If the chance that any of five telephone lines is busy at any instant is 0.01, then what is the probability that all the lines are busy? - ANSWER (0.01)^5
Who should complete the control phase after the successful com
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If the chance that any of five telephone lines is busy at any instant is 0.01, then what is the probability that all the lines are busy? - ANSWER (0.01)^5
Who should complete the control phase after the successful completion and implementation of the first four phases of DMAIC? - ANSWER The complete team is the most desirable option.
To increase the power of experiments, what is the best option in the hands of the Six Sigma team? - ANSWER Increase sample size
Which of the techniques used in DOE helps you in eliminating errors due to nuisance factors? - ANSWER Blocking
Hypothesis testing is usually done to: - ANSWER 1) Statistically validate if the sample mean belongs to the population, 2) statistically validate if means of two groups are the same or if they are significantly different, and 3) statistically validate if variances of two groups are the same or if they are different.
What is the concept behind PDCA? - ANSWER Continuous improvement
What are the experiments called while performing one experiment with five repetitions? - ANSWER Replications
Which type of chart is used for small shifts in variation? - ANSWER CUSUM
What are the distinct types of variation that are displayed in control charts? - ANSWER Chance (common or random) and assignable (special)
Which of the following is an advantage of the production of a product in large lots? - ANSWER Machine efficiencies
A sample is to a statistic as a population value is to a: - ANSWER Parameter
A calculation for reproducibility results in a value of 0 (zero), while repeatability yields a positive number. Without any other considerations, what conclusion can be made regarding the reproducibility result? - ANSWER A reproducibility of zero means there is no operator effect on this measurement.
The average number of major storms in a city is 2 per year. What is the probability that exactly 3 storms will hit next year? - ANSWER 0.180 or 18%
Why are scatter diagrams useful in problem-solving? - ANSWER They show relationships between variables.
The advantage of using the modern designed method of experimentation, rather than the classical OFAT, is that: - ANSWER Fewer terms and measurements are needed for valid and useful information.
What does ANOVA stand for? - ANSWER Analysis of variance
Which quality tool would not be expected to be used during the results confirmation stage of a problem solution? - ANSWER Flow chart
Use a process flow chart in the Define and Measure stage.
If 6 consecutive samples were taken from a process and precisely measured, you can still expect differences. What type of variation would be the most difficult one to determine? - ANSWER Lot-to-lot variation
Which of the following inference tests does NOT require the knowledge of a test or population variance? - ANSWER Chi-square test
Which of the following is the LEAST likely candidate to assist in the problem definition stage of Six Sigma? - ANSWER Control charts
Control charts are used in the Measure and Control phases. Remember: The process must first be brought into statistical control by detecting and acting upon special causes of variation. Then its performance is predictable, and its capability to meet customer expectations can be assessed (Cp and Cpk), which is done in the Measure phase.
What is the name of the condition if you are running a 7x4 fractional experiment, and you know factors A, B, C, D, and E are independent of each other, but you suspect factors F and G are not independent. You conducted a small sub-experiment and discovered a high correlation between factors F and G. - ANSWER Collinearity
If P(A) is 0.6 and P(B) is 0.5 and the probability of either event happening is 0.85, what is the probability of both the events occurring? - ANSWER 0.25 (additive rule)
A process has a high variability and an off-centered mean. What is the first action the team needs to take? - ANSWER Center the mean
What is the use of scatter diagrams? - ANSWER Display correlation
Five samples are drawn out of a population of 200, with each sample being of size 5. The sample means are 2, 2.5, 3, 2.6, and 4. What is the population mean? - ANSWER 2.8
In the IT sector, time and effort spent in testing the software, fixing bugs, and retesting would be considered as what type of waste? - ANSWER Defects
What is the need to plot data points on the least squares line if a probabilistic regression model exists? - ANSWER To check for fit; there may be a calculation error.
The line fitted to the paired data points must be such that the sum of the squares of the vertical distances from the points to the line is as small as possible.
A team of Six Sigma has reached the control stage of DMAIC. The team has successfully reduced the defect of fabric critical stains from 73 to 1 per fabric roll. Now what type of control chart should the team recommend? - ANSWER A control chart based on the Poisson distribution such as the u-chart.
Continuous data:
I-MR Chart (individual data points, destructive testing)
Xbar and R Chart (subgroups)
Xbar and s Chart (subgroups with SD)
Discrete data (constant or varying subgroup size):
np Chart (Defectives, # of units rejected)
p Chart (Defectives, % of units rejected)
c Chart (Defects, # of defects)
u Chart (Defects, average # of defects)
What would be considered the most important element in the deployment of Six Sigma? - ANSWER Management support
What is the attempt to reduce the impact of human error in a process called? - ANSWER Poka-yoke
What is the major weakness of the one-factor-at-a-time experiment strategy? - ANSWER It fails to account for interactions between factors.
Process capability (Cp) describes a process, often in a stable manufacturing environment, which leads to the production of a product that conforms to client and design specifications. What would be the Cp value of an ideal process? - ANSWER Greater than 1 (>1)
What does OEE stand for? - ANSWER Overall Equipment Effectiveness
The determination of a temporal variation in multi-vary charting means: - ANSWER Variation over time
Which of the following pairs is the most useful in preparing control charts, when used together, for variables data? - ANSWER X-bar and R
Which of the following describes internal failure costs? - ANSWER The costs resulting from a nonconformance detected before a product or service is provided.
Choose the control chart that is used to monitor discrete data in Six Sigma. - ANSWER p Chart
If an experiment has an alias, you can say that the two factor effects are: - ANSWER Confounded
Why would a Six Sigma practitioner use an Exponential Weighted Moving Average (EWMA) chart? - ANSWER To identify small shifts in variation
What is the definition of inventory type waste? - ANSWER Any supply in excess process requirements necessary to produce goods or services just-in-time
Which type of control chart is ideal for destructive testing? (Destructive testing = a form of MSA where the part being measured is destroyed or altered, creating an issue in reproducibility.) - ANSWER I chart (since only one unit is required to plot results at a single point in time)
Which is NOT a direct benefit of a Six Sigma project? - ANSWER Helps improve Supplier Quality
When put together, what do Repetition and Replication help the Six Sigma team determine? - ANSWER Short-term and long-term variability
What is NOT true in regard to regression analysis? - ANSWER Least squares is required to determine the best fit straight line. (It is the most common procedure but other procedures are available).
What set of basic quality tools would be the most applicable for a work team to use when there is desire to follow procedures and work instructions more closely? - ANSWER Checklists and flow charts
Why are control chart subgroup sizes generally 3, 4, 5, or 6? - ANSWER 1) They are large enough so that averages of data will follow the normal distribution, 2) larger sizes permit an opportunity for process changes within the subgroup, and 3) they permit a separation of within time from time-to-time variation.
What is the variance for a distribution of means with a sample size of 36 and a population standard deviation of 3? - ANSWER 0.25
formula:
standard deviation/square root of n, squared
3/sqrt(36) = 0.05 squared = 0.25
What is NOT an advantage of control charts? - ANSWER They provide straightforward, easily interpreted information.
What is the most important benefit of implementing Lean? - ANSWER Achieving continuous flow of product
A Six Sigma team has been created to improve the process in which a company takes orders for its products. Which of the following tools should the team use to determine all the potential pitfalls and the actual defects that occur? - ANSWER Process FMEA
According to a national grocery store chain manager, only 6% of customers who have surveys mailed to their homes return them filled out completely. What is this type of sampling error called? - ANSWER Non-response error
Which approach talks about equipment effectiveness? - ANSWER TPM (Total Productive Maintenance)
Which Six Sigma role is most likely to define objectives for an improvement team? - ANSWER Sponsor
What is accuracy? - ANSWER Getting an unbiased true value (i.e., bias, linearity, and stability).
FYI: Getting consistent results repeatedly = precision (i.e., repeatability and reproducibility).
What should the Six Sigma Green Belt do in terms of actions if Cp = 1.3 and Cpk = 0.8? - ANSWER Center the mean
Cp (process potential index) and Cpk (process capability index) are used to measure process capabilities and both compare the process spread to the specification spread. However, Cpk also considers the centering of the process distribution.
If Cp and Cpk are greater than 1.00, we can say the process is currently marginally capable. If Cpk is not equal to Cp, then the process is not centered.
Which of the following is used to test the equality of medians from two or more different populations? - ANSWER Mood's Median
While plotting a multi-vary chart on the graph paper, what metric is used for horizontal scale? - ANSWER Time (Y: continuous)
(X: discrete, e.g., work-shift, employee, product thickness, etc.)
What is the basic assumption of a null hypothesis? - ANSWER That the variables are independent.
What does an F distribution closely resemble? - ANSWER A chi-square distribution (since it is the ratio between two sample variances or two chi-square distributions).
In hypothesis testing, if someone stated one minus the level of confidence, then which of the following statistics would be under consideration? - ANSWER The alpha risk
Which best defines "Overproduction" type of waste? - ANSWER Producing in excess over the need of a specified amount
A "pull" production system is a production systems where you make as much product as you can regardless of whether the customer needs it or not. True or False? - ANSWER False
An engineer is considering a fractional factorial instead of a full factorial to analyze a process because of the large number of variables under study. Apart from the possibility of studying a large number of factors with relatively few experiments, what other characteristic will support a decision to use a fractional factorial instead? - ANSWER The process is well known and only the main factors are of concern.
Fractional factorial designs consist of a carefully chosen subset (fraction) of the experimental run of a full factorial design. They are cheaper and faster to run but do not provide information about interactions between factors.
In the theory of control charts, the distribution of the number of defects per units that vary, closely follows the: - ANSWER Poisson distribution, as it is assumed for defects.
Normal: variable data
Chi-square: variance
Binomial: defectives
What are the typical phases of the Six Sigma improvement methodology? - ANSWER DMAIC (Define, Measure, Analyze, Improve, Control)
Conceptually, which tool that is used in the Six Sigma DMAIC implementation resembles the Process Decision Program Chart (PDPC)? - ANSWER FMEA (The primary purpose of PDPC, or a contingency plan, is to limit risk and avoid failure)
FMEA is used in the Define, Analyze, and Improve phases.
Identify the post-improvement tool which would be most beneficial when generating fresh ideas after the results of an improvement process have been disappointing. - ANSWER A post-improvement brainstorming session
What type of waste is "Patient is ready to be seen but doctor is not available?" - ANSWER Waiting
Identify the relationship between Waste and Defect. - ANSWER Defect is a type of waste.
While considering the stakeholder groups, which of the following terms is closely identified with the term "community"? - ANSWER Society
A scoop samples 100/trial. What must be the average number of defects to be an 80% chance that more than one defect will be found in the sample? - ANSWER 3 (This requires using the Poisson table in reverse.)
What is the key benefit of multi-vary charting? - ANSWER It assists in the breakdown of components of variation (such as positional, cyclical, and temporal) so that improvements can be made.
It also keeps track of time when measurements are made and graphically displays the variation in a process.
When a single gage is checked by comparing the results of different operators taken at different times, a reference is being made to the gage: - ANSWER Reproducibility
For 5 factors and 2 levels, the DOE setup has 16 runs. What type of experiment is being conducted? - ANSWER Half-fractional factorial
Total # of runs = levels^factors
2^5 = 32. 16 is half of 32.
Which control chart would best fit a process in which measurement data on a product is easily obtained? - ANSWER X-bar and R charts
What is takt time? - ANSWER Average customer demand for an article
Which is the one way to analyze variance by ranks? - ANSWER Kruskal-Wallis
Mann Whitney U and Freidman test also analyzes variance ranks.
Kruskal-Wallis and Mann Whitney U analyze variance between groups and Friedman analyzes variance within groups.
What are the factors that impact the shape of the t distribution? - ANSWER Sample size and degree of freedom
What part of 5S promotes all work stations for a particular job being identical? - ANSWER Seiketsu (Standardize)
A process A, B, and C are working in series with their first pass yields as A = 94%, B = 98%, C = 99%, then the total DPU is: - ANSWER 9 per 100
A x B x C = 91.19%. TDPU = -In(RTY) = 0.09 = 9 per 100
Which statistic can be used to determine the probability of variances occurring? - ANSWER Chi-square statistic
What should practitioners be very sensitive to while plotting control charts? - ANSWER 1) The type of control charts selected, 2) the sub-group size chosen, and 3) the interpretation of the charts.
To state that a model in an experiment is fixed indicates that: - ANSWER The levels used for each factor are the only ones of interest.
In single-factor ANOVA, the assumption of homogeneity of variance applies to: - ANSWER The variances within the treatment groups (i.e., in ANOVA, the assumption is that the natural variation within each factor or treatment is the same).
Using which of the following tools can basic information about data, such as central location, width, spread, and shape be visualized? - ANSWER Histograms
Who is NOT typically a relevant stakeholder in an important project? - ANSWER Potential competitors
Encot produces computer chips for large medical and technical corporations. To determine the number of defective chips from each batch of inspected products, what type of chart should its managers use? - ANSWER P chart (as it is used for discrete or attribute data; the percentage of units rejected in defectives of varying subgroup sizes)
Which of the 5S techniques is the first step in 5S implementation? - ANSWER Seiri (Sort)
The UCL and LCL on a traditional control chart are set how many standard deviations below and above the average? - ANSWER 3
Which of the following can a Six Sigma project reduce? - ANSWER Total Failure Cost (i.e., internal and external failure cost)
For a full factorial experiment with 23 treatments and 1 replicate, how many runs can you expect? - ANSWER 46 (23 + 23)
Which tool is specifically designed to identify risks of a potential solution? - ANSWER FMEA
After a solution pilot is deployed, what type of hypothesis test should be used? - ANSWER Paired t-test
A sample ______ is used to make inferences about the population ______. - ANSWER Statistic; Parameter
Who will be the primary user of the control plan? - ANSWER Process Owner
What is the appropriate mathematical model to describe the sampling distribution of the fraction defective in a sample from a controlled process in which p bar = 0.05? - ANSWER The binomial distribution in which p bar = 0.05 (since a binomial distribution focuses on defectives).
For a process working at 3 Sigma level, how many opportunities out of one million are considered to lie outside of the specification limits provided by the customer? - ANSWER 66,807
Sigma Level -> DPMO -> % Accuracy
6: 3.4: 99.9%
5: 230: 99.9%
4: 6,210: 99.4%
3: 66,800: 93.3%
2: 308,000: 69.2%
1: 690,000: 30.1%
In which stage of a DMAIC approach should the Six Sigma team decide on making a flowchart or value stream map? - ANSWER Analyze
In terms of ease of understanding and implementation, which of the following tools is considered best to inform employees of their work roles? - ANSWER Written instructions
Which of these are categorized under Precision in a Gage R&R study? - ANSWER Repeatability and Reproducibility
Reproducibility - ANSWER The variation in measurements obtained with one instrument used several times by different operators (i.e., appraiser variation).
Repeatability - ANSWER The variation in measurements obtained with one instrument used several times by one operator (i.e., equipment variation).
I-MR Chart - ANSWER Continuous data: individual data points, destructive testing.
Xbar and R Chart - ANSWER Continuous data: subgroups, n is between 2 and 9
Xbar and s Chart - ANSWER Continuous data: subgroups with SD, n >/= 10
np Chart - ANSWER Discrete data: constant subgroup size, defectives (# of units rejected)
p Chart - ANSWER Discrete data: varying subgroup size, defectives (% of units rejected)
c Chart - ANSWER Discrete data: constant subgroup size, defects (# of defects)
u Chart - ANSWER Discrete data: varying subgroup size, defects (average # of defects)
1-sample Sign test - ANSWER median (Dependent sample t or Z test)
1-sample Wilcoxon - ANSWER median (Dependent sample t or Z test)
Mann Whitney U - ANSWER ranks (Independent samples t or Z test)
Kruskal-Wallis - ANSWER ranks based on chi-square, more powerful than Mood's Median (One-Way ANOVA)
Mood's Median - ANSWER median based on chi-square (One Way ANOVA)
Freidman test - ANSWER ranks based on chi-square (Repeated measures ANOVA)
Bias - ANSWER Measure of accuracy; distance between the measured value and the actual value.
Linearity - ANSWER Measure of accuracy; consistency of bias over a range of measurements.
Stability - ANSWER Measure of accuracy; the ability of the measurement system to show the same values every time (i.e., the change in bias over time).
Define Phase - ANSWER Define the problem, project goals, desired outcome, and customer (internal and external) deliverables.
Measure Phase - ANSWER Measure the process to determine current performance; quantify the problem.
Analyze Phase - ANSWER Analyze and determine the root cause(s) for process variation and defects.
Improve Phase - ANSWER Develop, test, and implement solutions to improve the process and eliminate defects.
Control Phase - ANSWER Control future process performance by monitoring key factors and maintaining the gains.
Define Tools - ANSWER Project charter
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