Six Sigma Green Belt

six sigma

a customer focused, well defined problem solving methodology

For Six Sigma to be Effective

1. There must be a process in place;
2. The process must be brought into control statistically;
3. The processes must be improved (by reducing variation within the controlled processes and bringing them closer to the target)

DMAIIC

Define, Measure, Analyze, Improve, Implement, and Control

W. Edwards Deming

Special vs. common cause variation
The 14 points

profound knowledge

knowledge of systems, knowledge of statistics, knowledge of psychology, knowledge of knowledge

knowledge of systems

1. A system is a network of interdependent components that work together to try to accomplish an aim;
2. Systems are management's responsibility;
3. Management's job is to optimize the entire system over time

variation

use statistics to show patterns and types of variation, distinguish between special and common causes of variation

Psychology

need to tap into intrinsic motivation, build trust

knowledge of knowledge

Rational prediction requires theory and we build knowledge through systematic revision and comparison of theory based on comparison of prediction with observation

types of variation

common cause and special cause

common cause

Causes of variation that are inherent in a process over time. They affect every outcome of the process and everyone working in the process.

special cause

A cause that occurs once because of special reasons.

solutions to special causes

prevent, contingency plan

solutions to common causes

fix the system

stable process

normal variation; predictable, in control, have known process capability

Basic Theorem of Variation

If you always do what you've always done, you'll always get what you've always got

Corollary to the Basic Theorem of Variation

insanity is doing something over and over again and expecting a different result

process monitoring

must know central location, spread, shape, relationship of variation to time

location

process centered, process requirement

spread

observed, specifications

histogram

a graphical representation of data in a bar chart format

central location

mean, median, mode

variability

range and standard deviation

shape

skewness and kurtosis

x-bar

sample mean

µ

population mean

use median or mode

shape of distribution is not symmetrical

use mean

shape of distribution is symmetrical

range (R)

highest value - lowest value

standard deviation (s or σ)

√(∑(xi - x-bar)^2)/(n-1)

within + or - 1 σ

68% of values

within + or - 2 σ

95.5% of values

within + or - 3 σ

99.73% of values

expected limits of common cause variation

+ or - 3 σ

customer requirements are

6 σ from the mean in either direction

Grand average ( X- double bar)

the process average; the average of the sample averages

average range (R-bar)

average of the sample ranges

normal distribution

a bell-shaped curve, describing the spread of a characteristic throughout a population

minimum

lowest data point excluding outliers

maximum

largest data point excluding outliers

first quartile

the median of the lower half of the data set

third quartile

the median of the upper half of the data set

second quartile

median

Interquartile Range (IQR)

Q3-Q1

Minimum equation

Q1 - 1.5*IQR

Maximum equation

Q3 + 1.5*IQR

process monitoring is

performed to determine the type and amount of variation that is present in a process as time goes by

control charts

shows amount and type of variation present; describes the representative nature of a stable, predictable process

Upper Control Limit (UCL)

The largest value a subgroup average can take on in a control chart without causing the process to be called out of control

Lower Control Limit (LCL)

The smallest value a subgroup average can take on in a control chart without causing the process to be called out of control

Center Line (CL)

average measurement data

Upper Specification Limit (USL)

the largest outcome value that does not trigger a defective unit

Lower Specification Limit (LSL)

the smallest outcome value that does not trigger a defective unit

Nominal

the target value

control limits

The area composed of three standard deviations on either side of the centerline or mean of a normal distribution of data plotted on a control chart, which reflects the expected variation in the data. See also specification limits.

Specification Limits

range of variation that is considered acceptable by the designer or customer

constructing an x-bar and R chart

1. Identify characteristic, measurement method, and sampling scheme
2. Record data (time)
3. Calculate x-bar, R, x-double bar, and R-bar
4. If stable, calculate limits
5. Calculate control limits
6. Construct control charts
7. Plot initial data points
8. Interpret chart with respect to variation

UCL x-bar\=

x-double bar + A2*R-bar

LCL x-bar\=

x-double bar - A2*R-bar

UCLR\=

D4*R-bar

LCLR\=

D3*R-bar

Shewhart Constants

A2, A3, d2, D3, D4, B3, B4

out of control checks

1. Is the shape of the histogram what was expected?
2. Are all the sample averages between the control limits for averages?
3. Are all the sample ranges between the control limit for ranges?
4. Is the pattern of variation as time goes by random? (Western Electric Rules); passing these means there are no special cause variations

steps to drawing a control chart

1. Set sample identification
2. Set scales on averages and ranges charts to include control limits
3. Draw UCL, LCL, and Grand Average on x-bar chart
4. Draw UCL, LCL, and R-bar on R chart
5. Plot initial averages and ranges on the respective charts
6. Connect the dots and evaluate the pattern of variation

Constructing the IMR chart

1. Determine characteristic and sampling scheme
2. Record data
3. Calculate moving range
4. Calculate x-bar and MR-bar
5. Construct histogram
6. Use n \= 2
7. Calculate control limits
8. Construct control chart
9. Graph initial points
10. Assess variation
11. Prioritize for improvement project

Moving range (MR)

Difference between two consecutive points

UCLx\=

x-bar + 3MR-bar/d2

LCLx\=

x-bar - 3MR-bar/d2

UCLMR\=

D4*MR-bar

LCLMR\=

D3*MR-bar

P charts

track the proportion of defectives in sample

p chart methodology

1. Determine the characteristic to measure
2. Evaluate the data
3. Calculate the proportion defective in each sample, p
4. Calculate the average proportion defective
5. Calculate control limits
6. Construct the control chart
7. Graph the initial points
8. Evaluate and prioritize

UCLp\=

p-bar + 3√(p-bar - p-bar^2)/n

LCLp\=

p-bar - 3√(p-bar - p-bar^2)/n

Out of control checks p chart

1. A single calculated value of p above or below the control limit
2. Pattern of variation

Out of Control Charts

not stable, special because variation is present, stop and identify special cause

Western Electric conditions

1. single point out of limits
2. adjustment
3. Reduction in variability
4. 2 or 3 Consecutive points near one control limit
5. Run
6. Cycle
7. Trend

Western Electric Rules

indicate that the process is out of control

Single Point Out of Limits

point outside of UCL or LCL

Adjustment

two data points do something unnatural and it ripples through the chart

Reduction of Variability

funnel effect of data points

2 or 3 consecutive points near one control limit

what it sounds like

Run

7 or more consecutive increasing or decreasing points; 7 or more consecutive points one one side of the centerline

Cycle

the trendline cycles around the centerline

Trend

direction of change of a behavior or behaviors

process capability definition

the measured inherent reproducibility of the product turned out by the process; defines limits

Process Capability

the combination of people, machines, methods, materials, and measurements to produce a product or service

Measuring Process Capability

can be measured only if all special causes have been eliminated

components of process capability

design specifications, centering of natural variation, range or spread of variation

short term capability

show the capability at a specific instance in time

long term capability

show the expected capability of the process based on statistical projections using inherent process variability

histogram and control chart

must be performed before calculating any process capability measures

Percent Non-Conforming

reflects the proportion of the population that we normally expect not to meet the process specifications; tail areas of normal curve

zu\=

|USL - x-double bar|/σ

zl\=

|LSL - x-double bar|/σ

σ'\=

R-bar/d2 or MR-bar/d2

DPMO (defects per million opportunities)

A metric used to describe the variability of a process.

DPMO formula

Defects per million opportunities \= (\# of defects / \# of units*\# of opportunities for defects )*1,000,000

Sigma level

smaller of the two z values if they are different

Percent Non-Conforming formula

total of tail proportions