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68 Cards in this Set
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- Back
- 3rd side (hint)
Standard Deviation for a Population
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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 |
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Standard deviation for a sample
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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 |
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Mean for a population
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Written as u
average of values in the population |
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Mean for a sample
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written as x bar
averagare of values in the sample |
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1 sigma
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68% of all observations
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2 sigma
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95% of all observations
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3 sigma
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99.7% of all observations
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Six Sigma
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Management philosophy
3.4 defects per million opportunities |
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Opportunity
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Every chance to meet a customer’s requirement
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Defect
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When a CTQ fails to meet a customer’s requirement
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Defective
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A unit has one or more defects
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Throughput Yield
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of units processes correctly the “first time” (first pass yield through each step)
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TPY
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number units processed correctly the first time/
number of units |
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Attribute Data
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always ends up in counts or frequencies
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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) |
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Measurement Data
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on a continuous scale (infinitely divisible)
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KANO Model
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Attractive
One Way Must Be’s |
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2 branches of statistics
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Descriptive; Inferential
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Inferential
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Statistics are calculated from sample data to draw conclusions (infer) about the population parameters
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Descriptive
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Describes a data set
-Average of a data set -Median of a data set -Variation of a data set -Shape of a data set |
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2 types of statistical studies
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Enumerative; Analytic
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Enumerative
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-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?) |
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Analytic
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-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?) |
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Non-probability Sample
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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 |
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Probability Sample Methods
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Simple Random; Stratified Random; Systematic; Cluster
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Simple Random
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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 |
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Stratified Random
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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 |
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Systematic
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Probability Sample Methods
Random sample from the first k items Select ever kth item in the frame for sampling |
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Cluster
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Probability Sample Methods
Frame is divided into naturally occurring clusters or groups Clusters are then randomly sampled |
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Measures of Central Tendency
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Mean; Median; Mode
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Positive Skew
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Mean higher (to the right) than median
(It’s Skew-ished down on the right) |
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Negative Skew
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Mean lower (to the left) than the median
(It’s Skew-ished down on the left) |
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Z Transform
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used to convert a point on any “normal distribution” to it’s corresponding point on a “Standard Normal Distribution”
Z = (POI - u)/sigma |
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Measures of Variation
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Range; Variance; Standard Deviation
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Spec Limits set by
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Customer
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Control Limits set by
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Process
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Attribute Control Charts
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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 |
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Variable Control Charts
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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)) |
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Alpha Risk
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(α) (Reject the null hypothesis and it was correct / true)(Should not have rejected)
-Type I Error (Producer Risk) -CI = 1 – α |
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Beta Risk
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β) (Fail to reject null hypothesis and it was wrong / false)(Should have rejected)
-Type II Error (Consumers Risk) |
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Null Hypothesis
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(Ho) (always contains a statement of equality)
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Alternate Hypothesis
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(Ha) (opposite of the null; inequality)
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P-value
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the actual risk of rejecting the null hypothesis, when the null is actually true
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Alpha Risk
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is the risk we are willing to take
-If P-value is < alpha, we reject the null |
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1 Proportion Test
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compare proportion –vs- target
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2 Proportion Test
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compare proportion of one sample –vs- proportion of another sample
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Chi Square Test
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compare multiple proportions
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-Goodness of Fit (observed –vs- expected) (use Excel software, not Minitab)
-Test for Association (determine if one variable depends on another variable) |
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Proportion Tests
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1 proportion, 2 proportion, chi-square
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Means testing
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1 Sample -T test; 2 Sample -T test; Paired -T test; ANOVA Test
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1 Sample -T test
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compare mean –vs- target) (population)
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2 Sample -T test
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compare mean –vs- mean) (population)
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Paired -T test
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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 |
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ANOVA Test
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(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) |
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Variance Testing
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2 Variance Test; 1 Variance Test; Test for Equal Variance
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2 Variance Test
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(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) |
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1 Variance Test
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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) |
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Test for Equal Variance
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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
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(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 |
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Regression
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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 |
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R2
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percentage (%) of the total variation (Y) explained by the model (interaction of factors)
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R2 (adj)
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used to compare models with a different number of terms
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If problem refers to Means
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a inference test or a T- Test is used
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Problems refers to Difference between a sample mean and target value
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one –sample T-test
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Before and after differences of means between paired
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paired T- Test
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If problem talks about the variance differences between continuous data
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a variance test is required to test hypo
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When 2 samples are compared against one another
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two sample test is used
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When a sample is tested against a target
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a one variance test is used
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If the problem talks about testing for equal variances
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A test for equal variance is used
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