DEFINE PhaseThe following are example questions that will test your knowledge of the concepts within the DEFINE phase of a DMAIC and DFSS Six Sigma project. Show 1) The customer specifications for a process, referred to as the Voice of the Customer, will provide which of the following. There may be more than one correct answer. A) Upper Control Limit - UCL Answers: B,C,D Choices A and E are functions of the process. The goal is to have the Voice of the Process (VOP) perform within the Voice of the Customer (VOC) specs. You may get one, two, or all three of the customer specs and they may also provide attribute information, and more. 2) Which of the following are characteristics of the inputs to a process. A) these are referred to as the x variables Answer: A,B,D C is a characteristic of the effect, or y-variable. The team wants to CONTROL the inputs and MONITOR the outputs. 3) Inferential statistics is A) statistics derived from analyzing population Answer: B 4) The Weighted Average Cost of Capital (WACC) is commonly used to evaluate capital projects. The WACC is also known as what other terms, there may be more than one answer. A) Cost of
Capital Answer: A, B, C are all commonly used and interchangeable terms with WACC. Projects should exceed the WACC which is the cost of raising funds for a capital funding project according to your firm's targeted capital structure. See the Financial Savings module for more information on capturing savings for your Six Sigma project. 5) Pareto charts are very commonly used in Six Sigma projects, often in many phases and throughout all facets of a business. Which best describes the Pareto Chart. A) A timeline indicating the progression of the project Answer: C A Pareto chart is usually a vertical bar chart with occurrences on the y-axis and the categories along the x-axis. The are usually sorted with the highest or most frequent category on the left side and going right in descending order. At a high level, the Pareto Chart is looking to quickly identify 20% of the causes that are responsible for about 80% of the defects. 6) The tool used to ensure that all affected people are involved and engaged is the A) Stakeholder Analysis Answer: A A Stakeholder Analysis is similar to a "Communications Plan" that is used to measure the level of resistance of stakeholders. 7) The output of the Six Sigma methodology is ultimately intended to: A) increase profits Answer: A. Cash flow could also be an intention but the others are leading indicators to the ultimate goal of making money. Increasing sales isn't always good, only if it adds more profit. 8) The tool used to organize information about complex or unfamiliar topics for which the team may have little knowledge is A) Prioritization Matrix Answer: C The Affinity Diagram is the simplest mind-mapping, brainstorming exercise that visually organizes ideas (grouping technique) and similar concepts. It is used for new, complex, or unfamiliar problems. It is easy to use and can get the team moving forward together by bringing out each person's input, thoughts, and questions. See the Affinity Diagram module for more information. 9) In which type of distribution of data are all three measures of central tendency are approximately the same. A) Uniform Answer: B 10) Find the mean of the following data set: {1, 3, 8, 3, 7, 11, 8, 3, 9, 10, 0} A) 3.0 Answer: C 63/11 = 5.7 11) Using the following data set find the median. {1, 3, 8, 3, 7, 11, 8, 3, 9, 10} A) 6 Answer: B Learn more about the measures of central tendency. 12) Using the following data set find the mode. {1, 3, 8, 3, 7, 11, 8, 3, 9, 10} A) 6 Answer: C The mode is the most common value in the data set and is the measure of location for the nominal scale (which is a very low level statistic). Learn more about Data Classification. 13) A tool used to analyze the Voice of the Customer (customer requirements) is called: A) SPC Charts Answer: D See the Kano Model module for more information and study the categories for analyzing customer requirements. 14) Given the following findings on the number of defects that were produced among 10 machines, which is the proper category listing from left to right when creating a Pareto Chart. Machine 4: 98 defects A) 4,3,9,Others,7 Answer: D Many times the number of categories you want shown can be manipulated but as general rule show enough categories on the Pareto Chart to represent at least 80% of the defects from highest to lowest going left to right and the "Others" amount is shown on the right. 15) Sometimes the Problem Statement and scope of a Project Contract will get refined upon early findings of the Six Sigma team in the Define phase. Which of these tools can help create a more accurate Project Contract: A) SPC Answer: C and D This information can help assess whether the scope is correct, the baseline is accurate and target is achievable. The sooner the better to understand any changes to the Project Contract. 16) What is the future value given that the projected interest rate is 6% annually for 10 yrs. Each the end of each month a payment of $100 will be deposited. There was an initial deposit (or present value) of $2,000. A) $4,900 Answer: C Ensure the units are consistent. Convert the 6%/yr to an monthly rate which is 0.5%. There are 120 periods over 10 years. The payments made at the END of each month is $100. Click here to learn more about this topic. 17) Statistics that summarize a population are A)
inferential statistics Answer: D 18) Project Management is a key part of a Six Sigma project managers tool kit. Which person introduced a theories called Theory X and Theory Y and also expanded on Maslow’s hierarchy of human needs. A) Frederick Herzburg B) Douglas McGregor C) Elton Mayo Answer: B McGregor began teaching his theories to students at MIT in the 1950’s. Mayo studied the effects of worker output and fatigue as part of the Hawthorne studies in 1924. Although a primary goal was to study the effect of illumination of worker output, a key find was that people reacted positively to increase productivity as long as their individual needs were met and they were treated as human beings. The Hawthorne Effect indicates that people that are singled out for special attention tend to perform as anticipated. Herzburg studied the motivation to work and divided into two factors (the names of these factors vary). 19) Which type of diagram is used to show the complexity of a problem by showing all combinations or outcomes? A) Tree Answer: A 20) Which can be used to find and quantify a source of a problem? A) Pareto Chart Answer: A The Pareto Chart is probably one of the most commonly used tools to provide quick insight into a problem. 21) As part of a Six Sigma project, a heat treatment facility learned that they could reduce the temperature to heat treat their customers parts by 15o F and still maintain the necessary hardness and tensile strength required. For every 1o F of reduced temperature, the company estimates a savings of $2,000/month in reduced natural gas. What are the annual savings for this improvement? A) $30,000/year Answer: C The savings are $24,000/year ($2,000/month * 12 months) for every 1o F. Multiply $24,000 by 15o F = $360,000/yr. The other benefits are a reduced carbon footprint and this can help a company's ISO 14001 program as well. 22) What is the best choice of tool for using when the Six Sigma team is developing and prioritizing a list of options that includes controversial issues which is the reason that social interaction between team members is limited to avoid peer pressures. A) Nominal Group Technique Answer: A The word "nominal" refers to the restricted communications between team members. Click here to learn about some of the project management team tools. 23)
Rank the quality management tools from least complex to most complex: 1) PDPC Chart Answer: 2,1,3,4 There are more tools than shown above. A Tree Diagram is similar in complexity to the PDPC Chart. 24) True or False: The most important factor for a successful Six Sigma program implementation is the leadership and support from upper levels and top management. Answer: True 25) Put the following steps in order for Benchmarking your company's competition. 1) Understand own processes Answer: 1,3,2,4 26) What is the acronym for a high level process map? A) SIPOC Answer: SIPOC 27) What is the element that indicates a need for correction or adjustment in a process map. A) Feedback Answer: Feedback Each time a product goes through a loop, an adjustment or correction is done. It is feedback that is considered the element that indicates the need for this adjustment so the product gets out of the rework loop within conformance. Feedback may be used to tweak a process even if it is performing within specifications. This feedback may be used to tighten the output or move it in a controlled manner. 28) True or False: The four stages of teams are: Forming, Storming, Norming, and Performing Answer: True 29) Which of the following is not one of the nine basic dimensions of quality as defined by a number of quality gurus: 1) Conformance 2) Reputation 3) Aesthetics 4) Reliability 5) Performance 6) Features 7) Attitude 8) Durability 9) Response 10) Service Answer: 7) Attitude is the one not one of the 9 basic dimensions of quality. 30) Which financial metric is being described when the NPV is set to 0 and the r value is being solved for and then compared to the r value others projects. The ____ values for several projects of often compared to each other by a company. Those with the highest ____ value are expected to have the best financial benefit. Generally, if the r value for a project is > than the company's ROI it should be approved. 1) ROI Answer: 3 Learn about the common financial metrics that are likely to show up on a certification exam. 31) Match the incidents listed below in 1-4 with the Cost of Quality category A-D. A) Prevention Cost B) External Failure Cost C) Appraisal Cost D) Internal Failure Cost 1) A customer found a defect in a item and received a refund and a discount on a future purchase. 2) An inspector has to perform visual and nondestructive test to assure part compliance. 3) The company had to rework a large percentage of the defective parts to get them to pass and then expedite and pay a premium to ship them on time to the customer. 4) Company paid for education and training and then developed work instructions. Answer: 1-B, 2-C, 3-D, 4-A Learn more about the Cost of Quality and Cost of Poor Quality 32) True or False The 3 ELEMENTS of Project Management are: 1) Planning Answer: TRUE 33) If the IRR for a project has been calculated at 8%, what conditions from the list below, will most likely approve the project to move forward (assuming funds are limited) A) Company WACC is 7% Answer: A & C Learn more about the common Financial Metrics such as ROI, ROA, NPV, IRR, Payback Period, and the Future Value of Money. If funds were UNLIMITED, then the project with an IRR at 7.5% may also get approved if the WACC is 7%. But neither project is likely to be approved in the Company WACC is 10%. MEASUREThe following are example questions that will test your knowledge of the concepts within the MEASURE phase of a DMAIC Six Sigma project. 1) If more than 25% of the points on a R-chart are equal to zero then this is most likely a problem with what part of the measurement system? A) Stability Answer: D The measurement system should record data ten times greater than will be used in project metric. If you are using feet as a unit of measurement for your metric, then take all your measurements in inches (this is 1/12 resolution) and satisfies the 10-bucket rule. If you are using a metric measured in X.XX (hundredths), then record all your measurements in X.XXX (thousandths) What else may indicate poor gage resolution? Plateaus (flat spots) of the data on the r-chart and if r-bar is too small 2) Repeatability is variation "within", and reproducibility is the variation "among" or "between all". A) True Answer: True Repeatability would describe the variation within one appraisers own assessments across multiple assessments. Answers the question of how repeatable are his/her answers each time assessing the same thing. 3) Sampling taken of the first 100 patients in a hospital directory listed by alphabetical order is known as A) systematic random sampling Answer: D 4) A sampling strategy that employs a system such as using every 20th part that comes from a machine is an example of A) systematic random sampling Answer: A 5) A measurement of lumens, decibels, temperature, and ohms, are examples of A) continuous data Answer: A 6) Which subjective analysis tool is used to visualize the relationships between many inputs, x's, and an output, Y. This tool focuses on the causes, not the symptoms. A) Cause and Effect (Prioritization) Matrix Answer: B The Fishbone Diagram is usually the first in a line of subjective tools to help reduce the numerous trivial inputs to the vital few inputs that cause the effect (Y). The next tool can be the C/E (Prioritization) Matrix or the FMEA. 7) Which of the following yield metrics does not account for rework or hidden factory loss. A) Rolled Throughput Yield Answer: E Final Yield (FY) does not account for the hidden factory or rework. It is simply the final number of acceptable pieces at the end divided by the quantity started in a process. It does not tell you how many were reworked at each step of the process. 8) If there are 11 orders, and each order has 2 items, and there are 3 opportunities for a defect (such as incorrect item, wrong price, and damaged), then how many total opportunities are there for a defect? A) 22 Answer: 66 9) Which of the following are types of errors in conducting a survey or other methods of gathering the Voice of the Customer (VOC)? A) Coverage error Answer: All of the above 10) What is the probability that Z is greater than or equal to -1.96 and smaller than or equal to -1.4. Z is a standard normal random variable? A) 0.9821 Answer: C Reference the Z-table to help solve. 11) Given a normal bell curve (the empirical rule) which interval contains 68% of the measurements? A) +/-
1 sigma Answer: A Reference the normal distribution page. 12) Which measurement scale measures by rank only and does not contain any precise measurements? A) Nominal Answer: D 13) A person flips a coin six times and has landed heads each time. What is the probability that heads is the result on the next flip? Assume the coin is fair. A) 0.5 Answer: D The probability is the same each flip. Each flip has a 50/50 chance for each result. Both A and B are the same answer just expressed differently on paper. 14) Which of the following is not a component of measurement system error. A) Linearity Answer: C Reference the Measurement Systems Analysis page. 15) Which of the following measurement scale applies if measuring the circumference of a cylinder in millimeters. A) Interval Answer: D There is a defined absolute zero starting point in this case and it is continuous data that can have an infinite number of values. Reference the Data Classification page. 16) Which of the following devices are examples of attribute measurement devices. A) Plug gages Answer: A&D The other two choices are variable gages. Variable gages provide more information that attribute gages. 17) Which of the following are considered graphical methods. A) Scatter Diagram B) Histogram C) Fixed-Width Box Plots D) Stem and Leaf Plots E) Notched Width Box Plot F) Trend Analysis G) Line Chart H) Pie Chart I) Radar Chart J) Bubble Chart Answer: All of the above 18) What does the line that divides the box in a box plot represent? A) Median of the data set Answer: A Reference the Box Plot page. 19) The probability density function (PDF) of a continuous random variable is known to be 0.08x, where x is valid from 0 to 5. Find the probability (cumulative distribution function) of x being less or equal to 2.3. A) 0.08 Answer: D Reference the CDF page. 20) As a graphical method, Stem and Leaf Plots have grown in popularity since they easily handle large amounts of data and shows each data point. TRUE Answer: False Reference the Stem and Leaf Plot page. 21) The following information is provided. Find the Gage Error (GRR%) for the variable gage study. The average range is 1.6 and the value for the distribution of the average range is 1.19. The tolerance is 20%. A) 4.33% Answer: D The GRR = (5.15 * 1.6) / 1.19 = 6.924 The GRR% = (6.924 * 100) / 20 = 34.62%, which exceed the limits and thus the gage failed and should be replaced. 22) The following information is provided for a particular failure mode on a FMEA. Find the Risk Priority Number (RPN). Severity: 4 A) 600 Answer: C The RPN is the product of the three values. The higher the RPN, this higher risk that the failure mode presents to the customer and should be given priority to mistake-proof. See the FMEA for more details. 23) Match the following shapes with their representation in a flowchart Diamond A) Decision Answer: A diamond represents a Decision. A rectangle represents a Process. An oval represents a Start or End point. A parallelogram represents and Input or Output. 24) When the tables are used correctly, the Z-score is an indication of: A) the area under the curve outside of the control limits Answer: C 25) Which tool is best suited to find rework loops and non-value added steps. A) Process Map Answer: A 26) Given a perfectly normal distribution, what is the probability of z>0. A) 0.25 Answer: B & C which are the same 27) Which data classification is ranking customer satisfaction on a scale of 1-5. A) Ratio Answer: B 28) Which data classification is a measurement of Centigrade or Fahrenheit? A) Ratio Answer: B Ratio is not correct since zero degrees does not mean the absence of temperature. 29) Which data classification is for measuring lengths or weight? A) Ratio Answer: A See the Data Classification page for more information on four measurement scales: Nominal, Ordinal, Interval, and Ratio 30) Which measurement scales are categorical? A) Ratio Answer: C & D 31) Which measurement scales are numerical? A) Ratio Answer: A & B See the Data Classification page for more information on four measurement scales: Nominal, Ordinal, Interval, and Ratio 31) The amount of time
needed to manufacture each car on an assembly line is best described as _____ type of data. A) Ratio Answer: A 33) A given set of data has a mode of 15.2, median 15.7, and mean of 17.1, which best describes the distribution: A) Right skewed Answer: A Skewness is a measurement of symmetry and kurtosis is a measurement of "peakedness or flatness" of a distribution. In this example, the Sk value is >0 (for a right-skewed distribution) 34) Multi-vari charts are used most often to analyze which type(s) of variation? A) positional Answer: All of the above Click here to learn more about multi-vari charts. 35) Which of the following are true about calibrations? A) The standard used is the more important when calibrating a measuring device rather than the calibration sticker, interval, or maintenance history. B) Proper environmental conditions should be maintained for the measurement standards used for the calibration. C) Calibration interval should be adjusted when a characteristic on a gage is consistently found to be out of tolerance. D) All of the above Answer: D 36) Which statement(s) correctly describe the statistical term Degrees of Freedom? A) the number of independent pieces of information available to estimate a statistic Answer: All of the above Click here to learn more about Degrees of Freedom. 37) If a normal distribution has a mean of 35 and a standard deviation of 10, 95% of the distribution can be found between which two values? A) 0, 70 B) 15, 55 C) 25, 45 D) 45, 105 Answer: B. 95% of the distribution (area under the curve) is 1.96 standard deviations from the mean which can be estimated at 2.Therefore 35-20 = 15 is the lower value and 35+20 = 55 is the upper value. 38) Which of the following has a most significant impact on the shape of a normal distribution? A) Standard deviation or variance B) Median C) Mode D) Mean Answer: A 39) If a normal distribution has a mean of 35 and a variance of 25, 68% of the distribution can be found between which two values? A) 30, 40 B) 25, 45 C) 0, 70 D) 20, 50 Answer: A. 68% of the distribution (area under the curve) is about +/- 1 standard deviation from the mean. The standard deviation is the square root of the variance and therefore = 5. Therefore 35-5 = 30 is the lower value and 35+5 = 40 is the upper value. 40) A distribution of measurements for the length of widgets was found to have a mean of 50.00mm and a standard deviation of 1.50mm. Approximately what percent of measurements are between 47.00mm and 53.00mm? A) 100% B) 68% C) 95% D) 99% Answer: C. The measurements of 47.00mm and 53.00mm are two standard deviations away from the mean of 50.00mm. Therefore about 95% of the values recorded are between 47.00mm and 53.00mm. Answer: A. 68% of the distribution (area under the curve) is about +/- 1 standard deviation from the mean. The standard deviation is the square root of the variance and therefore = 5. Therefore 35-5 = 30 is the lower value and 35+5 = 40 is the upper value. 41) If the probability of one event occurring is 75% and another is 35%, what is the probability of at least one of the events occurring? A) 100% B) 68% C) 84% D) 26% Answer: C If 1 and 2 are two events in a probability experiment, then the probability that either one of the events will occur is: P(1 or 2) = P(1) + P(2) − P(1 and 2). P(1 or 2) = 0.75 + 0.35 - (0.75*0.35) = 1.10 - 0.2625 = 0.8375 = 84% 42) Which of the following are typically selected for inspection and auditing sampling plans? A) Tolerance B) Known Risks C) Validity D) Applicability Answer: B,C,D 43) Label the following test methods as destructive or nondestructive: 1) Liquid Penetrant 2) Eddy Current 3) Tensile Testing 4) Acid Etch 5) Ultrasonic 6) Voltage Breakdown 7) Radiography 8) Magnetic Particle 9) Spectroscopic 10) Fluoroscopy 11) Shear Testing Answer: Destructive: 3,4,6,9,11 Nondestructive: 1,2,5,7,8,10 ANALYZEThe following are example questions that will test your knowledge of the concepts within the ANALYZE phase of a DMAIC Six Sigma project. 1) Type I error and Type II error are respectively known as A) P-value risk Answer: C Alpha risk = Type I Error = Significance Level = Producers Risk = False Positive. This is when an EFFECT is detected that does not exist. Beta risk = Type II Error = Consumers Risk = False Negative. This is when an EFFECT is not detected when it does exist. 2) While ANOVA is "Analysis of Variance", it is used for which reason? A) Testing variances of two populations Answer: D ANOVA assumes homogeneity of variance which means the variance within each factor are equal. Usually used to test >2 means. 3) What other assumption(s) are required to use ANOVA: A)
Measurement system is linear and reproducible Answer: B,D Choice A is already confirmed, you should have an adequate measurement system as verified in the MEASURE phase. Choice C is the reason for using ANOVA, which is a test of the equality of the means (can be used like the student t-test to test the equality of two means). 4) Confidence Intervals are not always symmetrical, but what is true about confidence intervals when the sample size changes. A) As sample size, n, decreases the confidence interval spread increases. Answer: A,B. The larger the width, or spread, of the confidence interval the weaker the estimate of the mean or variance. Logically, the more data and samples taken within a population, the more confidence you will have in estimating the population mean or variance. As n approaches infinity, the sample average approaches the population mean. 5) The standard deviation of a standard normal distribution is A) always equal to one Answer: A The standard deviation of a standard normal distribution is always equal to one. the keyword is standard 6) Which of the following are characteristics of the normal probability distribution? A) 89% of the time the random variable assumes a value within plus and minus 2 standard deviation of its mean Answers: B,C,D 7) Which term measures only a linear relationship between two variables and is denoted by an "r" value and it will always range from -1.0 to +1.0? As the value approaches 0 their is less linear correlation, or dependence) of the variables. A) Coefficient of Determination Answer: D The most common incorrect answer is A. The Coefficient of Determination from 0-1 (0%-100%) represented by r-squared. The proportion of variability of the dependent variable (Y) accounted for or explained by the independent variable (x) equal to the coefficient of correlation value squared. Click here to learn more about Correlation. 8) A sample of 5 widgets from a population of 30 widgets is taken without replacement for review. Determine the probability of finding 2 defective widgets when the population is known to have 14 defective widgets and 16 non-defective widgets. A) 20.5% Answer: D Click here to learn more about the hypergeometric distribution. 9) What is the Confidence Interval for a population mean given the following information and using a 95% confidence level? Alpha risk = Level of Significance = 1 - Confidence Level = 0.05 A) 50 to 52.44 Answer: B The interval is 50 +/- 2.44, or 47.56 to 52.44. The other point of this question is to draw attention to how close B and D appear. Carefully select the correct response. It is easy to make quick mental assumptions without realizing it and selecting the wrong answer when you actually calculated it correctly. 10) What is the standard deviation for 20 flips of a fair coin? Assume the binomial distribution. A) 0.5 Answer: C The mean is 10. The answer is not 5 but rather the square root of 5. 11) Scores are collected for 10 students that took the same competency test before and after training. Which t-test should be applied to compare before and after average scores? A) 1 sample t-test Answer: C 12) For the question above what is the correct null hypothesis? A) MeanBEFORE = MeanAFTER Answer: A 13) A comparison on the average braking response time between two drivers when a light turns red. You have recorded the times and determined the data is normal. Which test would you use? A) 1 sample t-test Answer: B 14) Which of these are one-tailed test and which are two-tailed test? A) HO: Mean A = Mean B Answer: A is two tailed. B & C are one tailed. 15) Assuming a normal distribution, the mean salaries of personal trainers is found to be $40,000 with a standard deviation of $5,000. Determine the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500? A) 0.05 Answer: B Z score of 1.5 = 0.4332. Since we are looking at only one tail of the curve the answer is 0.5-0.4332 = 0.0668 16) Which is the most applicable t-test when testing two sample means when their respective population standard deviations are unknown but considered equal. The data is recorded in pairs and each pair has a difference, d. The degrees of freedom are n-1 where n = number of samples. The following are assumptions: A) One sample t-test Answer: B 17) Which test is best choice to use when comparing medians of non-parametric data? A) Kruskal-Wallis Answer: D. Click here to review hypothesis test flowcharts. 18) A hemming operation has an OEE of 86.4% and Takt Time is 4s/pc and a known defective rate of 2.0%. If a sample of five parts are selected, what is the probability that the sample contains exactly two defective parts? A) 0.02 Answer: D The OEE value and Takt Time are meaningless for this problem. It is important for Six Sigma project managers to sort through all the available information and use the correct inputs as well as selecting the correct formulas. Use: 19) A statistical test used to test a hypothesis of independence of two attribute variables is: A) Paired t-test Answer: D 20) Which is a parametric test used to test a hypothesis of two variances? A) Paired t test Answer: C 21) What is the Coefficient of Correlation between these two sets of data. Each data point is plotted for a monthly period for 12 months? Marketing costs: $6,421, $6,328, $7,856, $5,467, $4,265, $5,012, $8,023, $7,625, $4,569, $2,548, $6,985, $6,849 Cereal Sales: $55,462, $53,211, $68,021, $45,698, $40,120, $43,296, $70,231, 66,849, $42,065, $31,456, $61,365, $58,312 A) r = 0.9851 with strong correlation Answer: A 22) When calculating the Chi-Square value for attribute data there are two variables needed to compare proportions. The observed values and expected values are entered into contingency tables. How are the expected values calculated from a contingency table? A) Grand total / (Row total * Column total) Answer: C 23) Which test is preferred when comparing more than two means? A) ANOVA Answer: A The t-test is for comparing 2 means generally but ANOVA is used when comparing > 2 means. 24) Which of these are non-parametric test the use the MEDIAN and the measure of central tendency to describe the data where the data is ranked to conduct an one-way ANOVA. A) Friedman Test Answer: D The t-test is a parametric test. The other three are non-parametric tests. 25) Which of these are non-parametric test is not as robust as the Mood's Median test when analyzing outliers. A) Friedman Test Answer: C 26) Which of these are non-parametric test is used to determine if two independent sets of data are from the same population and is the option to use when t-test can not be since the data does not meet normality assumptions. A) Friedman Test Answer: D 27) Calculate the Coefficient of Variance from a sample of 1,000 widgets with a mean of 20.0 mm and a standard deviation of 0.4 mm. A) 2.0% B) 20% C) 8.0% D) 80% Answer: A. 0.02 = 2.0%. Click here to learn more about the Coefficient of Variance calculation (recall that this is different than Covariance). 28) What is the appropriate parametric test for means assuming you have two samples of <30 data points with unknown variances that are assumed to be equal? A) Pooled t test Answer: A 29) What is the appropriate parametric test for variances assuming you have one sample? A) Chi-square Answer: A 30) A sample of 5 parts are drawn without replacement from a total population of 30 parts. Determine the probability of getting exactly 2 defective parts. The population is known to have 14 defective parts. A) 35.76% Answer: A The hypergeometric distribution is applied. 31) Determine the Degrees of Freedom for a two sample t-test when one sample size is 20 and the other sample size is 25. The alpha-risk is 5%. A) 24 Answer: C dF = n1+n2-2 = 20+25-2 = 43. The alpha-risk is not relevant to this question. See the t-distribution page for more information. 32) Which statement(s) are correct about Correlation and Covariance. A) Covariance values range from +1.0 to -1.0 Answer: None are correct See the Covariance and Correlation pages for more information. 33) Based on the Scatter Diagram below what conclusions can be drawn about the linear Correlation. Assume the values increase on the x axis to the right and the y-axis to the top of the chart. A) Weak negative correlation Answer: A B is not correct since correlation values must be between -1.0 and 1.0. There is not strong evidence to suggest one "x" variable causes a direct impact on the "y" variable. Correlation, no matter how strong (positive or negative) it may appear, never implies causation. There could be other variables behind the one charted that could be a factor. 34) A correlation analysis provides a value (correlation coefficient) for what type of relationship between two variables? A) Linear Answer: A This analysis provides a linear relationship value but there may be a non-linear association of the two variables. 35) Which statements are true about defining the shape of a distribution? A) Kurtosis and
skewness are used to describe the shape of a distribution. Answer: A, B, C And if Sk > 0 then this represent a right-skewed distribution. There are natural distributions that will be right or left
skewed and will not meet the assumptions of normality. Click here and go to the bottom of the page to read more. 36) Statistical power is A) the likelihood of detecting an effect when an effect is present B) 1 – β (beta-risk) C) 1 - Level of Significance D) the chance of rejecting the null hypothesis when the null hypothesis is false Answer: A,B,D. Visit Power & Sample Size for more information. 37) Which statement(s) are correct about linear correlation. A) If the p-value is < than the chosen alpha risk then there is a statistically significant correlation. Answer: A, B Regardless of how strong a relationship appears there could be other variables involved. Regression is used to develop an equation such as y=mx+b, which is a simple regression equation to describe the nature of the relationship. 38) Which statement(s) correctly describe the Margin of Error. A) The Margin of Error (ME) is often expressed in the following formulas so it is the SE times an adjustment value which is a z-critical or t-critical value:
B) The ME is the entire width of a symmetric confidence interval. Answer: A,C Choice B is not correct since the ME is half the width of a symmetric confidence interval. Click here to learn more about Margin of Error. Click here to get a ME calculator along with several other Templates and Calculators. 39) The sampling distribution equals the relative frequency distribution when A) there are an infinite number of samples Answer: A 40) A Green Belt ran a statistical test and found that the p-value was >0.05. What statement below fits that result. A) There is not a difference or relationship with at least 95% confidence. Answer: A. See this section on p-value to learn more. 41) What distribution is used to compare (or infer) and sample variance with a known, same population variance? A) t-distribution B) Chi-square distribution C) F-distribution D) Normal distribution Answer: B F-distribution is the ratio of two sample variances. The t-distribution compares means. 42) A Black Belt is comparing the expected test results from 23 students in the same class. Which of the following statistical test is most applicable? A) ANOVA B) t-test C) paired-t test D) z-test Answer: A Analysis of Variance (ANOVA) evaluates the differences among means of >2 samples. ANOVA analysis determines whether at least two of the students have significantly different scores. 43) True or False: The standard deviation of the sampling distribution of the mean is called the Standard Error of the Mean. Answer: True. It measures how much the sample means differ from each other. 44) The Central Limit Theorem states that regardless of the population from which data is drawn, the sampling distribution of the mean when sufficiently large is: A) Unimodal Distribution Answer: D. Click
here to learn more about the Central Limit Theorem. 45) Which statement(s) are reasons for using a multi-vari chart A) generally inexpensive and quick to help identify where to investigate Answer: A and C IMPROVEThe following are example questions that will test your knowledge of the concepts within the IMPROVE phase of a DMAIC Six Sigma project. 1) A four level, three factor, DOE is being conducted but due to time and budget constraints a half factorial is used. How many treatment combinations are there? A) 64 Answer: D Recall that factors are the power which the levels are raised. Four cubed is 64, and a half factorial means that half of the full factorial combinations will be used, which is 32. 2) Which of the following are true of the Evolutionary Operations (EVOP): A) Used when process is not in control Answer: D EVOP is evolutionary in that it learns from existing behaviors to predict future treatments to improve the response. It is normally used when a process is in statistical control. 3) Waste Elimination is a key component of the IMPROVE phase and will involve cultural transformation and high assurance that team members and affected stakeholders are ready to change. What tools are commonly used (not all depending on the project) at this time. A) Stakeholder Analysis Answer: All choices EXCEPT C and H 4) The goal of IMPROVE is to make a fundamental change or prove through trials that a fundamental change is possible by eliminating waste and determining the relationship of the key input variables that affect the outputs of the process. When a process is in statistical control what are possible steps to improve it to a better desired performance level. A) Target and resolve the special causes Answer: B The special causes must be eliminated to have a statistically controlled process. It may be possible that a customer has unrealistic specifications or those that are too tight that it is not practical or financially viable, it may be possible to work with them and prove through testing and validation that the specifications can be opened or changed. It is not possible to select these values as you would like them, they are set by a formula through the process itself. They represent the Voice of the Process. 5) Which of the following are characteristics of a Latin Square Design DOE. A) Permit analysis of main effects only Answer: E 6) Which of the following are assumptions are the errors for a mixture and a factorial experiment? A) Have common variance Answer: D 7) In a Full Factorial experiment with 3 levels and 5 factors how many possible combinations are there. A) 243 Answer: A The number of possible combination = levelsfactors (35) which is 243. 8) In Fractional Factorial experiment is subset of combinations from a Full Factorial experiment. Answer: TRUE 9) If a half fractional factorial experiment is determined to be most practical and economical where there are two levels and five factors, how many runs will be performed in the DOE. A)
16 Answer: A The number of possible combination = levelsfactors so there are 32 total combinations and half of them combinations will be tested so that is equal to 16. 10) Which would be used to evaluate the significance of factors in a fractional or full factorial experiment? A) FMEA Answer: C 11) What are some advantages of fractional factorial
experiments? A) Less time involved than OFAT (one factor at a time) Answer: D 12) Which of these statements is incorrect about factorial experiments? A) Response = output = dependent variable Answer: C Factors are independent variables and inputs that are part of the total variation of the mean. 13) How many runs will there be given the information below for a Full Factorial DOE? 2 Levels A) 6 Answer: B LevelsFactors * Replicates = 23 * 3 = 24 14) Which is used to create a model of the effect on an output by the variation in two or more of the inputs? A) Linear Regression Answer: C 15) A set of data is analyzed and the following regression equation was generated: Pieces produced = 8.0 + 0.122 (hours of human work) Which statement(s) are true: A)
pieces produced is the dependent variable, y, (aka. the output) Answer: A,C,D The amount of hours of human work is the 'x' or the input. This is the independent variable. The dependent variable is 'y' which means the amount of pieces produced depends on the amount of hours of human work. Recall that y=mx+b. The slope of this formula is 0.122 and the y-intercept is 8.0. 16) Which term represents the approach to significantly reduce the non-value added steps within setups? A) SMED Answer: A SMED = single minute exchange of dies 17) Which term best describes small increment change leading to continuous improvement? A)
TPM Answer: D Muda is a term to describe the 7-wastes. 18) The Evolutionary Operations (EVOP) statistical principle is: A) used when manufacturing processes are not yet in control Answer: B EVOP is to applied on processes that are already in control and producing conforming product. The goal is to make small response improvements using large samples. The risk becomes minimal since the manufacturing process is already in control. 19) Hidden replications is the advantage in DOE that brings the power of efficiency. True or False Answer: True 20) Identify the number of factor levels required by the following response surface designs. A) Inscribed Central Composite (CCI) Answer: Inscribed Central Composite (CCI) = 5 factor levels The CCI and CCC are higher order designs. All four of them are considered response surface methodology designs. CCI, CCC, and CCF are types of central composite designs. 21) A 3D response surface experiment has the following equation: y = 6.0 + 0.2x1 +2.5x2 + 9.3x22 + 3.8x1x2 Identify the slope, curve, and twist components Answer: Two slope components: 0.2x1 and 2.5x2. The curve component is 9.3x22. The twist component is 3.8x1x2 22) Which of the following are considered Central Composite Designs? Which are considered Response Surface Methodology designs? 1) Inscribed Central Composite (CCI) 2) Circumscribed Central Composite (CCC) 3) Box-Behnken 4) Face Centered Composite (CCF) Answer: 1,2, and 4 are Central Composite designs. All of these are RSM designs. Learn more at DOE 23) The primary objective in removal of waste is to reduce the amount of time in the Order Production Cycle where starts at the time from of _________________ to the time of _______________ . In other words reduce the cash conversion cycle. A. Payment of raw materials | customer approval B. Receipt of an order | product development C. Receipt of an order | receipt of payment for that order D. Letter of Intent | shipment of the order to the customer Answer: C See the sections of Financial Savings and 7-Wastes for more insight. 24) R2 is a measure that describes the quality of regression which represents the proportion of variation that is explained by the regression model (equation). Which formula is correct below: SS = Sum of Squares A) R2 = SSregression/ SStotal B) R2 =(SStotal - SSerror) / SStotal C) R2 = 1 - [SSerror/SStotal] D) All of them Answer: D. They all are different formulas to get the same result. Recall the SStotal = SSregression + SSerror CONTROLThe following are example questions that will test your knowledge of the concepts within the CONTROL phase of a DMAIC Six Sigma project. 1) Which of the following tools is handed off from the Six Sigma Black Belt (or other Belt) to the Process Owner after control of the effect has been established and statistically proven? A) Pareto Answer: D The process owner uses a Control Plan to help monitor and react to Y and its behavior after the project is formally closed. 2) Which of the following are characteristics of the RPN? There may be more than one answer. A) The lower the value the lower the risk to the project output, Y. Answer: A,B,C It is also the EFFECTS * CAUSES * CONTROLS - which is another way of saying the SEV * DET * OCC. Visit the FMEA module for more information. 3) With 50 samples (n=50), a process has a p-bar of 0.25. What are the upper and lower three sigma limits (UCL/LCL)? A) 0.25 and -0.25 Answer: C Must use the formula to calculate the NP Chart control limits. 4) Which of the following a characteristics of the C-Chart, there may be more than one choice? A) Plotting number of defects Answer: A,C,D Visit C Chart for more information. 5) Which type of chart (of the choices below) is typically used when plotting continuous (can apply to attributes data) data to detect small changes over a small period of time? The moving average smoothens the variation of time therefore should not be used when looking for a point that is outside of the process control limits. A) I-MR Answer: C Visit Exponentially Weighted Moving Average Chart for more information. The most recent data point is given the most weight and as time progresses the weight of the older points decreases. The term exponentially means that the weights of the older points decrease exponentially with time. CUSUM charts use equals weights for previous data points. 6) Which of the following a characteristics of the U-Chart, there may be more than one choice? A) Plotting number of defects Answer: A,C,D Visit U Chart for more information. 7) Which of the following a characteristics of the NP-Chart, there may be more than one choice? A) Plotting number of defects Answer: B,D Visit NP Chart for more information. 8) If the Rolled Throughput Yield is known to be 47.5% and there are three processes what is the Normalized Yield (NY). A) 47.5% Answer: C There are three processes so K = 3 There is a 78% chance of a unit passing through one process step without rework. 9) If the Normalized Yield (NY) is 78.0% what is the normalized defects per unit? A) 0.248 Answer: A The normalized defects per unit equals the negative natural log (-ln) of the NY. 10) The following data will be applied to the questions 10-15. This type of knowledge may be used in the Measure and Control phase.
What are the Total Opportunities for a Defect (TOP)? A) 15,000 Answer: A The total opportunities is the number of widgets multiplied by the number of potential defects in each widget which is 1,000 * 15 = 15,000. 11) How many units were found to have zero defects? A) 110 Answer: B 12) What is the Defects Per Unit (DPU) rate? A) 0.110 Answer: C Defects per unit is the number of defects found among all units sampled. Divide 228/1000 = 0.228. 13) What is the Defects Per Million Opportunities (DPMO) rate? A) 12,000 Answer: C DPMO = 228/15000 * 1,000,000 = 15,200 There were 228 defects found among 15,000 total opportunities therefore, applying the same ratio there would be 15,200 defects expected over the long term if there were one million opportunities. 14) What is the Process Yield? A) 98.48% Answer: A The Process Yield is the percentage of time a defect is not created when an opportunity exist. 1.52% is the % defects (228/15,000) and the Process Yield is 100% - the % defects which is 98.48%. Do not confuse % Defects with % Defective. The % Defective in this example is 110/1000 = 11.00% 15) What is the long term process sigma estimate (assume zero sigma shift)? A) 1.13 Answer: D Get the DPMO and Sigma Calculator Template to further explain all of these calculations and run your own scenarios. 16) To monitor a project after it is closed you decide to gather 17 samples of a widget each day for two weeks and examine the diameter specification measured in micrometers. Which is the most applicable control chart? A)
x-bar, r chart Answer: B When gathering >8-10 samples the x-bar, s chart (which uses the standard deviation) becomes a better estimate for the process variation than the range. 17) The Rolled Throughput Yield of 6 process steps 65%. The Throughput Yield (TPY) of processes 1,2,4,5, and 6 are 98%, 87%, 89%, 92%, and 99% respectively. What is the TPY of Process 3? A) 65% Answer: B The RTY is the product of all process TPY's. So set up the following and solve: 0.65 = (0.98*0.87*0.89*0.92*0.99) * (TPY of Process 3) TPY of Process 3 = 0.940 = 94% Get the RTY Template to further explain all of these calculations and run your own scenarios. See the RTY module for more information. 18) Which of the quality gurus is credited with creating control charts while working at Bell Laboratories? A) Ishakawa Answer: D 19) Given a normally distributed set of data we know the following: The mean length is known to be 510.7 mm The customer specifies that the LSL is 507 mm and the USL is 513 mm. Determine the total % of parts that can be expected to be defective? A) 0.66% Answer: B This is a two-part problem. FIRST: Determine the % of parts >513 mm. z = (513 mm - 510.7 mm) / 1.49 mm = 1.54 Referring to a z-table that score equates to 6.8% SECOND: Determine the % of parts <507 mm. z = (507 mm - 510.7 mm) / 1.49 mm = -2.48 Referring to a z-table that score equates to 0.66% The total expected defective parts related to the length are 6.8% + 0.66% = 7.46% 20) If a carbon monoxide alarm goes off indicating a high level alert but there is actually not a high level then what response(s) below describe this situation: A)
Beta Risk Answer: B 21) If a carbon monoxide alarm does not go off indicating a high level alert but there is actually a high level then what response(s) below describe this situation: A) Beta Risk Answer: A,C,D 22) If conducting a 2-sample T test and your conclusion is that the means are different when they are actually not would represent: A) Beta Risk Answer: B,D 23) If conducting an F-test and your conclusion is that the variances are the same when they are actually not would represent: A) Beta Risk Answer: A,C 24) Instead of choosing the alternative hypothesis (indicating there is a difference), and incorrectly selecting the null hypothesis (that there is not a difference) is an example of: A) Beta Risk Answer: A,B,C. The EFFECT was not detected when in fact there is an EFFECT. 25) In this phase a Six Sigma Project Manager uses ___________ to monitor and analyze key metrics to determine if the process is moving or staying with control limits. A) SPC Answer: SPC = Statistical Process Control. 26) Which of the following statements are true:
A)
1,2 Answer: B Click here for more information of Cpk and Cp 27) Fill in the blank with the most common response: For subgroups <10 of continuous data, use the range to estimate process variation and use a _____ type of SPC chart: For example, if appraisers are measuring parts every 30 minutes and sample and measure 6 consecutive parts each 30 minute interval then the subgroup size is 6 and the range should be used to estimate the process variation. A) X-bar, R Answer: A The NP-chart is used for attribute data. The Xbar-S chart is used when plotting subgroups of size >=10. See SPC Charts for more information. 28) A FMEA is an important tools created in the Measure Phase and revised (updated) in the Control Phase. It's also commonly used in the manufacturing environments of all types. Select the benefits below of a FMEA (may be more than one answer). A) Define the value-added process steps of a value stream map Answer: B,C,D Learn more about the FMEA here. 29) Which of these are Predictive Maintenance techniques to help control a process: A) SPC Answer: C,D There are other techniques discussed here. 30) Which of following charts are most effective in detecting small but gradual shifts in a process performance? A) I-MR Answer: C and D Learn more at EWMA and CUSUM 31) Which statement(s) are TRUE about Attribute Control Charts: A) P chart is the most sensitive B) NP chart reflects the number of defects per unit C) C chart reflects the number of defects Answer: A and C Attribute Control Charts are a key element within SPC and must be a part of a Six Sigma Project Manager's toolbox. Click here to learn more. 32) What is the general association for each of the following Japanese techniques? A) Kanban Answer: Kanban - to control process flow Poka-Yoke - mistake proofing to detect and/or prevent process nonconformance Kaizen - small incremental change. 5S - workplace organization 33) A 3-step process has the following yields after the improvements were made: Y1 = 98.7, Y2 = 99.4, Y3 = 97.8 What is the Total Defects Per Unit (TDPU)? A) 0.41 B) Not enough information C) -0.041 D) 0.041 Answer: D This is a two-step problem. First find the RTY: RTY = 0.987 * 0.994 * 0.978 = 0.959494 TDPU = -ln (RTY). Therefore, the TDPU = -ln (0.959494) = 0.041 34) A Six Sigma team is calculating the final z-score to close out a project. The data shows an average of 102 part per minute, standard deviation of 10, and the customer has provided an USL of 142 parts per minute. Determine the z-score A) 40 B) 4.0 C) 10 Answer B. See the z-score module. The point of interest, x, = 142. Therefore z = (142-102) / 10 = 4. 35) Which attribute control chart is used when:
Each observation is independent. The word "defective" is also sometime referred to as "nonconforming". This chart is also referred to as a control chart for fraction nonconforming. Answer: P-chart Return to DMAIC Six Sigma Certification options Templates, Tables, and Calculators Search for Six Sigma Jobs Return to the Six-Sigma-Material Home Page |