimitUWL Upper Warning LimitLWL Lower Warning LimitLCL Lower Control Limit¯̄x Process meanσ Process standard deviationn Number of observations per sample
W. Jammernegg: Variability Basics 30 – 46
Quality Control: Statistical process control
Range (R) - Chart
UCL = R̄ + 3× σR
LCL = R̄ − 3× σR
UWL = R̄ + 2× σR
LWL = R̄ − 2× σR
UCL Upper Control LimitLCL Lower Control LimitUWL Upper Warning LimitLWL Lower Warning LimitR̄ Range meanσR Range standard deviation
W. Jammernegg: Variability Basics 31 – 46
Quality Control: Statistical process control
p-chart
p̄ = No. of defective goodsNo. of observations
Sp =√
p̄(1− p̄)n̄
UCL = p̄ + 3× Sp UWL = p̄ + 2× Sp
LCL = p̄ − 3× Sp LWL = p̄ − 2× Sp
W. Jammernegg: Variability Basics 32 – 46
Quality Control: Statistical process control
Classical control chart: KPI development
W. Jammernegg: Variability Basics 33 – 46
Quality Control: Statistical process control
A process is under control if
I all values are within the control limits.I not more than one value out of 40 is out of the warning limits.I two consecutive values are not out of the same warning limit.I no trend exists containing five or more values, which exceeds a warning limit.I no more than six consecutive values are either above or below the process
mean.I no trend of more than six values exists.
W. Jammernegg: Variability Basics 34 – 46
Quality Improvement: Process capability
Overview
1. Process Variability
2. Quality Control: Statistical process control
3. Quality Improvement: Process capability
W. Jammernegg: Variability Basics 35 – 46
Quality Improvement: Process capability
Process capability
W. Jammernegg: Variability Basics 36 – 46
Quality Improvement: Process capability
Process capability
Goal: Reduction of the defect rate and thereby continuous process improvement
I Process capability is defined by the production tolerance.
I Production tolerance = Upper tolerance limit – Lower tolerance limit= [UTL–LTL]
I The product is defective if the measurement is out of the productiontolerance.
W. Jammernegg: Variability Basics 37 – 46
Quality Improvement: Process capability
Process capability indices
cp = (UTL− LTL)/6σ
I If the target m = (LTL + UTL)/2 and the mean of the process ¯̄x do notcoincide, the usage of cp would lead to erroneous results.
I Therefore:
cpk = Min{UTL− ¯̄x , ¯̄x − LTL}3σ
W. Jammernegg: Variability Basics 38 – 46
Quality Improvement: Process capability
Measurements of process capability
I Process capability studies are only be meaningful if the process is “undercontrol”.
I Calculation of ¯̄x , σ by using process date, where the mean is within thecontrol limits of the control chart.
W. Jammernegg: Variability Basics 39 – 46
Quality Improvement: Process capability
Normal distributed parameter
W. Jammernegg: Variability Basics 40 – 46
Quality Improvement: Process capability
Process capability indices
I A process is capable if cpk ≥ 1.
I Otherwise the process is called not capable.
W. Jammernegg: Variability Basics 41 – 46
Quality Improvement: Process capability
Example
W. Jammernegg: Variability Basics 42 – 46
Quality Improvement: Process capability
Example
Process capability
I Quality design: UTL=85kg, LTL=75kg, m=80kg
I Quality control: ¯̄x=82,5kg, σ=4,2kg
I cp =
I cpk =
W. Jammernegg: Variability Basics 43 – 46
Quality Improvement: Process capability
Improvement: Process mean=Target value
W. Jammernegg: Variability Basics 44 – 46
Quality Improvement: Process capability
Improvement: Reduction of process variance
W. Jammernegg: Variability Basics 45 – 46
Quality Improvement: Process capability
Quality control / Quality improvement
W. Jammernegg: Variability Basics 46 – 46