Ever wondered if you had a list of Quality Tools and Formulas handy while on a Black Belt Project? You know all of them, just remembering the ones applicable in current phase is the key. Here is a list of Quality Tools and Formulas with Phase-vise applicability. Please note, this is only a list with their applicability Phase-vise. If you want any assistance, help, details on any of these, please ask@sevensolutions.in.

1. Quality Tools List
Date: 16/Apr/2012
Author: K. S. Alok Ranjan
About: List of tools, methodologies and formulas
used in Quality Improvement methodologies in Six
Sigma. For any enquiry, please
ask@sevensolutions.in or call +91 7503 03 3057

2. DMAIC BB Tools, Methodologies and Formulas Apr-2012
List of Phases involved in DMAIC BB approach with Tools and Methodologies used
1. Define Phase:
a. VOC – Voice of the Customer (Exploring customer CTQ)
b. QFD Diagram– Quality Function Deployment Diagram
c. CQT Drill Down Tree – Critical to Quality Drill Down Tree
d. KANO Diagram
e. Brainstorming and Multi Voting
f. Inside-Outside
g. Theme Selection Matrix
h. Scoping
i. Team Charter
2. Measure Phase:
a. SIPOC Model – Suppliers, Input, Process, Output, Customer Model
b. Process Mapping
c. Cross Functional Process Mapping
d. VOC – Voice of the Customer (Defining Specification and Defect)
e. Data Types – Understanding Data Characteristics
f. Sampling Techniques
i. Random/Probability
1st. Simple Random
2nd. Systematic
3rd. Stratified
4th. Clustered
ii. Non Random/Judgement
g. Gauge RnR
i. ANOVA-GRR – Analysis of Variance-Gauge Repeatability and Reproducibility
ii. Continuous GRR
iii. Attribute GRR
iv. Destructive GRR
h. Test/Retest
i. Calibration
j. X Bar-R Chart
3. Analysis Phase:
a. DPMO Worksheet
b. Sampling
c. Central Limit Theorem
d. Normal Distribution (Normality) Test
e. Run Chart
f. Scatterplot
g. Curve Fitting
h. Homogeneity of Variance
i. Estimates
j. Confidence Intervals
k. t-distribution
l. Benchmarking
m. Hypothesis Testing
n. Discreet Probability
o. t-Test – Statistical Hypothesis test
p. f-Test – Any Statistical test where test statistic has an F-Distribution under the Null Hypothesis.
q. Poisson Probability Distribution
r. Binomial Probability Distribution
s. Chi-Square test
t. ANOVA – Analysis of Variance (1,2,3,4... Way)
u. Multi Voting
v. Fishbone
w. Pareto Chart
x. Correlation
y. Regression Analysis (Simple & Multiple)
z. FMEA – Failure Mode and Effects Analysis
aa. Continuous Zst, Zlt
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3. DMAIC BB Tools, Methodologies and Formulas Apr-2012
bb. Discreet Zst, Zlt
cc. GLM
4. Improve Phase:
a. Screening DOE – Screening Design of Experiment
b. Optimization DOE – Optimization Design of Experiment (2 level Ascent/Descent & Simplex)
c. 3 level CCD/CCF
d. EVOP – Evolutionary Operations
e. TPC Analysis – Technical, Political and Cultural Resistance Analysis
5. Control Phase:
a. ANOVA-GRR – Analysis of Variance-Gauge Repeatability and Reproducibility
b. X Bar-R Chart
c. Acceptance Sampling
d. Mistake Proofing
e. Control Charts
Formulas and Calculations
a. Sample Mean: Arithmetic average of all Data Points in a data set
– Data Point
– Mean
n – Number of Samples
b. Population Mean: Arithmetic average of all Data Points in a data set
– Data Point
– Mean
N – Number of Data points
c. Mode: Most frequently occurring data point in a set
d. Median: Middlemost data point in a odd numbered data set of of two middlemost data point in an even numbered
data set.
e. Range: Difference between the maximum and minimum data point.
f. Sample Variance: Measure of Spread. It gives an idea of how widely spread the values of the random variable are
likely to be; the larger the variance, the more scattered the observations on average.
- Variance,
– Mean
n – Number of Data points
g. Population Variance: Measure of Spread. It gives an idea of how widely spread the values of the random variable
are likely to be; the larger the variance, the more scattered the observations on average.
- Variance,
– Mean
N – Number of Data points
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4. DMAIC BB Tools, Methodologies and Formulas Apr-2012
h. Sample Standard Deviation: Measure of the Spread. Dispersion of the Data
s – Standard deviation
– Variance
i. Population Standard Deviation: Measure of the Spread. Dispersion of the Data
– Population Standard Deviation
– Variance
j. Sample Size Formula for Continuous Data Population:
n – Number of Samples
Z – Calculated field of .
For 0.05 it would be Z97.5 which is 1.96 and for 0.01 it would be Z99.5 which is 2.58. [Need to understand
this bit more]
– Representation error allowed in the example. 0.05 (5%) or 0.01 (1%)
– Population Standard Deviation
- Interval of Error allowed for the Population Mean. E.g. (So is 5) or (So is 2) etc.
k. Sample Size Formula for Discreet Data Population:
n – Number of Samples
Z – Calculated field of .
For 0.05 it would be Z97.5 which is 1.96 and for 0.01 it would be Z99.5 which is 2.58. Thumb rule until I do
some RnD on net and find out.
– Representation error allowed in the example. 0.05 (5%) or 0.01 (1%)
– Average Population Proportion Non Defective
= [Need to understand this bit more]
- Interval of Error allowed for the Population Mean. E.g. (So is 5) or (So is 2) etc.
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