Lean Six Sigma Green Belt - Practice Exam 1

If residuals for a regression model are distributed normally, then about 95% of the standardized errors will lie within ________ interval. (-1, +1) (-2, +2) (-3, +3) (-6, +6)

(-2, +2) For data that are normally distributed, the empirical rule tells us that 95% of the observations fall within 2 standard deviations of the mean. Therefore, 95% of the observations with a standardized residual fall between -2 and +2.

A Belt gathered the following defect data for a shoe production line and wanted to assemble it into a Pareto chart. What is the correct order from left to right in the chart? Data: Cutting—58, Forming—67, Stitching—46, and Sealing—62. A) Forming, Sealing, Cutting, Stitching B) Sealing, Stitching, Forming, Cutting C) Stitching, Sealing, Cutting, Forming D) Forming, Cutting, Sealing, Stitching

A A Pareto chart is a bar chart for attribute (or categorical) data categories that is presented in descending order of frequency.

In the case of a sign test, if a tie occurs, how do we manage these ties? A) Set them aside and apply the test on the remaining data. B) Assign the tie terms to the mean rank value. C) Assign the tie terms to the median value. D) Set the tie terms to the highest ranked sign.

A When performing the sign rank test, ties are ignored because ties produce a difference of zero. A difference of zero cannot be assigned a plus or a minus sign; therefore, they are ignored. The test is applied to the rest of the data.

Which of the following tests would be used to compare the means of the three teams? 2-sample t-test 1-sample t-test ANOVA test Mood's median test

ANOVA Test For comparing means of more than two samples, an ANOVA test is used.

What is another name for an Ishikawa diagram? *Fishbone diagram *Cause and effect diagram *6 M diagram *All of the above

All of the above Ishikawa diagrams (also called fishbone diagrams, 6M, herringbone diagrams, or cause and effect diagrams) are causal diagrams created by Kaoru Ishikawa that show the causes of a specific effect.

Which of the following sources for errors can be quantified using statistical analysis? *Error in measurement *Bias in sampling *Error in sampling *All of the above

All of the above There are four types of error contributing to uncertainty when trying to infer with data. 1. Error in sampling 2. Bias in sampling 3. Error in measurement 4. Lack of measurement validity

Customers make a purchase decision based on a number of factors. In Lean Six Sigma, we refer to these decision points as: *Critical to quality. *Cost to quality. *Critical to quantity. *Cost of the quantity.

Critical to Quality CTQ trees (critical to quality trees) are the key measurable characteristics of a product or process whose performance standards or specification limits must be met in order to satisfy the customer.

Process capability is a function of: *Customer requirements. *Process performance. *Customer requirements and process performance. *None of the above.

Customer requirements and process performance. Process capability is the inherent ability of a process to meet the expectations of the customer. Process capability is a function of customer requirements and process performance and can be calculated by the VOC to VOP ratio, where VOC is the voice of the customer and VOP is the voice of the process.

Which of the following is applicable when nonparametric testing is done? A) A hypothesis test for the sample groups that come from unknown distribution cannot be transformed into normality. B) It does not require that data are drawn from normally distributed populations. C) It looks at the median rather than the mean of populations. D) All of the above are applicable.

D A nonparametric test makes no assumptions about normality. The nonparametric test uses the median instead of the mean for the test. Therefore, if distribution is not normal or distribution is unknown and data transformation to normality is not possible, a nonparametric test should be used.

Which of the following describes the use of contingency tables? A) They evaluate the connections between two sets of categorical variables. B) They are an effective way to arrange frequency data. C) They help in finding out relative probabilities. D) Evaluate the connections between two sets of categorical variables. They are an effective way to arrange frequency data and help in finding out relative probabilities. E) Evaluate the connections between two sets of categorical variables and are an effective way to arrange frequency data.

D Contingency tables are used to evaluate the connections between two sets of categorical variables. They are an effective way to arrange frequency or count data and help in finding out relative probabilities to evaluate associations between these variables using chi-square statistics.

What is one of the advantages of the EWMA control chart? A) An EWMA control chart is easy to use. B) EWMA control charts are widely applicable. C) It is easily interpretable. D) It can provide the forecast on the process mean for the next time period.

D EWMA control charts are as good as CUSUM control charts. However, EWMA control charts are also capable of providing the forecast on the process mean location for the next time period.

What is the main responsibility of a Six Sigma Master Black Belt? A) To impart training to the employees B) To provide financial support to Six Sigma projects C) To run Green Belt and Black Belt projects D) To drive Six Sigma culture in the company

D Six Sigma Master Black Belts are at the top in Six Sigma belts hierarchy. The main responsibilities of a Master Black Belt are to drive Six Sigma culture and mentor Black Belts to lead various improvement projects. Master Black Belts also identify improvement opportunities at the strategic level and lead some high-impact strategic-level improvement projects.

A plant manager wants to determine which raw materials supplier he should pick for a new product line that is coming out. After doing research, the plant manager collected some data on the delivery cycle time for each supplier. Supplier A's mean cycle time is 2 days, and Supplier B's mean cycle time is 3 days. What is the alternative hypothesis for this example? A) The mean cycle time for Supplier A is equal to 2 days. B) The mean cycle time for Supplier B is not equal to 3 days. C) The population mean cycle time for Supplier A is equal to the population mean cycle time for Supplier B. D) The population mean cycle time for Supplier A is not equal to the population mean cycle time for Supplier B.

D The plant manager is comparing two suppliers in terms of their delivery cycle times. The null hypothesis states that the population mean cycle time for Supplier A equals the population mean cycle time for Supplier B. The alternative hypothesis states that the population mean cycle time for Supplier A ǂ the population mean cycle time for Supplier B.

T/F Alpha and beta risks are related to each other when the sample size is large (more than 30).

False

T/F A 1-sample t-test is used when you want to compare the median of a sample to a target value.

False A 1-sample t-test is a test for the comparison of means. It is used to compare the mean of one sample with a target value. It is used when the data are normally distributed.

T/F For non-normal independent samples, we should prefer the Kruskal-Wallis test over the Mood's median test if samples have lots of outliers.

False For non-normal independent samples, we should prefer the Kruskal-Wallis test over the Mood's median test if samples have lots of outliers.

T/F Inferential statistics use the population to develop conclusions.

False Inferential statistics use a random sample of data taken from a population to describe and make inferences about the population.

T/F The Mann-Whitney test is used to test the equality of means from two sample groups.

False Mann-Whitney is used when comparing medians from two sample groups because it is a nonparametric test.

T/F Rolled throughput yield adds the consideration of rework.

False Rolled throughput yield excludes rework and scrap in the calculation.

T/F While drawing a sample, we do not need to worry about the sample being a representative of the whole population.

False The sample should be the representative of the entire population under study in order to draw meaningful inferences.

T/F When conducting a hypothesis test, sample size does not contribute to the confidence interval of the test, regardless of the type of data.

False The sample size plays a significant role in the confidence or confidence interval. Larger samples provide better results by decreasing the width of CI and reducing the standard error.

T/F In statistical hypothesis testing, you must establish the type 2 error first and then define the value of the type 1 error.

False We must establish the type 1 error first by defining the confidence level prior to considering the type 2 error. Increasing the sample size reduces the type 2 error; however, increasing the confidence level reduces the type 1 error.

SPCs are the ways to control the process that: *Eliminates poor quality. *Measures process variability. *Measures product specifications. *Identifies quality problems.

Measures process variability SPCs are used to measure and monitor process variation. They helps to understand whether there is any special cause variation in the process or not. Therefore, they help in identifying and addressing quality issues.

Poka-yoke is also known as: *Thorough integration. *Mistake-proofing. *On-site inspection. *Kaizen.

Mistake-proofing. Poka-yoke is a Japanese term that means mistake-proofing.

Bill Smith coined the term Six Sigma and is known as the Father of Six Sigma. He was an engineer with: *Motorola. *Allied Signal. *General Electric. *Honeywell.

Motorola The term "Six Sigma" was coined by engineer Bill Smith while working at Motorola in the 1980s.

Which control chart is used for rejection data with the same number of units in each sample? *P chart *U chart *Np chart *C chart

NP Chart The np control chart is used for discrete data when we want to plot defective/rejection data with a constant sample size.

A Six Sigma project was finally concluded by a Belt with the control plan draft completion. When should the control plan be closed? *As soon as the champion signs off *Never *After a month *After the project's expected benefits are realized

Never A control plan has a description of each process step and the input/output parameters that need to be kept in control to ensure optimized performance. They are living documents and should be periodically reviewed and updated as necessary.

Is the distribution shown in the graph normal? Mean = 14.91 St Dev = 5.147 N = 68 AD = 1.794 P-Value = <0.005 *Yes *No

No Because the p-value is ˂ 0.005, which is less than α (alpha) = 0.05, data follow a non-normal distribution.

Which chart would be used to look for variation and trends in the data in case of discrete data after a Belt has put data through the smoothing process? *Individual moving range chart *P chart *X-bar R chart *Pareto chart

P chart The P chart would be used to look for variation and trends/patterns in case of discrete data. The individual moving range chart and X-bar R chart are used for continuous data. The Pareto chart is used to identify the vital few significant Xs out of a list of various Xs.

A call center manager is reviewing a fitted line plot. The manager is trying to decide if the number of call representatives during a shift impacts the resolution time of a call. While reviewing the fitted line plot, it can be seen that as the X increases, so does the Y. What kind of impact does the X have on the Y? *Positive impact *Negative impact *No impact *Not enough information to know

Positive impact When looking at a fitted line plot, a positive impact or positive slope happens when the Y increases as the X increases. The call center finds the same relationship between X and Y, hence X has a positive impact on Y.

What does the "s" denote in X-bar and S charts? *Sample *Sample standard deviation *Process standard deviation *Statistics

Process standard deviation Both S charts and R charts measure subgroup variability. The S chart uses the standard deviations within subgroups as plotting points and represents the entire process variability by capturing within subgroup as well as between subgroup (subgroup-to-subgroup) variations. Therefore, the "s" denotes process standard deviation.

Hypothesis testing is done on a test that is conducted on the basis of observing a process that is modeled via a set of: *Random variables. *P-values. *Standard deviations. *Null values.

Random variables. A test statistic is a random variable used to determine how close a specific sample result falls to one of the hypotheses being tested. That is, the test statistic tells us if H0 is true, how likely it is that we would obtain the given sample result.

The difference between the highest value and the lowest value in the data set is known as the: *Breadth. *Range. *Standard deviation. *IQ range.

Range Range = Maximum - minimum

If there is a deviation in the control plan, what should the BB have in the control plan to take care of this situation? *FMEA *Control charts *Reaction plan *None of the above

Reaction plan The control plan should contain the reaction plan or response plan. In case of any deviations to the original control measures deployed, the reaction plan should show what needs to be done.

Improving the process capability (Cpk) will ____________the requirements of quality control activities such as inspections and testing. *not change *increase *completely eliminate *reduce

Reduce A process with higher capability has a very low probability of generating defectives. The higher the process capability, the better the process is at meeting specifications. Therefore, the chances of deploying quality control activities are reduced when the process capability improves.

What is the term for the closeness of the agreement between the results of successive measurements by the same operator that are taken by a single instrument and carried out under the same conditions of measurement? *Repeatability *Bias *Linearity *Reproducibility

Repeatability Repeatability is the variation in measurements obtained by one individual measuring the same characteristic on the same item with the same measuring instrument.

During analysis, a Belt has observed that the actual experimental response data varies slightly from the predicted values. This can be a result of: *Inefficient estimates. *Residuals. *Sample data. *Gap analysis.

Residuals Residuals, or errors, are the differences between predicted values and actual experimental Y values.

In Lean enterprise, which of the following is not an example of a visual factory? *White outlines on floor for proper inventory placement *Visual dashboards *Monitor displaying process KPIs *Sign boards in the lobby area *Risk analysis using FMEA templates

Risk analysis using FMEA templates FMEA is not a part of the Lean visual factory and is generally not displayed in the factory.

Which of the following charts will be used to study observed data for trends or patterns over a specified period of time and focus attention on vital changes in the process? *Data forward chart *Scatter plot *Min/max plot *Run chart

Run chart A run chart shows trends and patterns over time and is used to assess the stability of the process.

___________ are measurements of potential consequences (±) on other areas of a process as a result of changes in the primary metrics. *Parallel process metrics *Industry standards *Tertiary metrics *Secondary metrics

Secondary metrics The purpose of defining and measuring secondary metrics within an improvement project is to measure the effects on other areas as a result of changes in the primary metric.

Which of the followings is not a 5S technique? *Sort *Set in order *Shine *Standardize *Simulate

Simulate 5S stands for sorting, set in order, shine, standardize, and sustain.

When the data accuracy varies over time, what is the problem with the measurement system? *Repeatability *Stability *Linearity *Bias

Stability Stability-related issues address changes in the accuracy or bias over time. Bias is an error resulting in the difference between the true value and the measured value. Linearity is the accuracy across the measurement range of the measuring device. Repeatability issues are variations due to precision problems, not due to accuracy.

The accuracy of a measurement system addresses: *Stability, bias, and linearity. *Repeatability and reproducibility. *Stability and sensitivity. *Precision and sensitivity.

Stability, bias, and linearity. Measurement accuracy describes the difference between the observed average and the true average based on a master reference value for the measurements. Stability is accuracy over time. Linearity is accuracy throughout the measurement range. Bias is offset from the true value.

According to the central limit theorem, _________is the measure of the dispersion of the distribution formed by sample means around the population mean. *standard error *mean deviation *mean spread *mean error

Standard error As per the central limit theorem, the standard deviation for the distribution of sample means is known as the standard error. The value of the standard error is σ/√n, where σ is the population standard deviation and n is the sample size drawn from the population.

T/F By using the empirical rule, we estimate the probability of an event occurrence with reference to the standard deviation from the mean of normal distribution.

True The empirical rule is an important rule in the field of statistics and is often known as the three-sigma rule or the 68-95-99.7 rule. By using this rule, we can estimate the probability of an event occurrence with reference to the number of standard deviations from the mean of normal distribution. This rule also provides a way for a distribution's normality test. If too many data points are falling outside of the three standard deviation boundaries, this might suggest that the probability distribution has skewness and is thus not normal.

T/F Cost of poor quality, or COPQ, indicates visible (hard) costs as well as hidden (soft) costs.

True Cost of poor quality (COPQ) captures visible (hard) costs (e.g., scrap reduction and cycle time improvements) and hidden (soft) costs, which are hard to identify, (e.g., gaining lost sales and customer loyalty).

T/F Hypothesis testing can help in avoiding high costs of experimental efforts by using historical data.

True Experiments involve high cost, time, and effort to determine the significance, while hypothesis testing can help in avoiding these experimental efforts by using historical data.

T/F In the Box-Cox transformation, "y" transforms to "ln y" when the value of λ (lambda) is zero. ("ln y" is the log of y to the base e.)

True In Box-Cox transformation, each value of "y" is raised to the power of λ. When λ (lambda) approaches zero, "y" transforms to "ln y."

T/F The objective of Lean is to reduce or eliminate waste to make the process shorter, faster, and low cost.

True The essence of Lean is to concentrate effort on removing waste while improving the process flow to achieve speed and agility at a lower cost.

T/F The voice of the process (VOP) represents the performance and capability of a process to achieve both business and customer needs.

True VOP is usually expressed as an efficiency and/or effectiveness metric in a process. It represents the process performance and capability to achieve both business and customer needs.

T/F Kanban is designed to reduce the idle time in a production process. The main idea behind the kanban system is to deliver exactly what the process needs as per the demand for it.

True Kanban is a visual system for managing work as it moves through a process. Kanban visualizes both the process (the workflow) and the actual work passing through that process. The goal of kanban is to identify potential bottlenecks in your process and fix them so work can flow through it in a cost-effective manner at an optimal speed or throughput that matches the demand.

T/F The Z-score indicates how many standard deviations apart an individual data point is from the process mean.

True Z = (x - µ)/σ, where x is an individual data point, µ is the mean, and σ is the standard deviation. The graphical significance of Z is as shown in the figure below.

T/F Kanban is used in conjunction with pull systems to align the inventory of products or materials and ensure that they are available on time at the right place.

True Kanban provides production, conveyance, and delivery information. A kanban system will not allow any goods to be moved within the facility without an appropriate kanban (or signal) attached to the goods. Kanban is the technique used to pull products and material/information through and into the Lean manufacturing system/Lean office.

T/F Lean enterprise is based on the premise that anywhere work is being done, waste generation is also occurring.

True Lean is systematic identification of waste and its elimination. Lean considers customer inputs and conducts a "war on waste." The waste is also known as muda.

T/F Measurement error is the difference between the actual value of a characteristic being measured and the value obtained by the measurement system.

True Measurement error is defined as the effect of all sources of measurement variability that caused an observed or measured value to deviate from the true value.

T/F The purpose of measurement system analysis is to qualify a measurement system for use by quantifying its accuracy and precision.

True Organizations are primarily concerned with the accuracy and precision of measurements to determine the usability and reliability of the data.

T/F Process mapping describes how activities are performed and how the work effort flows.

True Process mapping is the technique to illustrate the flow of a process. It describes how activities are performed and how the work effort flows. Process mapping can proceed from the macro perspective to the level of detail required to identify opportunities for improvement.

T/F EWMA and CUSUM charts are able to detect any small shift in a process mean, which is not possible with a conventional Shewhart control chart.

True Shewhart control charts are unable to detect process shifts within 1.5 σ. In order to overcome this limitation, EWMA and CUSUM charts can be used for sensitive processes. They are able to detect any small shift in process mean.

T/F The X-Y diagram is a tool used to show the how and what relationship between two sets of data.

True The X-Y diagram is a tool used to identify and collate potential Xs and assess their relative impact on multiple Ys (including all Ys that are customer-focused).

T/F Having an alpha of 0.05 is the most common risk level when running a statistical test.

True The alpha risk is the probability we could be wrong in saying something is "different." An alpha of 0.05 is the most common one in the field of inferential statistics.

T/F Bias in sampling can be explained as a sample that is collected in such a way that some members of the intended population are less likely to be included than others.

True The biased sample is defined as a statistical sample of a population in which all participants are not equally balanced or objectively represented. Sampling bias occurs when a sample data is not appropriately representative of its population.

T/F The company XYZ Co. deals in flashlight manufacturing and exports to three major countries. In business unit A of XYZ, there are too many flashlight returns, and flashlight sales have decreased by 25%. This is an example of a business case.

True The business case is a high-level articulation of the area of concern. This case answers two primary questions: What is the business motivation for considering the project? And what is our general area of focus for the improvement effort?

T/F The central limit theorem states that as the sample size becomes large, the sample mean distribution will form a normal distribution no matter what the shape of the population distribution of individuals is.

True The central limit theorem states that as the sample size becomes large (> 30), the distribution of sample means will form a normal distribution no matter what the shape of the population distribution of individuals is.

During a hypothesis test, a Six Sigma team lead discovered that the null hypothesis was not rejected when a difference between the means existed. What type of error occurred? *Type 2 *Mistake *Type 1 *Alpha

Type 2 A type 2 error indicates failing to reject the null hypothesis when a difference exists. On the contrary, a type 1 or alpha error indicates rejecting the null hypothesis when in reality it is true (i.e., there is no difference).

Which Lean tool is used to understand the sequence of process activities, various downstream and upstream flows, and other relevant information to deliver a product or a service? *Service value *Production flow *Value-added product flow *Value stream

Value Stream The Lean method requires understanding of the flow through the value stream and other relevant information when products and services are delivered. Hence the value stream is used in a Lean practice.

Which hypothesis test would you use when you want to compare median scores of two dependent samples of a dependent variable that is not normally distributed? *Mood's median test *2-sample t-test *Wilcoxon sign test *Chi-square test

Wilcoxon sign test The Wilcoxon signed-rank test or Wilcoxon sign test is a no-parametric analysis that statistically compares the medians of two dependent samples and assesses for significant differences. The Wilcoxon sign test is the nonparametric alternative of the dependent samples t-test or paired-t test.

Control limits are the bounds: *Within which the process is expected to operate. *Set by the customer. *That are the same as specification limits. *None of the above

Within which the process is expected to operate Control limits are the upper and lower bounds in a control chart that are determined by the process itself. They can be used to detect special causes of variation. They are usually set at ±3 standard deviations from the central tendency.

Which control chart should be plotted for continuous data when the subgroup size is between 3 and 5? *Moving average chart *X-bar S chart *X-bar R chart *X chart

X-bar R chart X-bar R charts are used when the subgroup size is greater than 1 and typically less than 9 or 10. Because the subgroup size is 3 to 5 in the given question, an X-bar R chart will be used.

Six Sigma is based on a process approach, also known as a problem-solving strategy. Which equation explains this process approach? *y = mx + c *y = f(x) *y = fx + c *y = f(x +c)

y = f(x) The y = f(x) equation is known as the process approach, transfer function equation, or problem-solving strategy that is used in Six Sigma. This equation focuses on the impact of x (independent variable) on y (dependent variable).

Calculate the cycle time (in seconds) if the process has a throughput rate of 6,500 units per hour? *0.30000000000000004 *0.55 *1.8 *108

0.55 Cycle time = Time in sec per unit = 1/(6,500/60 × 60) = 60 × 60/6,500 = 0.55 sec.

To show the benefits of a project in terms of monetary value, what is the standard period of time considered post project completion? 6 months 12 months 24 months 3 months

12 months In a Six Sigma project, it is expected that the savings of a project will be calculated in terms of the monetary value for a period of 12 months from project completion. These savings are considered the tangible project benefits.

What is a distribution plot that has two peaks called? *A transformed distribution *A Weibull distribution *A bimodal distribution *A normal distribution

A bimodal distribution The number of peaks in a distribution denotes the number of modes. Mode is a measure of central tendency that captures the highest occurring data point in a given data set. A data set with two modes is called bimodal. Normal distribution has a single mode or peak. We can use the transformation function on each data point of a given data set to get transformed distribution, and it is generally the case when we want to transform non-normal distribution into normal distribution. Weibull distribution has generic distribution functions with shape and scale parameters.

In order to support green initiatives, ABC Ltd is considering subsidizing public transportation for its employees to get to work. ABC queried its managers and learned that if the managers use their personal vehicle, it takes an average of 55 minutes with a standard deviation of 8 minutes for them to commute to work on weekdays. However, the management set a policy of taking not more than 50 minutes for their daily one-way office commute. One day ABC conducted a survey of 70 employees. It showed an average of 34 minutes commuting time with a standard deviation of 6 minutes when they use the metro public transportation system. Assuming that commute times follow a normal distribution in both directions, which of the following statements is true? A) The probability of employees arriving on time using personal vehicles is significantly higher than when using the metro public transport. B) The probability of employees arriving on time using the metro public transport is significantly higher than when using personal vehicles. C) Both the probabilities are the same, as both follow the same distribution. D) If the standard deviation is higher, the probability goes down. Therefore, the metro system is worse.

B Commute time data for both transportation mediums (personal vehicle and metro system) follow normal distribution. If z1 and z2 are the sigma levels for the two modes in order, then z1 = (policy_target - avg_time_taken)/std. dev. = (50 - 55)/ 8 = -5/8. Similarly, z2 = (50 - 34)/6 = 14/6 = 7/3. As z2 > z1, the probability that employees would arrive at the office on time using the metro transport service is significantly higher than by using their personal vehicles.

FMEA is used to identify and prioritize risks. What does FMEA stand for? A) Fault measures for effective actions B) Failure mode and effects analysis C) Future mistakes and elimination actions D) Fault monitoring and evaluation analysis

B FMEA stands for failure mode and effects analysis. This is a step-by-step technique for identifying all the potential failure modes in a design, a process, equipment, or a product or service. We derive an risk priority number (RPN) in FMEA, which is a product of severity, occurrence, and detection ratings.

In descriptive statistics, population standard deviation is denoted by _____, and sample standard deviation is represented by ______. A) s; σ B) σ; s C) p; s D) µ; s

B Population parameters in statistics are often denoted by Greek symbols. Population standard deviation is represented by σ, pronounced as sigma, while sample standard deviation is defined by s.

Which of the following is not the primary reason of the regression analysis? A) It is used when we expect a cause-and-effect relationship between the output and inputs. B) It is done only and only when we want to establish a nonlinear relationship between output and input(s). C) It helps to study about how to predict output using the input(s). D) It determines the mathematical equation between output and input(s).

B Regression analysis is done when we expect cause-and-effect relationship between the output and inputs. We can determine the regression equation (a mathematical equation) between the dependent variable and the input or independent variables that is used to predict the values of the dependent variable (Y) for the given values of independent variables (Xs). However, regression analysis can be done for linear as well as nonlinear relationships between output and inputs.

Which of the followings summarizes data about the shape, dispersion, and center of the data? *SIPOC *Multi-vari chart *Box plot *Pareto chart

Box plot A box plot summarizes data about the shape, dispersion, and center of the data graphically.

Below is the multi-vari chart to study the variation in metal strength due to metal type (15/18/21) and heating time (hours.). What should you conclude? Metal 15: 30 min 21.4, 1 HR 20.3, 1.5 HR 17.2 Metal 18: 30 min 20.2, 1 HR 24, 1.5 HR 21.3 Metal 21: 30 min 19.2, 1 HR 20.3, 1.5 HR 22 A) There is no interaction between metal type and time. B) Metal 15 shows a lot of variation for different time values. C) Metal 15 shows a lot of variation for different time values, whereas Metal 18 has superior strength on average as compared to the other two types. D) Metal 18 has superior strength on average as compared to the other two types.

C As shown in the multi-vari chart, Metal 15 has a lot of variation in response in the range from 17.33 to 21.33, while Metal 21 has the least variation among the three in the range of 19.33 to 22. Metal 18 has the highest strength value for a period of 1 hour and has superior strength on average with the value 21.88.

Which of the following is an example of discrete data? A) A train is running late by 3 hours. B) A race car consumed 23 gallons of gas. C) The number of phone calls answered was 35 for the day. D) It took 3 hours and 32 minutes to complete the marathon.

C Discrete data is based on counts. Only a finite number of values is possible, and the values cannot be subdivided meaningfully.

Which is the easiest and most effective way to map the process? A) Interview the process owner. B) Interview the manager of the department. C) Walk through the actual process from beginning to end. D) Take pictures of the factory floor during each shift.

C The easiest and most effective way to map the process is to conduct a process walk thoroughly. It is a great way to learn the process and confirm if what you have been told or documented is the reality.

What type of control chart would be used to monitor the number of defects in the output of a process for making rope? *I-MR chart *X-bar R chart *C chart *P chart

C chart For plotting defects data that is the attribute data, we use the C chart for a constant sample group size. I-MR and X-bar charts are used for continuous data. P charts are used for defective data.

The Mood's median test uses ________ distribution for computing the differences while comparing group central tendencies. *binomial *rank *chi-square *F

Chi-square In inferential statistics, the Mood's median test is a nonparametric test. It is a special case of Pearson's chi-square test. To compare the counts of sample values that are greater than the overall median and less than or equal to the overall median, the Mood's median test uses contingency table.

Which test statistic is associated with the goodness of fit test? *t *Z *chi-square *F

Chi-square The goodness of fit test is one of the chi-square tests. It uses chi-square test statistics to draw inferences and is popularly used to compare a group's probability distributions.

Which statement is not correct for the regression analysis shown here? Regression Equation: Rating = −0.7560 + 0.15453 Conc + 0.21705 Ratio + 0.010806 Temp + 0.09464 Time A) This regression is an example of multiple linear regression. B) Conc, Ratio, Temp, and Time factors have a significant impact on rating. C) Around 70% of variation is explained by the independent variables. D) Conc, Ratio, and Temp factors have a significant impact on Rating.

D There is more than one independent variable, so it is an example of multiple linear regression. R-Sq. (adj) explains 68.9% (close to 70%) variability in the dependent variable by independent variables. Since the p-value of Conc, Ratio, and Temp factors is less than 0.05, they have a significant impact on the dependent variable at 95% confidence level. However, the p-value corresponding to Time factors is more than 0.05, and so Time has no significant impact on Rating.

In which of the following cases is it best to use multiple linear regression (MLR)? A) Assessing whether or not one dependent variable can be predicted from a set of independent variables B) Determining how much variance in a dependent variable can be explained by independent variables C) When the BB does not know which independent variables will create the best prediction D) All of the above

D When there is one dependent variable (Y) and one independent variable (X), we use simple linear regression to predict the value of Y. In case of more than one independent variable (X), we need to use multiple linear regression. Also, because we do not know which independent variable (X) will have a significant impact on Y, this needs to be checked using multiple regression. It is used to determine how much variance in a dependent variable can be explained by multiple independent variables.

Six Sigma's general approach to solving complex problems of a process when the causes and solution are not known is called: DOE. SIPOC. DMAIC. FMEA.

DMAIC DMAIC provides the method for applying the Six Sigma philosophy in order to improve processes.

An organization has carried out financial evaluation of the Six Sigma project because the organization wants to: *Know the opinion of the finance department. *Determine the worth of the project. *Engage the chief finance officer during the project. *Encourage the project team.

Determine the worth of the project. Financial evaluation of the project is done to determine the financial worth or value of the project.

The improvement project team in a manufacturing unit is working on a project to improve customer satisfaction ratings on newly introduced products. They have proposed an action plan to improve the product ratings. During the implementation stage, the team wants to track the improvements in month-to-month ratings. Which hypothesis test should they use to compare the ratings before improvement, during improvement, after a month, after 2 months, and after 3 months? For each of the four paired samples, they have 12 records for product ratings. *Mood's median *ANOVA *Friedman *2-sample t

Friedman The Friedman test compares medians of three or more matched groups. The Mood's median test compares medians of three or more non-matched groups. The 2-sample t-test and ANOVA tests are applied to compare means of two groups and more than two groups with normal data, respectively.

What is the Japanese term that translates to the "real place," or where the work takes place? *Heijunka *Gemba *Hoshin Kanri *Jidoka

Gemba Gemba simply refers to the location where the value is created or the work takes place. Heijunka refers to production load balancing. Hoshin Kanri is strategic planning technique using the catchball concept. Jidoka refers to autonomation, or automation with a human touch.

Which of the following control charts should be plotted for individual continuous data points? *I-MR charts *X-bar R charts *X-bar S charts *Np and P charts

I-MR charts Individual values (I) and moving range (MR) charts are used when each measurement represents one individual value.

Graphic

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Graphical Question

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T/F Shewhart control charts have the most recent data points on the right-hand side of the plot.

True Control charts plot the data in time order (i.e., increasing time from left to right with the most recent point on the right-hand side of the chart). Therefore, we must plot the data in a control chart when the data is collected to maintain time order in plotting.

Which of the following is not an aspect of control charts? *To evaluate actual performance *To compare actual performance with goals *To define objectives *To take corrective action

To define objectives Control charts help in evaluating the performance of the process and comparing the actual performance with goals. Decisions are made based on control charts and the variation observed.

In which company can you trace the history of Lean manufacturing from its early origins? Honda Toyota Ford Motorola

Toyota

Which element of waste best describes the unnecessary movement of materials, products, and/or services? *Overprocessing *Motion *Transport *Waiting

Transport The unnecessary movement of goods, services, and/or products from one place to another is called transport waste. This typically involves using a forklift truck or smaller similar equipment to maneuver products around the factory. The situation is typically caused by overproduction and inefficient building layouts.

T/F A higher sigma level denotes better performance of a process.

True A higher sigma level corresponds to a higher yield, resulting into better performance of a process.

T/F A hypothesis test is the way to convert the practical problem into a statistical problem and then to find the statistical solution.

True A hypothesis test is the way to convert the practical problem into a statistical problem and then to find the statistical solution. It assumes two mutually and exhaustive hypothesis statements—null and alternate—as a base to conduct the test.

T/F A process can be defined as a series of actions or steps taken to achieve a particular end.

True A process is a sequence of interdependent and linked procedures that, at every stage, consume one or more resources (employee time, energy, machines, money) to convert inputs (data, material, parts) into outputs. These outputs then serve as inputs for the next stage until a known goal or end result is reached.

T/F An extreme high or extreme low value in the sample data can impact the 1-sample variance test because it inflates the variance of the sample.

True Any extreme outlier value can increase the overall sample variance, resulting in unreliability of the 1-sample variance test. Therefore, while conducting a variance test, outliers in the sample data need to be addressed.