Lean Six Sigma Final

Statistics and Six Sigma

What is the difference between a population and a sample?

Population: A collection of samples you could take, entire set.

Sample: A subset of the population that is selected for analysis

In practice, which is better to use, a population or a sample?

In practice, using a sample is almost always better than using a population because it is more time-efficient, cost-effective, and practical for large groups

What is the definition of nominal, ordinal, interval, and ratio data? What is the difference?

Nominal - Categorical, no order, no numerical value. EX: Marital status, eye color, country of origin.

Ordinal - Categorical, meaningful order, but unequal spacing between values. EX: Race results (1st, 2nd, 3rd), customer satisfaction (poor, good, excellent).

EX: Interval - Quantitative, order, equal spacing between values, no true zero Temperature in Celsius or Fahrenheit, IQ scores.

EX: Ratio - Quantitative, order, equal spacing, and a true zero point Height, weight, age, time, Kelvin temperature.

What do you call terms like mean, median, and mode? What do they show you, and how do you calculate them?

They are measures of central tendency for approximately the middle.

Mean - Represents the average value. Add up all the values in the data set and divide by the number of values

Median - Shows the middle point of the data, which can be more useful than the mean for data with extreme values (outliers) because it is not affected by them. Middle number or average of two middle numbers. 

Mode - Most common number in a dataset. A data set can have one mode, multiple modes, or no mode at all.

The 50th percentile represents what measure of central tendency?

Median

_% of the data falls between 3 standard deviations from the mean?

99.7%

What is the difference between mean and standard deviation?

The mean is a measure of the central tendency or average of a dataset, while the standard deviation is a measure of the dispersion or spread of the data around that average.

How do you calculate variance of a dataset?

• Find the mean (μ).

• Subtract the mean from each value → deviations.

• Square each deviation.

• Add the squared deviations.

• Divide by N (total number of values)

Alternatively, it is simply the standard deviation squared.

Discrete vs Continuous Data

Discrete = countable, separate values

• Number of students

• Number of cars

• Shoe sizes (even though they include decimals, they come in fixed steps like 7, 7.5, 8)

Continuous = measurable, any value in a range

• Height

• Weight

• Temperature

• Time

What does skewness mean? What is the difference between positive and negative skewness?

Skewness describes the side of the distribution where the few, extreme data points lie.

Positive = right skew

Negative = left skew

What does DFSS mean in DFSS-DMADV?

Designing for Six Sigma

What does CTQ mean?

Critical-to-Quality. It refers to the key product or service features that customers value most and are essential for a high-quality outcome, it must be controlled to guarantee that you deliver what the customer wants. 

In Six Sigma, what does DMAIC stand for and what is it used for?

DMAIC = Define, Measure, Analyze, Improve, Control. It is used to improve utilization for existing processes.

What does GEMBA mean?

Going to the source/plan of action. In a supply chain context, Gemba refers to the physical locations where work is done and value is added, such as:

• The factory floor or manufacturing line

What are common sources for collecting the voice of the customer?

• Existing company information

• Employees, customers, suppliers

• Trade associations

• Competitors

What are some methods for collecting the voice of the customer?

• Observations 

• Interviews 

• Focus Groups (8-12 people)

• Surveys 

What is the difference between VOC and VOP?

VOC = Voice of Customer

• External

• Not under company control

• Leads to specification limits

• Specification limits are chosen by customer, they don’t have to actually say something

VOP = Voice of Process

• Internal

• Can usually be controlled

• Leads to control limits

• Control limits are determined statistically

• Teacher shows up on time

What is the difference between a standard and benchmark?

Standard = Minimum requirement

• comes from market or government

Benchmark = Aspirational/Voluntary goal

• We want to achieve 1,000,000 sales

What does an affinity diagram do?

It groups all effects into one big effect.

• All parking complaints are grouped into one group (parking, parking fees, availability of parking)

What does QFD stand for and what is it used for?

Quality Function Deployment is a structured planning and decision-making tool that translates customer needs and wants (“the voice of the customer”)

→ into specific product or process requirements. House of quality is usually used in DFSS.

What does DPMO stand for and what does it measure?

Defects per million opportunities. DPMO measures how many defects occur per one million opportunities for a defect to happen in a process.

It tells you:

• How often errors occur

• How good (or poor) a process is performing

• How close a process is to meeting Six Sigma quality levels

D / (N * O) times 1,000,000

What does Gage R&R stand for and what is it used for?

Gage Repeatability and Reliability 

• If the same operator repeats then we would say it is repeatable 

• Reproducibility is when someone else repeats the prices 

What is an operational definition?

The precise definition of the characteristic and how it is measured. It removes ambiguity and ensures all data collectors collect data in the same way.

What does a scatter chart measure?

One variable relative to another.

What are the 5 values which the box and whisker plot specifically measures?

Minimum, Q1, Median (or Q2), Q3, Maximum.

True or False: A scatter chart can be a combination of any 2 types of variables?

True, it can be both independent, both dependent, or one independent and one dependent.

The number _ represents no correlation between variables.

0

What does the correlation coefficient mean? It takes values from _ to _ ?

The correlation coefficient is a statistical measure that tells you how strongly two variables are related and in what direction. -1.0 to 1.0

The grey area is the box in the box and whisker plot, and it takes what % of the data?

50%

If two sets of data have the same range, do they also have the same standard deviation?

No, not necessarily.

What is the IQR formula? What is it used for?

IQR = Q3 - Q1. The interquartile range (IQR) is used to measure the spread or variability of the middle 50% of a dataset.

What are the formulas for the largest value and smallest value within the upper and lower limit, respectively?

Largest value within the upper limit:

• Q3 + 1.5(Q3 - Q1)

Smallest value within the lower limit

• Q1 - 1.5(Q3 - Q1)

WHat does RPN stand for and how is it measured?

Risk Priority Number and the formula:

= Severity * Occurrence * Detection

• The scale for each individual value is from 1-10, and is more severe the higher the number

What is the range of possibilities for what the Risk Priority Number can be?

1 to 1000

You want to ____ severity, occurence, and ____ improve detectability.

Reduce, Improve.

Who introduced statistical process control (SPC) ?

Waller Shewhart 

What is the difference between common cause variation and special cause variation?

Common Cause: Always present and you cannot get rid of it.

• Ex: Small variations in your daily commute time (23 mins instead of 25 mins)

Special Cause: You can avoid it

• Ex: Major car accident

What is a box and whisker plot?

A box and whisker plot is a graphical representation of a dataset's distribution using its five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. It visually displays the spread of the data, the central tendency, and potential outliers by showing the middle 50% of the data in the box and the lowest and highest values in the whiskers.

Median has 5 measurements, what are they?

• Q2

• 5th decile

• 50th percentile

• Middle value

• Central value

What is type 1 and what is type 2 error?

Type 1:

Definition: Rejecting the null hypothesis (H₀) when it is actually true.

Meaning: You think there is an effect or difference, but really there isn’t.

Example: A company tests a new drug.

Null hypothesis (H₀): The drug has no effect. Type I error: You conclude the drug works, but in reality it doesn’t.

Type 2:

Definition: Failing to reject the null hypothesis when it is actually false.

Meaning: You miss a real effect — you think nothing is happening, but actually it is.

Example: Same drug test:

Null hypothesis (H₀): The drug has no effect. Type II error: You conclude the drug doesn’t work, but in reality it does.

True or False: Process Variation includes common cause variation and special cause variation?

True 

In improving a process, we first focus on reducing ____

Variability

True or False: Six sigma was first introduced by General Electric (GE) ?

False. It was first introduced by Motorola.

What is the difference between an independent and dependent variable?

Independent = I control it

Dependent = Depends on the independent variable

Ex: Testing the effect of study hours on exam scores

Independent variable: Hours spent studying

Dependent variable: Exam scores (what you are measuring)

The primary purpose of six sigma is…

Reducing Defects

What is the minimum number of oriectors required?

None of the above; 2

In benchmarking, we select a similar ____ from any industry to follow

Process

True or False: A control chart plots metrics from process over time and provides a basis for comparing process performance. 

True 

What is the z score formula?

x - mean / standard deviation