Central Limit Theorem and Sampling Distributions in Statistical Quality Control

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24 Questions

What do control charts deal with in quality engineering?

Online quality control

Which type of control methods are typically used in the design phase of a product/process/service?

Off-line control methods

What was the example given for optimal experimental design and ANOVA in the USA?

Fisher's experimental design

What is the output response that was considered for the Improvement of Injection Molding Process as mentioned in the text?

Injection pressure (minimize)

How many input factors were considered for mold design in the engineering example provided?

4

What does DoE stand for in the context provided in the text?

Design of Experiments

What condition must be satisfied for the Central Limit Theorem (CLT) to work well in Statistical Quality Control (SQC) problems?

The individual random variables must be identically distributed

Which distribution is followed by the sum of squares of standard normally distributed independent random variables?

Chi-squared distribution

What happens to the distribution of a chi-squared random variable when the degrees of freedom increase?

It approaches a normal distribution

In ANOVA, if the null hypothesis is rejected, what does this indicate about the groups being compared?

There is a significant difference between at least one pair of groups

What type of graphs can be used to visualize ANOVA results in Minitab?

Boxplot

Which distribution results from the ratio of two independent chi-squared distributed variables?

F distribution

What is the purpose of robust design using Taguchi Methods?

Maximize yield (profit) and minimize cost

In the Statapult example, what does ANOVA stand for?

Analysis of Variance

What is the concept behind the Central Limit Theorem (CLT)?

It defines the distribution of the sum of independent random variables

What do the levels in Plasma Etching represent?

Different power settings used during etching

'Does setting significantly affect traveling distance?' What statistical method could help answer this question?

Analysis of Variance (ANOVA)

What is the main goal of identifying key decision variables in screening experiments?

Identify factors to maximize yield and minimize cost

What is the null hypothesis in the ANOVA Means Model?

𝜇1 = 𝜇2 = ... = 𝜇𝑎

Which component is considered as random in ANOVA Grand Mean Random Error Component?

𝜎 2

In ANOVA Calculations, what does 𝑆𝑆𝑇 represent?

Total sum of squares

What distribution does 𝐹0 follow if 𝐻0 is true in ANOVA?

F distribution

Which parameter determines whether to reject the null hypothesis in ANOVA?

𝐹𝛼,𝑎−1,𝑎(𝑛−1)

What does the Treatment Effect refer to in the Linear Statistical Model?

Effect due to level i

Learn about the Central Limit Theorem (CLT) and important sampling distributions derived from the normal distribution as applied in Statistical Quality Control (SQC). Explore how the CLT can approximate the sum of independently distributed random variables to be normal, and its practical application in SQC problems.

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