Six Sigma Green Belt Training Program

3.4 defects per million products

1) Questions to students – what 6 sigma is?

Basic purpose: To improve Quality

What’s Quality
 Conformance to specification
 Customer Satisfaction
 Abide by standards
 Less Wastage
 Relative Utility (Fitness for Use)

Anything we want to improve on must be easily measurable

Parameters to measure:

Eg of phone: we use of diff types of phone:

What’s the primary purpose of phone- to talk!......all phones fulfil this.
What a particular cust. Wants from a phone varies cust. To cust. – (entertainment device, business
device etc.)

1) Make Sure you create a product which Creates Expectation/ Excitement in the prospective customers
2) Performance: product must do what it is expected to do. And do it without a fail. This was customer
develops a Perception

Therefore, Quality is equal to P/E i.e (Perception/ Expectation)…………….what I got / what I thought

General values P/E can take:

P/E < 1 (Dissatisfied cust) - forbidden territory in a 6 sigma class

P/E = 1 (just satisfied cust) - not a guaranteed loyal customer- he searches for better option
P/E < 1 (Satisfied cust) - customer with delight ----> loyal customer------> repeat business (source of 95% of
business)

Six sigma is a thing which has brought Quality to be linked with business. Earlier it was an operational issue. Now,
Management revers quality
Quality should translate into money.

Why quality was not a factor in 16th century/ 17th century

People did make products but they were more of artist (quality was implicit/embedded in whatever they did/
thought. They always did quality work. People were specialized in whatever they did. They were perfectionist. High
degree of ownership and inheritance of vocations.)

With industrial revolution, volumes became high. Machines replaces humans. Therefore, that link of ownership was
lost. Reputation issue got lost. Numbers became more important.

World learnt this during second World War. They introspected. 30% of soldiers who died were due to malfunctioning
equipment. Not due to enemies.

1947- IOS (internation organization of standards was formed) , now known as ISO.
First time, standards were written for manufacturing. Now we have an industry standard to be complied with.

But all those standards we for END FINISHED PRODUCTS. No standards for PROCESSES.

All focus was on perfection in end product. This was done through comparison-----> INSPECTION. The role of
Inspector became most important in the industry. People made products, other group of people inspected.

In formal terms, his job was to find mistakes-----That was the only parameter to judge HIS performance. So, He was
responsible for maintaining the quality on the long run. Ideally, it should be the responsibility of the one who is
making the product.

Probability of Quality was only 50% (Probability of finding error by inspector----0.5)

Moreover, Inspection also costs money------on persons, process of inspection, time taken during inspection etc.

X= Cost of first time production of product

Y= Correction/ making the correct product and repackaging

Y= X*5

Therefore, one round of correction costs 5 times the cost of first time production.

Eg. Assembly line of a TV-------------say 100 TVs throughput through assembly line in one hour
Repair of TVs possible, only 20 per hour.

More I doubt my manufacturing process, higher cycles of inspection.

Irony is,…….more the inspections, better perception about the product.

World Realised this when japan invaded America----- 70’s

Japan broke US Economy. Companies crumbled. One such company- Motorola

Timeline:
1975- Moto was no. 1 in communication devices.
1980 – Moto faced survival probs with fierce Japanese competition.

CEO Bob galvin wanted to know what went wrong.

He was given a feedback by an employee that their quality stinked.

We have as many people manufacturing our pagers as many as those repairing them!!!

Disgression: Any arising defect in a product during use gives a perception that the product with never work the
same again.
Imagine- jisko bannaate waqt hi sudharna padey vo kya kaam karega?

The problems was:

PANASONIC products (Japanese) never failed. Stole their market share.

So What was the difference?

Americans focused on what, Japanese focused on how. If you want a product to performs without defect, make it
without defect. Manufacture it defect free, it will work defect free..

A recent eg:

Indian consumer electronics company

Indian chairman said….we are a customer focused company……Japanese picked the phrase…..they were impressed
and asked how Indians managed it…(Indian boasted about the penetration of their service facilities)….Japanese
whispered…is your quality that bad?

Paradigm shift-

We have longer warranty periods,…….confidence of companies in their manufacturing has improved.

Making Products defect free……so that it stays defect free

The above phrase was known as six sigma

MOTO Gave the world Six Sigma. (1988)
Perfected over 8 years.

General Motors still trying to beat Toyota.(<------------Impact of quality)

MALCOLM BOLDRIDGE National quality award in America:

Any company which aspires to win that awards has to beat Japanese counterparts on quality and then share what
they did to achieve that.

MOTOROLA won it in 1988. It had to share the secret!------SIX SIGMA.

CONCEPT OF SIX SIGMA

Dr.J.M.Juran-------Father of total quality management-------during 1950s tried to advise US industry that inspection
doesn’t mean quality. US industry ignored him, blinded by their own prevalent economic glory. He wrote a book
---handbook of quality---bible for quality professionals. Published in 1954 for first time.

JM Juran was ALWAYS associated with mgmt. quality

He had written in it:

US Auto industry was improving at an evolutionary state (Very slow)
Any company which improved at revolutionary rate (Fast paced), it could break the backbone of US industry.

Japanese hired/invited/kidnapped him to apply his thinking to their processes.

Dr.E.Deming -------always associated with operational quality

Disgression: Japanes are does, they respect Deming more than Juran, because Deming was more of a shopfloor
person.

Will Smith- make it defect free, it runs defect free

Done in 7 steps:

1) Understand Customer Needs:

Customer bhagwaan hai. We assume ourselves what he needs <---- Very wrong.
Always Own these two processes, whatever else you may outsource:
 Understanding Customer’s Needs.
 Design
Product Design

Features that customers like (addresses the E-Expectation part)

Eg:
Nike does only market and product design.
Everything else is outsourced------procurement to India, production to China, distribution to Dubai

It has only 400 employees in the world. AND IS SUCCESSFUL.

2) PROCESS
Every process has Key Process Parameters (Input Variables of the Process)
KPIV- Key Process Input Variables

That input variable of the process that has a direct impact on the output that is delivered by the process

i.e what should be ensured so that process happens correctly------> output is good-----customer is satisfied.

For these input variables, we set standards.

Whole concept of six sigma is to control KPIVs, so that if they stay within operating standards, process can’t
go wrong, and thereby, outpur is always in desired form.

PROPER DEIFINITION OF SIX SIGMA

A disciplined, data -driven approach and methodology to help eliminate defects in a process…from manufacturing
to transactional and from products to service

Significance of Six Sigma:

Import from Study Material

3.8 Sigma 6 Sigma

2000 lost/hour 7 articles lost per hour
15 mins each day One unsafe minite of dirinking water every month
1.7 incorrect ops per week

7 hours each month One hour without electricity every 34 years

Quality is not an effect but the cause.

Six Sigma and PPM are connected.---read from slide

Mumbai Dabbawallahs process is better than 6 sigma.

IRCTC online reservation system is unmatched----best online reservation system in the world. It’s a global
benchmark.

Challenge:

Improving from 75 to 95% is very easy-----the ground fruits-------------2sigma

Improving from 95 to 98% ---low hanging fruits-----------3sigma
98-99 --- -----4 and 5 sigm
99-99.7 -- ---- 6 sigma

Effort become higher as you go up the sigma. Cost increases disproportionately. That’s why most companies don’t go
for more that 4 to 5sigma.
But this is true for 80% industry only.

Medical, Aerospace, aviation etc are exceptions. There you need six sigma.

At whatever point customer is happy…that you neeed to achieve. That varies from industry to industry.

JAPAN doesn’t believe in six sigma…they believe in zero defects.

GE is most recognized and respected for Six Sigma. That too, only for 2 processes

Backoffice financing - both happen in india

Noiseless motors for washing machines -

SUNDARAM FASTNERS CHENNAI- a good example.

Six sigma has two terms- 6 and sigma

6 sigma has three wayS of interpretation:

Mathematical
Operational Useless/Can’t function without 3rd one
Management

Sigma is deviation from standards.

Sigma = standard deviations

6sigma=a measure of process performance
1 sigma- low
6 sigma- almost perfection

6sigma- a management philosophy driven by 6 key things:

1. Customer Focus- CUSTOMER IS EVERYTHING

Internal customer External Customer

6 sigma gives importance to both

The more who focus on internal customers, externa customer satisfaction just becomes the by-product.

Who’s internal customer- manufacturing persons

Means…design KPIVs such that you satisfy the requirements of persons involved in manufacturing (survey satisfies
requirements of planning person efficiently, planning satisfied requirement of design personel and so on)

2. Boundaryless collaboration- All departments working together towards the common goal of customer
satisfaction.
Support each other

3. Proactive Management – anticipate and act rather than react before problem becomes a problem

Eg:
qty of plankton doubles everyday
Pond with fill in 50 days.
Frog needs 10 days to come up with action plan

On which day must frog react.

Answer: 39th day.

4. Data Driven Decision - always base decisions on data. Not on qualitative experience.
 Dr. Demings process.
“In gods I trust, everybody else get data”
“Change is not necessary, because survival is not mandatory”

5. Stay in touch with process

Always stay in touch with ground processes. Be alert about what’s actually happening. Not just what’s being
reported.
Being interested in what you need to know, not just what you want to know.
Digression:
Fables of Managements: bird cat and cow story
Walrus story

6. Inspire perfection, tolerate failure- improvement always happens only through risks. Risks are taken when
there’s insurance against failures.

SIX SIGMA ROLES AND RESPONSIBILITIES:

CHAMPION

MASTER BLACK BELT

Teach Six Sigma
Monitor BB Projects
Work on pipeline proejcts
A resource pool

BLACK BELT: Lead 6

Project teams
Measure/Analyse
Improve/Control
Is only 6 sigma expert. Dependent on green belt person’s reporting of domain process.

GREEN BELT: Learn/Use Six sigma tools.

Work on Six Sigma Projects
Part of the Job
Is a domain expert along with 6 sigma knowledge.
That’s why green belt is so much in demand. Most critical resource!!

DEMING on processes:
 Don’t change employees. Change systems. Systems are cause of 85% defects.

TWO METHODS of SIX SIGMA

1. DMAIC - for existing processed===== design>measure>improve>control

2. DMADV - for new processes-> design>measure> deisgn>Verify

DMAIC vs DMADV
Import from study material (Smartart)

DMAIC
Define>Measure>Analyse>Improve>Control

Details in material

DEFINE: Identification of CTQ (Critical to quality)- That specific measurable attribute of the output
which is of maximum concern to the customer where we do not meet requirements.
Scope of project in order to improve that CTQ

Measure: Establish the gap in what customer wants and where we are.
Expected capability – current capability.
This gap is expressed in sigma level.
Eg. Our process is 1 sigma level. Customer expects 2.5 sigma.

Analyse: Identifying root causes due to which performance is impaired. Why we are not able to satisfy
customer expectations.
Eg: through Fish Bone, Pareto, YYY, Regression etc., correlation, scatter diagrams.

At the end of analysis, we have validated root causes.

Improve: Innovation, Breakthrough, thinking….to improve the system.

Control: Sustaining the improvements.

What’s the meaning of keeping KPIVs within standards?
Reduce the variation.

What’s data all about?

It’s the basic primary thing through which we draw any inference about a process.

To gather data, you need a data collection system/ measurement system

For that you need to have

i) a method statement:

5W 1H
Why How
What
When
Where
Who

ii) Measuring Instruments

The above two combine to form data collection system.

Process Performance:

Mean is not a good parameter to judge performance. It averages out the variance.

Std. Deviation formula

Activating Data Analysis Add in in Excel

File> Options > Add-ins >practice once

In the notebook hereafter

6 sigma is a method to achieve 3.4 defects per million.

Not that if you have achieved 3.4 defects per million, you have achieved 6 sigma

Eg. Hypothesis
Customer req. = 60hr + 6hours
LSL = 54 hours
USL = 66 hours
T = 60 hours

Suppose Sigma = 6 hours

So, between the service window desired by customers, only 68% (corress to + 1sigma) values lie.

To fit more values, try to reduce sigma (std. deviation) somehow. This way you will be able to fit more values
between upper and lower specification

*Sigma Level of a process

How many sigma you can fit within the customer desired window.
Eg. If you’re able to fit 1 std. deviation within customer , it will be 1sigma process.

As sigma Value goes down, sigma level of a process goes up

Eg. In the above example, if sigma value goes down from 6 to 3, sigma level of process rises from 1sigma to
2sigma. (Ofcourse, given that service requirement (USL-LSL) is constant, which usually is the case)

Curve becomes taller and narrower

DEFINE
Step 1 Determine the CTQs
 Identify customers- list customers, define customer segments, narrow the list to most
relevant customers
 Gather VOC- gather verbatim VOC and determine service quality issue
Surveys
Interviews
Be a customer
Focus group
Cust observation
Listening Posts
Competitive comparison
One to one meeting (most reliable since the data will be most reliable)
*this is not a customer satisfaction survey, it’s a customer dissatisfaction survey, which a customer best
articulates in a one to one meeting
*Ask standard questions- unanimously decided, common set of questions.
*Open Ended Questions, no Yes/No questions. Let the customer describe his problems. But problem
should be specific.
*Ask at a time where you are most likely to get a neutral response.
  Organise VOC

Suppose,
You have got 50 negative statements (anyway only negative reviews are to be considered)
Prioritize the problems.
Debate on Unique meaning statements, eliminate similar meaning statements –
This is achieved through affinity diagrams. (Affinity diagram belongs to family of tree diagram. It is
not a statistical tool. It’s a management tool)
In affinity diagrams-All similar meaning statements are arranged vertically in a column. Different
meaning statement arranged in different columns.

 Prioritise VOC

Generally, any DMAIC project will take only 16 weeks. In such a short span of time, you can address
hardly 2-3 CTQs at max. For each CTQs, you’ll have to make about 10-15 changes in the process.
So, draw an affinity diagram for one VOC, derive multiple CTQs, prioritize top CTQs to be addressed,
and then make changes to address those selected CTQs

Reduce the scope of the changes, but don’t increase the duration of DMAIC project. Because, if you
increase the time, the sustainability of interest goes away. Efforts become futile.

 Translates VOC

KANO MODEL

Refer Material (Chart)

Put the CTQs into Kano Model- Categorize them as Delighters, Competetive priority, Must-Be’s.
Prioritize Must Be’s.
There are various must be’s generally-(page 33, lower end of study material)
Step 2 Define the project

Charles Darwin- “A problem well defines is a problem half solved”

While defining the project (i.e the addressing of CTQs), 5 questions need to be answered

 What is the pain felt by the customer?

 Is the problem chronic (consistent and persistent)- should have been going on for at least last 6
months?
 How will it benefit the organization by addressing the CTQ?
*Every action to improve CTQ must be profitable for the firm (in the long run, factoring in the gains due
to improved quality)

 How big is the pain?

 Where is the pain process? (DMAIC is for process driven problems, not for even driven
Step 3 Charter
 Business Case
 Problem and goal statement
 Project scope
 Milestones
 Roles and Responsibility

Refer to study material for template of a charter

It is a Complete formalization of scope of the project:

Scope
Purpose- in terms of process improvement and financial gains
Roles and responsibilities
Timelines

Defines the project

What to include and what to exclude
Existing Sigma level and target sigma level

While drafting the problem statement:

Within the first one-two lines, bring out the chronic nature of the problem (since when) and how big
(number/metric) the problem is!

Things that should not be in a problem statement:

 Cause of the problem. (It should be addressed by Root cause analysis, not DMAIC. DMAIC is
only for problems with unknown causes)
Digression
RCA
JDI (Just do it projects)
DMAIC (for unknown causes)
Step 4 Map the process

Tool which we use for mapping the process is known as SIPOC- refer to page 57 of study material.
SIPOC- Supplier- Inputs-Process-Output-Customers
Read Page 57 to 67

Supplie Inputs Process Output Customer

r (actions/ Verbs)
Start with the step that is delivering the pain. Do
backtracking upto a point where the link is no more
relevant to the CTQ.

Should have 4-7 steps/ links.

<4 too narrow scope

 Snake diagram CTQ
NO Signal
Output of step 1 becomes input for step 2 (a
measurable
Eg. parameter)

Step 1: Enable Wifi in laptop

Step 2: Connect to wifi
Step 3: Activate Internet application
Step 4: High Buffering time

DMAIC addresses the biggest problem- the resistance to change by involving people who are part of change making
process, to implement the change.

In the meeting, 5Ws and 1H must be decided for each of the five points under Charter.
Every decision must be unanimous. Each ‘NO’ from a panelist of the team means exclusion of one whole department

Separate Topic:

SIG SIGMA IS EXECUTED BY A TEAM OF CROSS FUNCTIONAL Individuals

Problem: whenever a customer need is not satisfied.

When does a problem gets qualified to be solved through DMAIC

 Problem has to be cross functional-
CUSTOMER

Organisation
Working for vertical growth
Eg: Revenue, Market Share etc.
Sales Planning Purchase Ops Logistics Customer
Goals: Resources cost down Optimize Cycle time
revenue up down resources reduction
 Work across departments to satisfy the end customer

Problems arise at boundaries of two departments (blame game). Cross functional people are required to
douse that fire.
All stakeholders must be involved in problem solving. End to End representation is very important. Otherwise
solution for one dept. will become problem for another dept.

HOD needs to select right functions for cross functional teams

Representatives should be right persons. Should be a decision maker. Should be respected by peers. Should
not be a fence sitter. Should be self-motivated. Should believe in change. Should believe in doing something
extra.
 SKILL
ATTITUDE CYNIC (positive skill, negative attitude) STARS (Positive Skills, Positive Attitude)
(mostly ‘On call members’ Only 20% in an organisation
‘bought’ in
an
organisation, DINOSAURS (Negative Skill, Negative Attitude) RATS(Negative Skill, positive attitude)
not inspired
after an age
of a person

Ideal Six Sigma team should have a few stars (40%) and a lot of rats.(60%)
Rats are future stars!
Eg. Of Hospital (nurse, ward boy, pharmacy)

 Has to be chronic in nature, not sporadic

 Without any known solutions

Session 2 - 12th August 2017, Saturday

Detailed Process Mapping

Every process has two type of activities-

 Value added activity - any activity in the process for which the customer is willing to pay for.
Eg. Procurement of raw material - value added
Storage of Raw material -non-value added
Logistics, warehousing -non value added
Maintenance downtime -non value added
 Non value added activity-
 Value Enabling Activities

In process mapping, we bifurcate the two types of activities.

Digression

In a flowchart, put only 1 activity in 1 rectangle.

In six sigma DMAIC, we do matrix flowcharting, not linear flowcharting

Each row is called a SWIMLANE

Customer

Sales

Planning
Matrix flowchart is much more useful in visualization

Which activity is going on in which department. Where the work is getting transferred from one department to
other.

Generally misunderstanding/ bottlenecks happen at the interface of two departments (Internal customer
dissatisfaction)

In value stream mapping, we identify from the flowchart which activity is value added and which is non-value added.

Every decision activity (depicted by diamond in a flowchart) Is a non-value added. (They add delay to the process)

Start with an assumption that every activity is non-value added. Then try to disprove the assumption. If not able to
disprove, try to eliminate as much as possible.

Value Enabling activity: Which are non-value added, but they are essential. Eg.HR, Finance.
Any multiple reviews of docs, rework, holding, delay etc. are non-value adding.
Eg of improvements in industry: Mother godown models have been replaced by Hub and Spoke models.

Value added: make them more effective (do them right) Do not take any ad-hoc action
Value enabling: minimize their cost right now. Do in the Improve stage
No value added: minimize, if not eliminate of DMAIC

For Every Value-added activity

 Process time = PT (time taken to actually do the process)
 Lead Time/Cycle Time = LT or CT (time taken from input to output, including unproductive time)

Efficiency = PT/LT
Ideal Value = 1

For Every Value Enabling

Reduce cost. ‘Do more with less’.
MEASURE
Understand what is our baseline capability of a CTQ to meet the customer requirement. This is measured in terms of
Sigma Level. (i.e what %age of CTQ is meeting the customer requirement)

Two types of data:

 Continuous or Variable (Measurement of some parameter on a defined scale, Eg.25 degree centigrade)
 Discrete or Attribute (Count data, either satisfied or not satisfied, what is being measure is itself the unit of
measurement, Eg.25 Students)

Generally, attribute data is weak for statistical analysis. It has very less predictive capability.

Exercise:
Identify the type of data
 Amount of time taken to respond to call: continuous
 No. of blemishes per sq yard attribute
 Daily test of water acidity Continuous
 Length of screws in a sample continuous
 No. of employees who had accident attribute

Whenever collecting data, make a good data collection plan. Define meaning of each term eg…duration of a working
day, meaning of holiday etc.

Sampling (refer definitions from study material also)

 Random (generally used when the population is homogenous, when there is no suspicion of any kind of bias-
location bias, time bias, operator bias)
 Stratified (when there is heterogenous population. We convert heterogenous population into homogenous
strata and then do random sampling on each stratum)
 Sequential (ideally, it is just a part of stratified sampling)- involves set of continuous pieces.
Eg, whenever there is a changeover in the assembly line, we do sequential sampling to check whether the
product has stabilized or not)

How do you calculate sample size?

For Variable Data

Sample size = n
(Thumb rule: every 10 out of thousand,
 Also, if Zalpha/2 = 1.96, which is the critical value for 95% confidence, we calculate sample size by

n = [(Zα/2.sigma)/ delta]2

where delta is precision (generally taken to be 98%)

Mean = x

For dicrete data

n = [zalpha/2/delta]2 x p(1-p)

but generally, these equations are seldom used. Mostly, we’ll decide sample size based on experience. As six
sigma professionals we do not challenge experience

In six sigma, we’ll focus on usage of statistics….not ‘why’ of statistics.

Tools for data variation

1. Line graph/ Trend Chart - for variable data/ continuous data

2. Bar Graph - attribute
3. PIE- - % data

Whenever we have a normal distribution, we use mean

When we don’t have normal distribution i.e when we have skewed data, we use median
When we have ordinal data, or ordered data, or ranked data….we use mode

(Eg. When a set of people rate a service, we use mode to guage the general perception, not the mean or media.
Mode gives the most popular rating)

Whenever using any survey…whenever using a rating….use less no. of nodes. Eg…while desiring results from 1 to
10….do not use 1, 2,3 4….10 as options…..Use only 1, 5, 9. Then the results will be more useful to analyse. It’s kind of
decisive)

How to know whether our data is normal or skewed, here minitab comes handy
If you don’t have minitab, calculate mean and median both. If median is withing 20% deviation from mean value (it is
close to a normal distribution), use mean, otherwise use median)
Test 1: Test for normality
Whether my data is normal

Step 1: Open the sample data preloaded file

Step 2: Stat>Normality Test> Double click the file > Anderson Darling Test> OK

Step 3: this appears

Step 4: We have critical p value as 0.05 (opposite of alpha)

If P value > 0.05, the data is normal. In our example P value is 0.970, so the data is normal.

Read about confidence interval and natural variation

Eg.
Suppose for a process
Mean = 65
CI = 65+ - 0.59
 If we were to actually improve the data, we’ll have to exceed this CI.
Digression

(Input for succeeding process based on output of preceding process

EXAMPLE:

I will set the conveyor speed of my assembly line based on speed at which glass bottles are being made.
Say 65 pieces per hour
But 5% time, this will not be the case…may be outliers.
If the outliers are greater than 5%, then there is a problem.

Therefore, 5% of data will always NOT be following those guidelines.)

Risk = 0.05
This helps calculating ‘z’…. which has a fixed value for corresponding value for confidence level.

For risk = 0.05 or confidence level of 95%, we have z=1.96

Therefore, P value decides whether data is normal or not normal.

Testing of assumptions
Hypothesis testing
 Null hypothesis (Probability of achieving null hypothesis is 0.05)
What I am ‘claiming’.

 Alternate hypothesis
That

If P value is high, NULL is true.

In normality testing, we want to ‘fail’ to reject the ‘null’

We either reject the null or fail to reject the null (not ‘accept’ the null).

If P>0.05, we fail to reject then Null

If P<0.05, we reject the null.
Test 2: Spread/ Distribution

To test spread, we use histogram. Taller the histogram, lesser the spread. Wider the histogram, higher the
spread.

CASE:

Customer Specification
USL = 90
LSL = 60 75 +-15
Target = 75

Available data
X bar = 72
Sigma = 6

Therefore, on lower side, our process is 2 (4-5) sigma whereas on higher side, it is just 3 (6) sigma.

We observe, there is a gap of 3 b/w 72 (actual mean) and 75 (Customer specs).

To improve the process, I’ll have to shift the mean as well as decrease the std. deviation.

As per SPC, the natural spread of a process is +- 3 sigma.

By observing the output of our process and the desired customer specification, we decide whether we need
to treat the mean or the standard deviation or both.

To treat the mean, correct the ‘what’

To treat the std. deviation, correct ‘how’

Test 3: Stability (whether all individual values are within the control limits i.e + - 3sigma limits)

We use control charts.

Only a stable process can be a capable process.
Cycle Time = Process Time + Lead Time
To reduce the cycle time, break down the entire cycle into smaller parts, and then analyze which part has
higher variation. (found out using histogram). Try to treat that part of the process where there is high
variation (flatter histogram)

BOX PLOT:

Refer Study Material

Inter Quartile Range

For a single process variation analysis, use histogram

For a multiple process comparative analysis, use box plot

Use Carpet File in Minitab to plot group box plot

Whether a process is capable or not”

Process Capability , Cp = (USL-LSL)/ 6sigma

If Cp> 1 , process is highly capable
If Cp =1 , process is just capable
If Cp < 1, process is incapable
But ther’s a catch, Cp equal to 1 when numerator is qual to denominator even when the entire data is
skewed to either left or right.

So formula evolved to

Cpkupper, Cpu = (USL -Xbar)/3sigma Lesser of the to is Cpk minimum or

Cpklower, Cpl = (Xbar-LSL)/3sigma Cpk reported

Derived from above formula

3Cpk = (USL- Xbar)/Sigma

Z= (USL- Xbar)/Sigma

Means how many std. deviations we have between mean and upper service level. (that is nothing but the
sigma level of the process)

Difference between Cpk and Ppk

Sometimes we group values in groups of 5, 10,1 5 or say any number.

Then we calculate mean of each group.
Then we form a data set of means of various groups. Then we analyze the data

If you’re considering the average of averages, the it is called Cpk

If you’re considering all individual data, it’s Ppk

Therefore, Cpk is for sample, Ppk is for population.

Multiply Cpk with 3, You get sigma level

For Attribute Data

Step 1: check whether data is reliable. For this we use MSA (Measurement System
Analysis). It helps us keep the error variation to the minimum.
Whenever there is visual inspection,

Overall Variation has two components

 Part to Part Variation
 Measurement System Variation (It further has two components) Should not be more than
30% of Overall variation.

Ideal- not more than 10%

of total variation
 o Reproducibilty
o Repeatability (It further has two components)
 Guage Reproducibility
 Operator reproducibility

Defects (total no. of defects in a sample, where each object can have multiple defects also) vs Defective (how
many defective pieces are there in a sample, with an object with multiple defect counted only once)
Poisson (used for defects) vs Binomial (used for defective)

Repeatability - when a single operator is able to repeat his reading for the same part measured more than
once, he is repeatable. Otherwise, there is error of repeatability

Reproducability - Different values for different operator. Error of reproducibility.

Error is high, percentage of Measurement system error is high in overall variation.

Guage reproducibility: Same measuring instrument reporting different values for different observations.

When data type is defective, we take AAA (Attribute Agreement Analysis) (stats>quality>attribute agreement
analysis)
Understand the interpretation of kappa

Whenever there is low kappa score for an operator (lower than 0.9)
Find if his repeatability is low
If yes, train the operator

Otherwise
Find if his reproducibility is low,
If yes, make changes in the measurement system

Whenever the Overall kappa score is low (lower than 0.9), entire measurement system is to be scrapped)

WHEN WE USE Defect Data……

Guage Repeatability and reproducibility (GAGE R&R)

File name: tHICKNESS

sTATS> qUALITY>GAGE STUDY>GAGE R&R

check if Gage R&R contribution is less than 10% (displayed in log)

If not,

Check study variation to be <30%. (displayed in log)

Wherever human intervention is there in recording the measurement and humans are reporting a value, Gage R&R is
required.

Defective = DPU = (No. of Defects)/ No. of Samples inspected

Defects = DPU x 10^6 = PPM

Defectives:
P= (No. of Defectives)/No. of Samples Inspected
DPU = 20/200 = 0.1

PPM = DPU x 10^6 =100000

Corresponding Sigma level = 2.7 (Using sigma tables)
DPO (Defects per opportunity) = No of Defects/ (No. of Samples x opportunities per unit)
= 20/(200 x 5) = 0.02

DPMO (defects per million opportunities) = DPO x 10^6 = 0.02 x 10^6 = 20000
Sigma level = 3.5