Six Sigma Mbb

Front 1

Standard Deviation for a Population

Back 1

Written as sigma

Square root of the variance for a population:

square root of (sum of the variances from the mean squared)/ the number of items in the population

Front 2

Standard deviation for a sample

Back 2

Written as S

Square root of the variance for a sample: square root of (sum of the variances from the mean squared)/ the number of items in the sample minus 1

Front 3

Mean for a population

Back 3

Written as u

average of values in the population

Front 4

Mean for a sample

Back 4

written as x bar

averagare of values in the sample

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1 sigma

Back 5

68% of all observations

Front 6

2 sigma

Back 6

95% of all observations

Front 7

3 sigma

Back 7

99.7% of all observations

Front 8

Six Sigma

Back 8

Management philosophy

3.4 defects per million opportunities

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Opportunity

Back 9

Every chance to meet a customer’s requirement

Front 10

Defect

Back 10

When a CTQ fails to meet a customer’s requirement

Front 11

Defective

Back 11

A unit has one or more defects

Front 12

Throughput Yield

Back 12

of units processes correctly the “first time” (first pass yield through each step)

Front 13

TPY

Back 13

number units processed correctly the first time/
number of units

Front 14

Attribute Data

Back 14

always ends up in counts or frequencies

Hint 14

Nominal (no order or value of data; categories by name or location)

Ordinal(by order; A,B,C,D; 1,2,3,4)

Count(# of occurrences; integer values only)

Front 15

Measurement Data

Back 15

on a continuous scale (infinitely divisible)

Front 16

KANO Model

Back 16

Attractive
One Way
Must Be’s

Front 17

2 branches of statistics

Back 17

Descriptive; Inferential

Front 18

Inferential

Back 18

Statistics are calculated from sample data to draw conclusions (infer) about the population parameters

Front 19

Descriptive

Back 19

Describes a data set
-Average of a data set
-Median of a data set
-Variation of a data set
-Shape of a data set

Front 20

2 types of statistical studies

Back 20

Enumerative; Analytic

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Enumerative

Back 21

-Used to draw conclusions about a population value or parameter
-Simpler type of study
-Finds out the “what”
-(example: What is the percentage of invoices paid on time?)

Front 22

Analytic

Back 22

-Used to study the cause and effect relationships
-Intent is to improve or influence future results
-Finds the “why” behind the “what”
-(example: Are late payments on invoices caused by the vendor?)

Front 23

Non-probability Sample

Back 23

Samples “not” selected from frame

Probability of being selected is “not” known

Subject to bias

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Probability Sample

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Samples selected from frame

Have known probability of being selected

Preferred method

Front 25

Probability Sample Methods

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Simple Random; Stratified Random; Systematic; Cluster

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Simple Random

Back 26

Probability Sample Methods

Random numbers used to select items from the frame

Most basic type of sampling

Every item in the frame has the same probability of being selected

Front 27

Stratified Random

Back 27

Probability Sample Methods

Items in frame grouped by some classification criteria

Simple random sample from these strata

Every item in the strata has the same probability of being selected

Front 28

Systematic

Back 28

Probability Sample Methods

Random sample from the first k items

Select ever kth item in the frame for sampling

Front 29

Cluster

Back 29

Probability Sample Methods

Frame is divided into naturally occurring clusters or groups

Clusters are then randomly sampled

Front 30

Measures of Central Tendency

Back 30

Mean; Median; Mode

Front 31

Positive Skew

Back 31

Mean higher (to the right) than median

(It’s Skew-ished down on the right)

Front 32

Negative Skew

Back 32

Mean lower (to the left) than the median

(It’s Skew-ished down on the left)

Front 33

Z Transform

Back 33

used to convert a point on any “normal distribution” to it’s corresponding point on a “Standard Normal Distribution”

Z = (POI - u)/sigma

Front 34

Measures of Variation

Back 34

Range; Variance; Standard Deviation

Front 35

Spec Limits set by

Back 35

Customer

Front 36

Control Limits set by

Back 36

Process

Front 37

Attribute Control Charts

Back 37

Defectives:
P Chart (use any time) (good or bad)
NP Chart (constant sample size)

Defects
C Charts (constant area of opportunity)
U Chart (use any time)

Remember “C-U” is “count you”
counting number of defects

Front 38

Variable Control Charts

Back 38

X-bar-R: subgroup size > 1 and < 10
trends average values (X-bar)and range (R) of the subgroup)

X-bar-S (subgroup size > 10) trends standard deviation (S) of the subgroup

I-MR (subgroup size = 1)
Trends individual observations (I) and the moving range (MR))

Front 39

Alpha Risk

Back 39

(α) (Reject the null hypothesis and it was correct / true)(Should not have rejected)
-Type I Error (Producer Risk)
-CI = 1 – α

Front 40

Beta Risk

Back 40

β) (Fail to reject null hypothesis and it was wrong / false)(Should have rejected)
-Type II Error (Consumers Risk)

Front 41

Null Hypothesis

Back 41

(Ho) (always contains a statement of equality)

Front 42

Alternate Hypothesis

Back 42

(Ha) (opposite of the null; inequality)

Front 43

P-value

Back 43

the actual risk of rejecting the null hypothesis, when the null is actually true

Front 44

Alpha Risk

Back 44

is the risk we are willing to take
-If P-value is < alpha, we reject the null

Front 45

1 Proportion Test

Back 45

compare proportion –vs- target

Front 46

2 Proportion Test

Back 46

compare proportion of one sample –vs- proportion of another sample

Front 47

Chi Square Test

Back 47

compare multiple proportions

Hint 47

-Goodness of Fit (observed –vs- expected) (use Excel software, not Minitab)
-Test for Association (determine if one variable depends on another variable)

Front 48

Proportion Tests

Back 48

1 proportion, 2 proportion, chi-square

Front 49

Means testing

Back 49

1 Sample -T test; 2 Sample -T test; Paired -T test; ANOVA Test

Front 50

1 Sample -T test

Back 50

compare mean –vs- target) (population)

Front 51

2 Sample -T test

Back 51

compare mean –vs- mean) (population)

Front 52

Paired -T test

Back 52

compare mean difference between “paired” observations)

-Sample size must be the same
-Same observation (paired); same part or device
-Looking at the difference between two observations; then comparing the difference to a target (usually a difference of zero), which is basically a 1 Sample-T

Front 53

ANOVA Test

Back 53

(ANalysis Of VAriation)(comparing multiple means)

(Comparing variance of means of more than 2 groups)
-Within Group Variation (caused by random error)
-Between Group Variation (caused by the factor itself)
-One Way ANOVA (stacked or unstacked)(one factor)
-Independent (use ANOVA graphs – individual plots)
-Normally distributed (use graphical summary)
-Equal variance (use test for equal variances)

Front 54

Variance Testing

Back 54

2 Variance Test; 1 Variance Test; Test for Equal Variance

Front 55

2 Variance Test

Back 55

(compare variance –vs- variance)
-F test (for normal distribution; more sensitive test)
-Want to perform normality test for each sample first (individually); don’t group them t together; will determine if you use the F test or Levene’s test
-Levene’s Test (for any continuous distribution)

Front 56

1 Variance Test

Back 56

compare variance –vs- target)
-No Minitab command for 1 Variance testing

-Use Confidence Interval (CI) and use Std. Dev. in Graphical Summary to see if CI contains the target value (fail to reject null)

Front 57

Test for Equal Variance

Back 57

comparing 3 or more groups)
-Bartlett’s Test (for normal distribution; more sensitive test)
-Levene’s Test (for any distribution)

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Correlation test

Back 58

(tests only for a linear relationship)
- Measures the strength and direction of a linear association between two variables.

- Sample correlation coefficient (r) – (Pearson Coefficient) – the measure of correlation
- Population correlation coefficient (ρ) (we infer the population from the sample)

- Positive r – both variables tend to increase or decrease together [Strong Positive (+1)]
- Negative r – as one variable increases, the other variable decreases [Strong Negative (-1)]
- No Correlation (0) (only looking at linear relationship)

Always Utilize Scatter Plot to visualize correlations

Front 59

Regression

Back 59

Purpose – measures the strength of association between independent factors(s) and a dependent variable.

-Can be used to develop a predictive model for relationships based on observations

Regression can identify curvilinear relationships
-Quadratic (curvature exists)
-Cubic

Front 60

R2

Back 60

percentage (%) of the total variation (Y) explained by the model (interaction of factors)

Front 61

R2 (adj)

Back 61

used to compare models with a different number of terms

Front 62

If problem refers to Means

Back 62

a inference test or a T- Test is used

Front 63

Problems refers to Difference between a sample mean and target value

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one –sample T-test

Front 64

Before and after differences of means between paired

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paired T- Test

Front 65

If problem talks about the variance differences between continuous data

Back 65

a variance test is required to test hypo

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When 2 samples are compared against one another

Back 66

two sample test is used

Front 67

When a sample is tested against a target

Back 67

a one variance test is used

Front 68

If the problem talks about testing for equal variances

Back 68

A test for equal variance is used