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Welcome to the program on
Enhance Product quality thru’
Six Sigma & 7 QC tools
by
H K Varma [email protected] 6298622 426 62986
Our Mission
Knowledge + Training =
Prosperity
Program schedule
• 10.00 – 11.15 Session I• 11.30 – 1.00 Session IILunch break 1.00 to 2.00
• 2.00 – 3.30 Session III• 3.30 – 4.50 Session IV• 4.50 – 5.00 Q / A• 5.00 ----------- Close
Globalization and Liberalization .....
• The challenge is even higher with continued reduction in tariffs and lifting of quantitative restrictions on imports .
• Import liberalization has led to free availability of global products at cheaper rates across the developing world.
• In fact those unable to face the growing challenges are forced to put down the shutters.
• The survival mantra has become
• “Survival of the fittest”
Mfg Cost Var Output at TP Stores cr. 4000241 3972 +/- in WIP 178
PBIT Misc Output -2061191 Input Cost
3731 Dir Malt 3000NOPAT Dir Lab 86
810 Mktg PBIT Sales/Serv 6000 Malt OH 47929 Cost of Sales 3972 Shop OH 261
ED on Sales 794 PGOH 36TAX OD Adj Pers Rel Exp 89 Comm Exp 163
EVA 381 -65 T&C 54 Alloc Exp 189361 Sales Pr Exp 8
Corp alloc NDC 1986 ODE 63
WACC Estb 3112% Other Exp 41
Cap Chg MMI 1034449 Cap Emp WIP 370
3738 Net F Assets FG 53601 Curr Assets Cust OS 3073
4597 Oth contl A 67Net WC
3137Curr Liabilities Vendor Cr 1273
1460 Cust Adv 33OCL 154
Areas of focus
1. Reduction in Material & labor costs2. Reduction in Cycle time and Lead time3. Reduction in Rejections , Wastage4. Increase in Productivity
How Six Sigmacan help
improve EVA
Six Sigma• Every mistake an organization or person makes ultimately has
a cost, – the need to do a certain task over again, – the part that has to be replaced, – time or material wasted
• Six Sigma is a scientific problem solving tool for– meeting your customer's needs (Time , speed , Quality )– minimizing wasted resources (Errors , rework , Hidden
factory , variations +/-)– maximizing profit in the process ,thru’ disciplined data
collection and analysis to determine best solutions
Six Sigma - approach
Six Sigma is a scientific tool for Process Improvement
Six Sigma helps to improve the quality of process outputs by identifying and removing the causes of defects (errors), and
Minimizing variability in manufacturing and business processes
Six Sigma - objective• Man-kind accepts all creations of God , Black –White ,
Short-tall , fat-slim with all distortions / discrepancies ,but ....
• When it comes to creations of another man-kind thesame men don’t accept any variation be it color ,aesthetics , size , weight etc
• Primary objective of Six Sigma is therefore to– “do it right the first time” FPY (FTR) , and– “do the right things right” SOP
• Hence a need to minimize the process outputvariations
Performance Scale & CTXs1. A performance scale represents
units, such as time, length, size, and so on, indicates the measured value of your CTX
2. The goal of Six Sigma is to come as close to your performance target as often as possible (Hitting the dart)
3. You can get close, but you will always have some variation
Say 12.5mm
> 12.5mm< 12.5mm
Why Six Sigma1. The sigma scale is a universal
measure of how well a critical characteristic performs
2. The higher the sigma score, the more capable the process.
3. Products with more characteristics (CTQs),need Six sigma quality standards to ensure final product performance
4. Even if the milestone of Six Sigma may take time to reach, the act of working toward that goal drives breakthrough changes.
Sigma
Percent defective
Defects permillion
1 69% 691,462
2 31% 308,538
3 6.7% 66,807
4 0.62% 6,210
5 0.023% 233
6 0.00034% 3.4
7 0.0000019% 0.019
Note the difference1. Conventional quality 3 % d ,2. Under Six Sigma it is 3 out of a
million
Conventional quality 3 % d
3.4 3.0% d 30,000
Higher Sigma >>> Lower defects
Top Commitment and accountability
• A Six Sigma initiative begins at the top.
• The top management of an organization must actively commit to the Six Sigma initiative,
• Six Sigma, through its voice of the customer (VOC) tools, drives business processes to meet customer requirements
• The objective of Six Sigma is to ensure high quality and reliability of products, services, and transactions
• Six Sigma must include performance measures that are readily accessible & visible (Output , FTR , m/c breakdown etc)
Principles of Six Sigma
Six Sigma begins with one general-purpose equation
• Y = f(X) + E , where
• Y- is the outcome, the result you desire or need.
• X- represents the inputs, factors, or pieces that are needed to create the outcome. You can have several Xs.
• f- is the function, the method or process by which the inputs are transformed into the outcome.
• E- is the presence of error or variation in the process
• Common cause variation is : operating within +/- 3σCommon cause
1. Every outcome is the result of the inputs and the process that acts on it, plus the error that creates variation.
2. If good things happen, you want to know how to make them happen again. and
3. If bad things happen, you surely want to know how to prevent them next time.
4. Regardless of complexity, every result has one or more causes
5. The more you can single out these causes and understand them, the better your opportunity to change it for the better.
Determine the cause
Cause-Effect Diagramsub-causes
High MMI+
Shortages
External
Internal
SupplierLT high
RM n/awith Supplier
MatlRej
Rate settldelay
K Card Trigdelay /not trgr
Delayby buyer
Excess supplyfrom Supplier
K Qty large
Dispatchdisciplinemissing
Materialremains un-used
Extra matlbrought - buyer
K Card triggeredin spite of Matl availability
SAP stk highphy not avail
BOM error
Back-flashnot taking place Process Rej
un-accounted
K Card Triggeringdiscipline
Matl recdin last 3-4 daysof month
Cat.no. changed/clubbed under Kitting
Matl keptat diff loc
Effect
……… Xs ………
Importance of measurement
1. Until you include measurement and numbers in your knowledge, you're bound to the world of gut-feel, guessing, and marginal improvement.
2. You may work very hard, and even bring significant resources to improve goal, but without measuring your Ys and Xs, your ability to improve will be incomplete
3. Measurement begins with the Ys, and then extends to the Xs to understand the causes.
4. Data and Measurements are the foundation of Six Sigma
Vital few vs Trivial many1. Typically, only a few select variables (Xs) determine the
quality of a given outcome! 2. Basically It amounts finding those critical few(Xs) that give
you the leverage ie 80-20 rule , where 20 percent of the inputs account for 80 percent of the influence on the output.
3. After you determine that a factor is insignificant, don't waste time and energy putting attention on it. ie ,weed out the many trivial variables that take your time but offer no real advantage
4. DMAIC in Six Sigma helps you find the critical few(Xs) to follow a structured process for defining, measuring, and analyzing all the cause-and-effect relationships
The basics of a Six Sigma project
1. When a particular problem isselected to become a potential SixSigma project, it goes through acritical transformation :
2. By stating the problem in statisticallanguage, you ensure that you willuse data, and only data, to solve it.
3. This forces you to abandon gutfeelings, intuition, and best guessesto address your problems
Practical Problem
Statistical Problem
Statistical Solution
Practical Solution
Results
Determining Ys needing improvement
1. Identify which process output variables (Ys) need improvement to solve the business problem .
2. The Ys in need of improvement must be easily identifiable and quantifiable.
3. If there are more than two Ys, there's a good chance that your project is too large in scope.
4. You may have to break the project into two or more projects to be successful.
5. You must be able to express the magnitude of the problem (defect level) in some unit of measure (for example, hours, inches, percent late, and so on).
Y – Output needing ImprovementInputs
Xs Process
Collecting data
1. Don't be discouraged if your data is not perfect at this time.2. You can improve the integrity of your data when you are in
the Measure phase, plan to update the quality of your data at that time.
3. Verify that your data is long-term, not short-term, when estimating the base- line performance.
4. Short-term data is a snapshot of what's happening and could mislead you.
5. It also doesn't represent all the potential sources of variation that are contributing to your problem over the long-term, such as seasonal effects etc
Identifying & Tracking ImprovementPe
rcen
t exc
eedi
ng th
e op
erat
ion
time
-Y Improving “Y”
0
1
2
3
4
5
6
7
Knowing the baseline level of performance allows you to calculate the potential financial benefits when you target a level of improvement
Improvements put in place
Base line
Objective
Developing Objective and Process Entitlement• Setting the objective for the project's level of improvement
is a triangle activity. The key inputs are : 1. Your own opinion of what success is. 2. Another input comes from a concept called entitlement.3. Benchmarking is another input.
• Finally, listen to VOC• Entitlement is the best performance a process, as currently
designed, has demonstrated in actual operation (Associated with St Variation)
• Entitlement is an extremely powerful Six Sigma concept, used to determine the potential level of improvement
FTY
Yield =(352 – 103)/
352= 70.7%= FTY
& The Hidden Factory
The
Hidden factory is due to
The inability to correctly comply
with required specifications the
first time
Hidden Factory103
98.6%
The extra efforts put to get these 98nos.
accepted is HIDDEN FACTORY
352 347
Group 1 2 3 4Items In (Nos) 1200 1200 1200 1200
Accepted after change note 133 89 64 9
Reworked 121 70 43 6
Scrapped 53 23 13 3
Calculate Hidden factory
First Time Yield (%) 75% 85% 90% 99%
Ultimate yield (%) 96% 98% 99% 100%
Hidden factory (%) 21% 13% 9% 1%
ExerciseHidden Factory - Answers
Focus should be at improving the FTY
& reducing the Hidden factory
}
The Hidden factoryThe hidden factory is work that is done above and beyond what isrequired to produce a product or a service.....Work that gets ingrained into the organization when you don’t ask"Why are we doing this, since this is not adding any value?“"That's the way we have always done it." If you have heard this, you probably have a hidden operation.
Opr i Verification Opr i+1
AnalysisOff-linerepair Scrap
Fix ?Yes No
If problem
OEE = Availability * Performance * Quality Yield
Time available for production - downtime Time available for production
Performance :: Speed Loss Performance = Actual output rate
Std Output rate
Quality Yield :: Quality Loss
Total no. of parts produced – Defects Total No.of parts produced
Availability :: Downtime loss
Support Variable Calculation Calculated data Result
Planned Produ time Shift Length-Breaks 480 - 60 Min 420 Min
Operating Time Planned Prod Time-Down Time 420 - 47 Min 373 Min
Good Pieces Total Pieces-Rejects 19271 - 423 pcs 18848 PcsOEE Factor Calculation Calculated data OEE %
Availability Operating Time / Planned Prod time 88.81%
Performance Actual output rate / Ideal Run rate 86.11%
Quality Good Pcs / Total Pcs 97.80%Overall OEE Avail * Perf * Quality 74.79%
Production DataShift Length 8 Hrs=480 MinShort Breaks & Lunch 60 MinDown Time 47 MinIdeal Run rate 60 pcs per MinTotal pcs produced 19271 pcsReject pieces 423 pcs
Measure1. Measure : Is collecting useful data
1. Establishing relationship 2. Measure Variation , and also 3. Measuring gap
2. Variation is everywhere, and it diminishes your ability to consistently produce quality results, meet schedules, and stay under budget leading to performance problems
3. Until you include measurement, and numbers in your improvement efforts, you're bound to remain in the world of gut feel, educated guessing, and marginal improvement power
Significance of data
• To determine how well we fulfill customer requirements
• To determine how close are we wrt target
• To track accomplishments
• To determine when improvement is needed
• To track use of resources and how efficiently they are used
eg OEE ( A , P , Q )
• To provide information that supports improvements
• The data may be variable(measurable) or attribute(Go – NoGo ,
Good-Bad etc)
Type of data
• Subjective– Data is difficult to quantify – Could be 7% , 9% etc !– Very often decisions based on subjective data turn out to
be wrong and may cost organization money and time.• Objective
– Data is more reliable as it is countable / measurable– Accordingly they are classified as :– Variable (Time , length size etc) , measured and expressed
on continuous scale– Attribute ( Go-No-go , good taste , bad taste , No of
occurrences etc) or
Measures of Distribution1. Mode is the value observed most frequently and is
associated with the highest peak of a distribution. 2. Mean: The most common measure of central tendency is the
mean - widely called the average . It's important to understand that the mean is theoretical rather than real.
3. Median : The median is the point along the scale of measure where half the data are below and half are above
4. The mode, mean, and median all fail to communicate the critical information of how spread out or narrowly dispersed the data is around its central location point.
5. Hence a need to find out two more measures ie6. Range (R = Xmax-Xmin) and Standard deviationσ = ( )
X=
Standard Deviation• The standard deviation-(σ) is by far the most commonly used
measure of dispersionThe long and short of variation• In fact, for any selected short period of time, the process
generally varies within the same rough limits – This natural level of variation is called the short-term (St)variation
• This short-term variation is purely random• It is caused by the combined effect of all the little things that
are too hard to include in your understanding of the process and is therefore also called Common cause or random variation, short-term variation.
Process Entitlement
1. This hard wall in the improvement path is called Entitlement (variation you can expect from a process under the best conditions ) of the process or
2. Random variation or ST variation3. Short-term, or entitlement, variation is used to compare
the capability of different processes to meet a specified goal
Histogram or Probability curve
1. Pictures of data helps you understand the process2. These pictures - called graphs or plots - are definitely better
than numbers at communicating your data to others.3. Plotting and charting data help you project
i. the central tendency and ii. the spread of variation (uniform or skewed)
4. One of the best tool used to project both these characteristics is called Histogram .
5. Bucket or Bin size selected should provide for 10 to 20 equal divisions between the largest and the smallest observed values.
A Picture’s worth a thousand words
Process capability of Tube filling plant
Sample Qty filled Sample Qty filled
1 19.50 14 20.702 19.30 15 20.403 20.20 16 20.204 20.30 17 20.175 19.80 18 19.606 20.80 19 19.407 20.50 20 19.318 19.90 21 20.259 20.00 22 20.34
10 20.40 23 19.9511 20.60 24 20.1712 19.70 25 20.4013 19.85
Plot Histogram , calculate Mean , Std Deviation
00.5
11.5
22.5
33.5
44.5
Mean 20.07Std Dev 0.43
Run chart(Control chart) & Histogram
18.70
19.20
19.70
20.20
20.70
21.20
1 3 5 7 9 11 13 15 17 19 21 23 25
DOE – Design of Experiments
• In the equation Y = f(x) , • ‘Y’ is called the response derived from the state at which ‘X’
is operating• X is called Cause -Input and Y is called Effect or Output• X1,X2,X3.. Input or Control factor , Y – Output or Response• Measure phase will help u establish this relationship• DOE helps to establish this relationship called • Y = f (X1,X2,X3..) + Variation
Specifications setting
• Understandable: Is the specification clearly stated anddefined so that there can be no argument about itsinterpretation?
• Measurable: Can you measure the characteristic'sperformance against the specification
• Believable: Can you and your coworker peers strive tomeet the specification?
• Attainable or achievable: Can the level and range of thespecification be reached?
The traditional and the Six Sigma views on specifications and the costs caused by poor quality
Cost
caus
ed b
y po
or q
ualit
y
Characteristic scale of measure
LSL USLTarget
Task of Six Sigma is to understand how well the VOP meets the VOC
Meeting Six Sigma standards
• The basic aim of Six Sigma is to ensure processes give first time right output leading to consistent performance with variations between +/- 3σ
• Most of the output of a process generally meets the specifications(CTQ-X) , except few , who deviate to varying extent , measured by standard deviation (σ)
• So some units may have – X +/- 1σ , some – X +/- 2σ ,and some – X +/-3σ specifications
2 approaches to Improvement DMAIC DFSS
• Six Sigma offers two approaches for improvement
1. Improve the process so that chances of defects are reduced ,ie reduce the standard deviation DMAIC
2. Change the design (DFSS) so that product can accommodate process variations
Additional Information
Process Performance
• 2σ = 30.8% Rej
• 3σ = 6.68% Rej
• 3.4σ = 3% Rej
• 4σ = 0.62% Rej
• 5σ = 0.0223% Rej
• 6σ = 0.0003% Rej
Gr 3 Run chart sd 0.3 , Performance 2σ , Rej 30.8%
9.5
9.6
9.7
9.8
9.9
10
10.1
10.2
10.3
10.4
10.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
XiX barUSLLSL
Target 10.0 +/- 0.30
+1σ = 0.176-1σ
USL10.30
LSL9.70
3.4σPerformance
=3%Rej
StdDeviation
Perf=0.6/0.176
= 3.4σ
Gr 4
Specs width1. 2σ = 30.8% Rej2. 3σ = 6.68% Rej3. 3.4σ = 3% Rej4. 4σ = 0.62% Rej5. 5σ = 0.0223% Rej6. 6σ = 0.0003% Rej
Bell curve - Probability curve
Higher Process Sigma – lower Rejection
• A low process sigma means that a significant part of the tail of the distribution is extending past the specification limit. More defects.
• So the higher the process sigma , the fewer the defects
1. 2σ = 30.8% Rej2. 3σ = 6.68% Rej3. 3.4σ = 3% Rej4. 4σ = 0.62% Rej5. 5σ = 0.0223% Rej6. 6σ = 0.0003% Rej
} Most of Indian Industries are here
This is the journey we have to undertake
Process capability of a process or characteristic to meet its specifications (VOC/VOP)
1. Capability : Ability to match the voice of your process-VOP to the voice of your customer-VOC
2. The simplest capability index is called Cp. 3. It compares the width of a two-sided specification to the
effective short term width of the process.
USL - LSL representsthe VOC-voice of thecustomer'srequirements and
Cp =( USL-LSL )
6σstEffective process width under Six Sigma = 99.7%
In this example , Process capability = 1
LSLUSL
Sigma (Z) Score
• Six Sigma level of quality is defined as 3.4 defects per million opportunities.
•The central tendency of the performance distribution is defined by its mean 푋•The amount of variation in the performance, or the width of the distribution, is defined by its standard deviation σ .
Process Sigma Score Z = 2*Sigma Value
σ
4σ
퐗
Simulation model
Statistically it is proven that shifting the process's St distributioncloser to its SL by a distance of 1.5 times its ST std. dev. wouldalmost cover the defects occurring in the long term.
The sigma (Z ) score of the shifted distribution isZshifted = Zst - 1.5 = Expected ZLT
1.5σST
SL
Process Capability Index C non-centered distribution - (Contd)
LSL USL
1. The measure of Cp shift is called Process capacity Index2. ie, Distance from the revised X to each of the specification
limits divided by half-width of the short-term variation (3σ)
퐂퐩퐋 = 퐗 퐋퐒퐋ퟑ훔퐬퐭
X
Process Capability Index 퐶
Specifications 9.70 / 10.30 9.60 / 10.40
σ 0.10 0.10
Revised 푿 10 > 10.10 10 > 10.10푪풑풖푪풑푳푪풑풌
퐶 = min (퐔퐒퐋 퐗ퟑ훔퐒퐓
, 퐗 퐋퐒퐋ퟑ훔퐒퐓
)퐶 = min(퐶 , 퐶 )
퐂퐏퐔 =퐔퐒퐋 − 퐗ퟑ훔퐒퐓
퐂퐏퐋 =퐗 − 퐋퐒퐋ퟑ훔퐒퐓
20.00
20.43
19.57
20.50
19.50
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
1 3 5 7 9 11 13 15 17 19 21 23 25
USL
흈 = ퟎ.ퟏퟔ
Sigma Value 3.1 Sigma
score Z 6.2
Cp 1.03Cpk 1.04 1.03
Run chart VOC USL/LSL , VOP ie UCL / LCL
Capability Improvement PlanSymptom Diagnosis Prescription
푪풑 = 푪풑풌 풂풏풅
푷풑 = 푷풑풌
Overall , your process or characteristic is centered within its specifications
Focus on reducing the long-term variation in your process or characteristic while maintaining on-center performance
푪풑 = 푷풑풌 Your process is operating at its entitlement level of variation
Continue to monitor the capability of your process. Redesign its entitlement level of performance.
The Seven QC tools
1. Check Sheets
2. Pareto charts
3. Histograms
4. Cause and effect diagrams
5. Scatter diagrams
6. Control Charts
7. Graphs
Identifying
Analyzing
Communicating
These tools are divided in to 4 broad categories
Scatter diagram1. Histogram plots only one distribution (characteristic) at a
time . Often one needs to explore the relationship between two characteristics .
2. Scatter plot helps to understand the relationship between two characteristics
3. The two characteristics can be an input and the other can be an output (X , Y) or can be two inputs (X , X ..)
4. The relationship could be :– Positive Correlation– Negative correlation– Positive or negative correlation possibility– No Correlation
Make Curb Wt. (Kg)
Fuel Economy (Km/liter)
Toyota Camry 1580 8.9
Toyota Sequoia 2400 10
Honda Civic 1200 13.9
Land rover 2300 8.9
Mercedes S500 2100 9.7
VW Jetta 1500 9.9
Chyyster 1800 10.4
Chevrolet 2030 11
Hyundai Tiburon 1450 8.2
Dodge Ram 2670 4.2
Fuel Efficiency vs Curb Weight
Y = Km/liter
X1 : Curb weightX2 : Fuel injection systemX3 : Tyre pressureX4 : ……………….
Establish the correlation thru scatter diagram.
Is the correlation ::1. Positive2. Negative3. No correlation4. Positive possibility exists5. Negative possibility exists
Gr 5
C4
Steps to create B & W plot
1. Rank the captured data of a characteristic (X ) from least to the greatest value
2. Determine the Median3. Find the first quartile Q4. Find the third quartile Q5. Create a horizontal line
joining X to X6. Repeat steps 1 to 7 for each
additional characteristic to be compared against the same output
Amblagms Ph Value
100 3.30101 3.35103 3.55102 3.60104 3.66105 3.70106 3.80107 3.85109 3.90108 4.05110 4.10
Ambla ( bet 100-110gm)
ph value
110 4.10102 3.60101 3.35105 3.79103 3.55100 3.30108 4.05106 3.80107 3.85109 3.90104 3.66
Correlation between variables
1. Coefficient of Correlation between two variables : (r)
2. r = ퟏ풏 ퟏ
∑ (풙풊 풙흈풙
풏풊 ퟏ )(풚풊 풚
흈풚)
3. The calculated correlation coefficient will always be between -1 and 1
4. ‘r’ closer to zero indicates absence of linear fit (No correlation)
r = + 0.99
r = - 0.61
r = - 0.03
No correlation
Chyavanaprash
0.0
1.0
2.0
3.0
4.0
5.0
6.0
98 100 102 104 106 108 110 112
ph. Value (Y) vs Ambla - gms (X1)
β : Line slope = ∑ ∑( ).
=0.19
β : Value at which fitted line crosses X axis = -16
Pareto ChartStratification of “Quality” category
710
290210
15040
0
200
400
600
800
1000
1200
1400
Stale Burned Undercooked Slicing Other
Stratification of the Quality category shows “Stale” and “ Burned” as the major causes of poor quality
The team decided to use Cause and effect tool for further analysis of the problem
Process Optimization toolsProcess tool RoleSIPOC Suppliers-Inputs-
Process-Outputs-Customers
Fundamental to application of Six Sigma strategy
CT (critical to) tree Areas of importance
Critical to quality , Delivery , cost ….
Cause & Effect diagram Fish bone diagram Method to capture potential causes and inputs effecting the output
ANOVA Analysis of variance Helps to analyze reasons for process variation
Tolerance analysis Helps to optimize product designs
POKAYOKE Error proofing Zero output defect
RPN ( Risk Priority Number)
• RPN is calculated as under– Severity * Occurrence * Detection level
• The RPN will range from 1 to 1000, with higher RPN indicating higher risks.
• Some organizations use threshold values , above which preventive action must be taken. Eg > 120 , > 200 etc
• Reducing RPN requires change in design or process• It is desired that a defective should not reach the customer 1st step is to prevent defectives reaching the customer• ie, Improving the ability to detect defects at the specific
process step ( not at subsequent step)
Control • A solution that isn’t sustained over the long term has little
value• They are basically a type of Run chart with control limitsWhy Control chart
– It shows nature of variation in the process over time– Helps in detecting changes in the process– Helps in controlling the process
• Specs : USL/LSL vs UCL/LCL– CONTROL is also capability , 푪풑 - Process Capability
Why Controls
1. Process behavior is complex and fragile and that hard-earned gains slip away if the process is left to itself.
2. The Control phase helps you make sure the problem stays fixed, and, if done properly, provides you with additional data to make further improvements to the process.
3. A well designed process exhibits inherent self control, but..
4. A poorly designed process requires frequent external control and adjustment to meet requirements.
5. A process with well built-in control acts like the heating and cooling system in a house: The system automatically maintains a comfortable temperature at all times.
Control Charts Background• Dr Shewhart in1920 observed that every process exhibits
some degree of variation• Since no two things can be produced exactly alike ,
variation is natural and should be expected • He defined that if a measurement falls within plus or
minus three standard deviations of its average, it is considered “expected” behavior for the process.
• This is known as common cause variation• He observed two types of variations in any process
Control Chart ( contd)
• If the process is operating within chance causes of variation( ie within Control limits ) , the process is said to be understatistical control
• Control charts can be used for• variable data ( Kgs , Cms etc )
– X chart, R chart or sd (휎) chartor
• discrete or attribute data ( No of defects in a product )– p chart , np chart , c chart and u chart
Variable Control Charts
• Variable Control charts are used to monitor measurablequality characteristics of a process eg Temperature ,dimension , weight , viscosity etc
• Variable charts can monitor only one quality characteristic ata time .
• Variable Control charts help to monitor both process meanand process variability
• Hence it becomes necessary to use minimum 2 control chartsto study the process. Ie– Range or Std Deviation– Process mean , with UCL & LCL
Control Limit factorsdev. by Statistical Quality Control and Management Institute
SampSize Factors for X charts Factors for R Charts Factors for S charts Samp
size
n A A2 A3 D1 D2 D3 D4 d3 B3 B4 B5 B6 n
2 2.121 1.880 2.659 0.000 3.686 0.000 3.267 0.853 0.000 3.267 0.000 2.606 2
3 1.732 1.023 1.954 0.000 4.358 0.000 2.574 0.880 0.000 2.568 0.000 2.276 3
4 1.500 0.729 1.628 0.000 4.698 0.000 2.282 0.880 0.000 2.266 0.000 2.088 4
5 1.342 0.577 1.427 0.000 4.918 0.000 2.114 0.864 0.000 2.089 0.000 1.964 5
6 1.225 0.483 1.287 0.000 5.078 0.000 2.004 0.848 0.030 1.970 0.029 1.874 6
7 1.134 0.419 1.182 0.204 5.204 0.076 1.924 0.833 0.118 1.882 0.113 1.806 7
8 1.061 0.373 1.099 0.388 5.306 0.136 1.864 0.820 0.185 1.815 0.179 1.751 8
Sample Sample observations X Range Std Dev1 9.26 10.44 10.39 9.87 10.26 10.04 1.18 0.492 10.92 10.08 9.97 10.16 9.30 10.09 1.62 0.583 10.10 10.61 8.62 10.24 10.17 9.95 1.99 0.774 10.17 9.24 10.60 10.08 10.51 10.12 1.35 0.545 10.29 10.36 10.39 10.58 9.96 10.32 0.63 0.236 9.84 9.52 10.11 9.65 10.18 9.86 0.66 0.297 9.84 9.77 10.47 10.25 10.28 10.12 0.70 0.3
…25 10.17 1.09 .48
UCL = 퐃ퟒ 퐑= 2.114*1.11= 2.35
SPC for Shaft lengths
D4 & D3 from control limit chart
Always start with R chart to ensure variability within samples (R- lowest to the highest)
R Chart out of limits
0.00
0.50
1.00
1.50
2.00
2.50
3.00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
A process is not in statistical control if any point falls outside the control limits.
First , control the process before going for 푋 or S chart
Observations
VOC = 10” +/- 0.60C = VOC/VOP
= ( . . )∗ .
퐶 = 0.44
USL = 10.60
LSL = 9.40
ConclusionThough the process is under control (All points within UCL & LCL), the process capability C = 0.44If , however the σ is reduced to ∶ 0.20 , 퐂퐩 = ퟏ.ퟎퟎ andIf , the σ is further improved to ∶ 0.15 , 퐂퐩 = ퟏ.ퟑퟑHence it important that SPC is under control and 퐶 푖푠 > 1
100%Within+/- 3 std Dev
95%Within+/- 2 std Dev
Apprx. 69%Within+/- 1 std Dev
Interpreting Control Charts :: Test Zones :: Each control limit represents
1 std deviation
UCL
LCL
Centerline
Rarely a pointwould falloutside thecontrol limits
The formulae
MR Chart UCL = D ∗ MRLCL = D ∗ MR
Sigma Score Z = 2* C =(USL − LSL)
6σ
C = min ( , )
20.07
21.11
19.03
20.60
19.40
18.80
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
20.80
21.00
21.20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Qty filledX bar
UCLLCL
USL
LSL
Sigma value
1.24 Process Sigma - Z
2.47
Cp 0.47Cpk 0.41 0.52
X Chart Gr 1퐗 σ20.07 0.43
Z = (ퟐퟎ.ퟔ ퟐퟎ.ퟎퟕ) ퟎ.ퟒퟑ
*2
퐶 = (20.6− 19.4)
6 ∗ 0.43= 0.47
퐶 = (20.60− 20.07)
3 ∗ 0.43= 0.41
퐶 = (20.07− 19.40)
3 ∗ 0.43= 0.52
VOC
18.8019.0019.2019.4019.6019.8020.0020.2020.4020.6020.8021.0021.20
1 3 5 7 9 11 13 15 17 19 21 23 25
Sigma value
1.24 Process Sigma Z
2.47
Cp 0.47Cpk 0.41 0.52
푋 σ20.07 0.43
18.80
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
20.80
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425
18.60
18.80
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
20.80
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425
18.80
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
20.80
1 3 5 7 9 11 13 15 17 19 21 23 25
Sigma value
2.21 Process Sigma Z
4.43
Cp 0.79Cpk 0.74 0.77
푋 σ20.07 0.18
Gr 1
Gr 3
푋 σ20.00 0.15
Sigma value
4.08 Process Sigma Z
8.16
Cp 1.36Cpk 1.36 1.36
Control Charts for Attributes
• Whenever it is difficult to take numerical measurement thequality is judged either conforming / non-conforming -Defectives based on attributes( Np and p charts) :– Leaks / does not leak , No. of counts scratches , holes ,
dents etc .• It can also be no. of non-conformities (defects) that appear
on a unit ( No of dents , a/c opening form , scratches , holesetc) : C & U charts :
• The inspection doesn’t require spl trained people as nomeasurements are involved .
P Chart ( Control chart for fraction non-conforming)
• ‘P’ stands for proportion• Measures the proportion of non-conforming units in a group of
units being inspected.• P chart is the most versatile and widely used attribute chart• It can be used for following purposes.
– To determine the avg. proportion (or fraction) of non-conforming units over a given time
– To signal a change in the avg. fraction non-conforming– To identify out-of-control points that call for immediate action– To suggest places to implement X and R charts
• Np chart is used when analyzing only one type of defect
np Chart
• If the sample size is constant ( eg 100 in this example )and there is only one reason for non-conformance(Defective) , the chart for attribute data is called npcontrol chart
• If for any chart the LCL works out less than zero , theLCL is set to Zero.
np Chart
Batch NoNo of non-conforming
1 142 183 134 255 196 189 18
10 1211 17
…26 13Total 417
No. of non-conforming sheet metal components - Batch size 100
퐔퐂퐋 = 퐧 풑 + 3 퐧 풑 (ퟏ − 풑 ) = ퟐퟕ.ퟎퟓ
퐋퐂퐋 = 퐧 풑 - 3 퐧 풑 (ퟏ − 풑 ) = ퟓ.ퟎퟑ
풑 = ∑ 푫풊풎풊 ퟏ
∑ 풏풊풎풊 ퟏ
= ퟒퟏퟕퟐퟔ = ퟏퟔ.ퟎퟒ
np Chart
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
For fixed batch size
• The chart seems to be in control as no point falls beyond the control limits
• Avg. being high , further
investigation (푿 , R ) may be
carried-out to arrive at the root
cause for defectives
퐔퐂퐋 = 퐧 풑 + 3 퐧 풑 (ퟏ − 풑 ) = ퟐퟕ.ퟎퟓ
퐋퐂퐋 = 퐧 풑 - 3 퐧 풑 (ퟏ − 풑 ) = ퟓ.ퟎퟑ
풑 = 16.04
Defective units of 5gm pouch Gr 1
Day Smudged Printing
Improper sealing
Uneven margins
Total defective
Total (n)Inspected
Fraction(p) Non-confo
1 19 27 322 21 26 213 21 17 444 12 24 365 11 22 236 11 32 327 11 19 268 8 25 239 13 25 28
10 30 29 2611 26 34 2212 17 19 2213 31 35 3214 11 30 3115 28 34 3816 23 29 1817 16 31 2318 28 27 2319 24 23 1620 22 20 31
C5
UCL = p + 3 ̅( ̅) LCL = p - 3 ̅( ̅)
c Chart
• Used for monitoring the non-conformities(defects) perinspection unit or in constant area of opportunity ( egFixed length of a unit , area :: Road length , Car bonnet ,PCB )
• Control limits are :
UCL = C + 3 C
LCL = C − 3 C
Control charts for attributes
• P or C chart give the average proportion of non-conforming units over a given time span
• To identify out-of-control points that call forimmediate action
• To suggest places to implement 푋 and R charts
• When the no. of units are not constant , u chart is usedinstead of c chart
The u Chart for complaints received
0.000
0.050
0.100
0.150
0.200
0.250
0.300
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
LCL= 풖 - 3 풖풏풊
UCL= 풖 + 3 풖풏풊
풖 = ∑ 푪풊풌풊 ퟏ
∑ 풏풊풌풊 ퟏ
Process characteristic or measurement
What type of data ?
What type of attribute data
?
P chart C , U chart
What subgroup size
?
MR 퐜퐡퐚퐫퐭퐗 −퐑 퐜퐡퐚퐫퐭
퐗 − 퐒 퐜퐡퐚퐫퐭
Defectives defects 2 - 101 > 10
1. Not every performance indicator can be a KPI !
2. Just because some particular indicator is easy to measure it
should not become a KPI .Doing so dilutes your focus on what's
truly important , wastes time
3. KPIs should reflect what your CEO expects from you
4. KPIs should contribute towards meeting his goals
5. "K" in KPI stands for "key," meaning "important" – not just to
you, but to your CEO. So, report true KPI's, not mere PI's!
KPIs
He wants to know :
Six Sigma Project stepsProcess out line
1 2
9 8 7
3
6
4
5
Calculate RPN no of each project using FMEA take projects with high RPN to start with
• Six Sigma : A powerful tool to control process variability to reduce rejections & defects
• Through a structured DMAIC process– Define : Breakthrough
results– Measure : Hidden
factory , Sd Deviation 흈푺푻 ,흈푳푻 , Mean , Bell curve
– Analyze : FMEA , SIPOC– Parreto , Cause Effect– Improve : VOP vs
VOC/VOB– Control : Variable and
Attribute• Process Capability : Z
score , Cp• Cpk - Capability Index• 7 QC tools / Control
Charts
Summarize
Our other Training ProgramsIn-company as well as Open prog.
• Enhance Productivity & Inventory turns thru Principles and Applications of Lean Manufacturing – 2days
• Vendor Management & Development - 1day
• Un-lock Working capital thru Effective Inventory Management -1day
• World class Mfg - 3 days
• SCM – 1day
• 5S & Visual Control Management - 1day
• Material & Inventory Management - 1day
• Materials – A profit centre - 2days
Our other Training ProgramsIn-company as well as Open program
• World class Mfg - 3 days– Enhance Productivity & Inventory turns thru Principles and
Applications of Lean Manufacturing – 2days– Lean Manufacturing – Basic Principles and applications - 1day
• Lean Six Sigma - 2days– Performance Excellence and 5S - 1day– Six Sigma – 2day
• Materials – A profit centre - 2days– Un-lock Working capital thru Effective Inventory Management -
1day– SCM - 1day– Vendor Management & Development - 1day
89
Our other Training ProgramsIn-company as well as Open prog.
Lean Manufacturing Principles and Applications - 2days
1. What is World class organization2. Lean business model to enhance
EVA (Economic Value Addition)3. Toyota Production House4. Takt Time , VSM and Line
balancing5. Operational Wastes :: Muda Mura
Muri6. Work excellence thru’ 5S7. Total Productive Maintenance &
OEE
8. Product Lead time9. Tool Change over time &
SMED10. Autonomation & Pokayoke11. Effective Gemba meetings12. Kaizen – Continuous
Improvement , Bench marking
13. Lean Inventory – Kanban14. Lean vendor base
90
Six-Sigma
1. Coverage of Six Sigma across industry .
2. Transformation of abstract Market need into customer specific need /VOC .
3. Approach towards Business Excellence (DMAIC , DMADOV) .
4. QPPO identification, Development of PPMs
5. Short term & long term Variations6. FTY & hidden factory7. Taguchi loss curve8. Cp / Cpk
9. Type of data10. The seven QC tools
Check sheetsGraphsHistograms Control charts
R chartX chart S chartMR chartp chartnp chartc chart
Pareto ChartsCause-and-effect diagramsScatter diagrams
91
Our other Training ProgramsIn-company as well as Open prog.
• Materials – A profit centre - 2days
1. Break-even analysis , Volume Discounts
2. Business model to make Materials dept a profit center
3. Action plan to achieve Supplier competitiveness
4. Supplier Relationship Mgt.(SRM)5. Vendor Assessment , Rating &
Ranking6. Vendor Development7. Healthy Vendor Base8. Supplier Negotiation9. Product Costing
1. Working capital cycle2. Optimum service levels3. EOQ , ROL , Safety stock4. Inventory plans Push vs Pull5. Kanban6. Third party logistics7. Measures of Inventory
• Inventory Ratio • Doc
8. Inventory Record Accuracy9. How to arrest stock discrepancy
• Bar code• RFID
Vendor Management & DevelopmentUn-lock the Working capital thru Effective Inventory Management
92
