Analyze Phase Review
Types of variation (3):
-Positional -cyclical -temporal
Correlation
-is finding a relationship between 2 or more sets of data. -measures the strength (strong, moderate, weak) and direction (positive or negative) of the relationship between variables -coefficient is r
Hypothesis testing:
-to compare means, variances, and proportions (e.g., paired-comparison t-test, F-test, analysis of variance (ANOVA), chi square) and interpret the results
p-value
-used in hypothesis tests to decide whether to reject a null hypothesis or fail to reject -commonly used cutoff point for the p-value is .05 -if p-value is < .05 , you reject the null hypothesis
Multi-var (chart)
-useful for analyzing the 3 types of variation -perfect for investigating the stability or consistency of a process, they help determine where the variability is coming from within a process
In order to find a correlation...
One needs an independent variable (x) that causes an observed variation, which is considered the dependent variable (y)
Correlation coefficient:
( r ) : *formula pg. 265* -provides both strength and direction of the relationship between the independent and dependent variables -values range -1 to 1 -strength of the relationship of x and y is measured by how close 'r' is to 1 or -1 -'r' that is close to zero is evidence that there is no relationship between x and y
Independent variable examples:
(x) -hours studied -hours of exercise -level of advertising
Dependent variable examples:
(y) -exam grade -weight loss -volume of sales
Positional variation
-'within-part', within-batch/within-lot -variation of a characteristic on the same product
Causation
-a cause that produces an effect, or that which gives rise to any action or condition -Ex. : "if a change in X produces a change in Y, the X is said to be a cause of Y" - 'there is no such thing as an absolute cause for an event'
Cyclical Variation
-part to part or lot-to-lot
Scatter plot:
-provides complete picture of the relationship between 2 variables -4 diff types of correlation exist in scatter plots
Temporal variation
-shift to shift, occurs as change over time
During a process study, a green belt is assigned to collect data at 5 measurement points within a sample. Five samples are picked each day for five consecutive days. Choose an appropriate graphical method from the choices below to display within sample, sample to sample and time variation in a single graph. A. Multivari chart B. Xbar R Chart C. Box Plot D. Pareto Chart
A. Multivari chart -allows the data to present positional (within sample), cyclical (sample to sample) and temporal (over time)
A process improvement team is comparing the mean differences between two processes. Process A: 10,14,15,16,11 Process B: 11,12,16,14,11 Assuming equal variances, analyze the data sets to verify if the null hypothesis: Process Mean A= Process Mean B is true at alpha risk of 0.05 A. No difference between the means of Process A and B at Alpha risk 5%. B. Process Means are different at Alpha risk 5%. C. Process means are different at significance level of 95% D. Insufficient information to test the hypothesis.
A. No difference between the means of Process A and B at Alpha risk 5%. -Use 2 sample t-test
As a process improvement professional, you are asked to collect data to conduct a multivari study for a process parameter. How do you plan your study? A. Collect data on variations from within part, part to part, over time B. Collect data from various manufacturing locations C. Collect data from multiple machines D. Collect data from multiple processes
A. To conduct a multivari study, one should first collect data from within part (positional), part to part (Cyclical), and over time (temporal).
At the 90 percent confidence level, what is the minimum sample size that would confirm the significance of a mean shift greater than 10 units per hour without considering the beta error? (Historically, the standard deviation of the hourly output is 25 units.) A. 1 B. 17 C. 24 D. Not enough information to calculate sample size
B. 17 n= (1.645)2 * (25)2/ 102 = 2.56 * 625/ 100= 16.91 approx 17. (n= Z^2*std dev^2/ E^2)
As an experimenter which of the following tools would you use to verify correlation and causation of an experimental data? A. Control chart and histogram B. Scatter diagram and Ishikawa Diagran C. Pareto Chart and Ishikawa diagram D. Scatter diagram and histogram
B. A scatter diagram provides a pictorial relationship between an independent variable and a dependent variable. An Ishikawa diagram provides cause and effect relationship. The combination of the two tools is key to understanding the relationship and degree of relationship.
A one-sample T study was performed on a supplier's lot: -T study μ = 10 vs ≠ 10 and Alpha Value=0.05 -The mean of 10 samples tested is 9.85. -The 95% confidence interval of the population mean is 9.75, 9.95. -P-Value = 0.046. A discussion with the process expert determined that the population mean can vary from 9.7 to 10.1 without impacting the product performance. Choose the best course of action: A. Reject the null hypothesis since it is statistically significant and reject the lot irrespective of practical significance. B. Fail to reject the null hypothesis since it is not statistically significant and accept the lot since it is not practically significant. C. Reject the null hypothesis since it is statistically significant and accept the lot since it is not practically significant D. Fail to reject the null hypothesis since it is not statistically significant and reject the lot irrespective of practical significance.
C. Since the P value is lower than the Alpha value, the null hypothesis of μ = 10 vs ≠ 10 is rejected. However, due to the practical significance that there is no impact to the product, the supplier's lot is accepted. NOTE: If the analyst had consulted with the engineer to understand practical significance beforehand, one tail hypothesis could have been performed for ≥ 9.7 and ≤10.1
The P value for a regression model is 0.07. If the cut off for the Alpha risk is 0.05 and the assumed Beta risk is 0.10, the regression model is: A. Statistically significant since the P value is smaller than Beta Risk of 0.10. B. Statistically significant since the P value is greater than Alpha Risk of 0.05. C. Not Statistically significant since the P value is smaller than Beta Risk of 0.10. D. Not statistically significant since the P value is greater than Alpha Risk of 0.05.
D. The p-value (0.07) is compared to Alpha Risk (0.05) and if the P value is smaller than the Alpha risk, then is considered statistically significant. In our example, since P value is greater than assumed alpha value, the regression model is not statistically significant.
