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Statistical Quality Control
Multiple choices:
1. If in a hall there are 18 persons then how many handshakes are possible?
a. 18*18
b. 18*17/2
c. 18*17
d. None of the above
2. If the number of trials be ‘n’ and the probability of occurrence be ‘p’ then the standard deviation
with respect to np, is given by:
a. (np)1/2
b. (np(1-p))1/2
c. (np)1/4
d. (np(1-p))1/4
3. For a biased coin the probability of occurrence of head is 0.4 ,if the coin is tossed twice then the
probability of occurrence of at least one head will be:
a. 0.76
b. 0.48
c. 0.64
d. 0.16
4. Factorial of 5 equals:
a. 60
b. 120
c. 24
d. 5
5. Combinatory of (4,2) equals:
a. 12
b. 8
c. 6
d. None of the above
6. ‘Economic Control of Quality of Manufactured Product’, a book by Walter A Shewhart in:
a. 1931
b. 1941
c. 1930
d. 1956
7. Quality is judged by…………
a. Retailer
b. Government
c. Customer
d. Hole seller
8. A run chart is a special chart of…………
a. Pie chart
b. Line chart
c. R chart
d. C chart
9. Universes may differ :
a. In average
b. In above average
c. At higher level
d. All of the above
10. ASQC and ANSI began in the year:
a. 1956
b. 1976
c. 1978
d. 1960
Part Two:
1. Differentiate between ‘Defect’ and ‘Defective’.
2. Explain the need of ‘short method’.
3. What does ‘Tchebycheff’s inequality theorem’ say?
4. Explain the usability of ‘stochastic limit’.
5. Write a note on ‘Cause and Effect’ diagram.
1. What marketing strategy should RSL adopt to remain competitive in the international market?
2. Has the company taken the right decision to forward integrate and enter into the highly volatile
garment market?
2. Has the company taken the right decision to forward integrate and enter into the highly volatile
garment market?
1. How could have the SQC approach, been useful in solving the immediate problems of Japan?
2. If you were among one of the management members, what would have been your first insight.
2. If you were among one of the management members, what would have been your first insight.
1. A sample of 30 is to be selected from a lot of 200 articles. How many different samples are
possible?
2. In Dodge’s CSP-1, it is desired to apply sampling inspection to 1 piece out of every 15 and to
maintain an AOQL of 2%. What should be the value of i?
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Six Sigma Green Belt
Multiple Choices:
1. The primary purpose of a control chart is to:
a. Set Specifications and tolerances
b. Compare operations.
c. Determine the stability of a process.
d. Accept or reject a lot of material
2. When a control chart is used on a new process, capability can be assessed at which of the following
times?
a. Before the chart is first started
b. After the first ten points are plotted
c. When the plotted points hug the centerline
d. After the process is shown to be in control
3. Precision is best described as:
a. A comparison to a known standard
b. The achievement of expected outgoing quality
c. The repeated consistency of results
d. The difference between an average measurement and the actual value
4. The overall ability of two or more operators to obtain consistent results repeatedly when measuring
the same set of parts and using the same measuring equipment is the definition of:
a. Repeatability
b. Precision
c. Reproducibility
d. Accuracy
5. Which of the following conditions must be met for a process to be in a state of statistical control?
a. Most of the product out by the process is in specification.
b. All subgroup averages and rang are within control limits.
c. All variation has been completely removed
d. Previously optimal process settings are used.
6. Which of the following measures of dispersion is equal to the sum of deviations from the mean
squared divided by the sample size?
a. Range
b. Standard deviation
c. Variance
d. Mode
7. An X and R chart is used to:
a. Indicate process variation
b. Specify design Limits
c. Interpret costs
d. Identify customer expectations
8. Which of the following is the most useful graphical tool for promoting and understanding the process
of capability?
a. A flowchart
b. A histogram
c. An affinity diagram
d. An Ishikawa diagram
9. The type of chart that presents the value of items in descending order is a:
a. Histogram
b. Pareto chart
c. U chart
d. Cusum chart
10. Measures of which of the following provide attributes data?
a. Temperature in degrees
b. Attendance at meetings
c. Weight in pounds
d. Length in metric units
11. The fraction of nonconforming products is plotted on which of the following types of control chart?
a. P chart
b. U chart
c. Np chart
d. C chart
12. A cause and effect diagram is a useful tool for doing which of the following?
a. Determining the flow of a process
b. Detecting shifts in a process
c. Developing theories based on symptoms
d. Arranging theories by defect count
13. Which of the following statistics would best describe the central tendency of a sample of data?
a. Mode
b. Mean
c. Standard deviation
d. Range
14. Which of the following type of tools or techniques is considered qualitative?
a. Histogram
b. Frequency distributions
c. Pareto chart
d. Process observations
15. Out of the following which technique is most useful in narrowing issues and limiting discussion?
a. Brainstorming
b. Quality function deployment
c. Cause and effect analysis
d. Mutilating
16. In statistics, an estimation error that is persistent or systematic is called:
a. Bias
b. Sensitivity
c. Random
d. Shift
17. For a normal distribution, two standard deviation on each side of the mean would include what
percentage of the total population:
a. 47%
b. 68%
c. 95%
d. 99%
18. If a distribution is normal, u=50 s=15, what percentage of data will be less than 30?
a. 59.18%
b. 40.82%
c. 9.18%
d. 1.33%
19. A company is receiving an unusually high number of returns from various customers. The first step in
investigating the problem would be to
a. Check the inspection records
b. Establish the correlation of the returns to shipments
c. Brainstorm the potential causes
d. Classify the returns by type and degree of serious
20. Which of the following is the best definition of a flow chart?
a. A diagram used to structure ideas into useful categories
b. An illustration used to analyze variation in a process
c. A picture used to separate steps of a process in sequential order
d. An analytical tool used to clarify opposing aspects of a desired change
21. Which of the following activities would NOT contribute to the effective functioning of a team?
a. Eliminating unnecessary activities
b. Development team performance measures
c. Defining process in detail
d. Monitoring each member’s performance
22. What is the standard deviation of the population-10, 4, 16, 12, and 8?
a. 4.00
b. 4.47
c. 16.00
d. 20.00
23. Which of the following tools would be most appropriate for collecting data to study the symptoms of
a problem?
a. Check sheet
b. Flow diagram
c. Force-field analysis
d. Activity network diagram
24. Which of the following measures is a sufficient statistic for the parameter u?
a. Median
b. Mid-range
c. Mean
d. Mode
25. Positional, cyclical, and temporal variations are most commonly analyzed in:
a. SPC charts
b. Multi-vari charts
c. Cause and effect diagram
d. Run charts
26. Which of the following describes the deming method for continuous improvement?
a. Cost of quality analysis
b. Process map
c. Tree Diagram
d. Plan-do-check-act cycle
27. In analysis of variance, which of the following distribution is the basis for determining whether the
variance estimates are all from the same population?
a. Chi square
b. Students
c. Normal
d. F
28. Which of the following statement best describes the set of value of a random variable?
a. It is finite.
b. It is an interval
c. It can be discrete or continuous.
d. It can be tracked by using control charts or scatter plots.
29. Which of the following is the best description of randomization?
a. A technique used to increase the precision of an experiment
b. A means of assuring representative sampling
c. The repetition of an observation or measurement
d. The relationship between two or more variables
30. When the order of items is not important, which of the following method is used to determine the
number of sets and subsets of items?
a. Combination
b. Permutation
c. Factorization
d. Simulation
31. Scatter diagrams are best described as:
a. Histograms.
b. Correlation analysis.
c. Pareto analysis.
d. Ishikawa diagrams.
32. A __________ is created to determine customers of a specific process.
a. Pareto chart
b. Flow diagram
c. Cause and effect diagram
d. Scatter diagram
33. A production line uses signs at specific points on the line to indicate when components or raw
materials need to be replenished. This practice is an example of:
a. Kanban
b. Poka-yake
c. Checkpoints
d. Hoshin
34. Which of the following is a good tool for planning cycle time reduction and concurrent operations?
a. A timeline
b. A Pareto diagram
c. An X and R chart
d. A PERT chart
35. Attribute and variable data are best described as which of the following?
a. Counted values measured values
b. Counted values visual features
c. Measured values counted values
d. Visual features counted values
36. All of the following are common ways for people to react to conflict except:
a. Competing
b. Collaborating
c. Avoiding
d. Sabotaging
37. A quality manager has chosen to survey customer satisfaction by taking samples based on the
categories of frequency of use, categories of use, and demographic. This technique is known as
a. Random sampling
b. Data collection
c. Stratification
d. Customer classification
38. Which of the following actions is Not used to reduce process cycle time?
a. Analyzing current processes
b. Reducing queue times
c. Setting priorities
d. Implementing activity-based costing
39. A company’s accounts payable department is trying to reduce the time between receipt and
payment of invoices and has recently completed a flowchart. Which of the following tool is the next
to be used by them?
a. Fishbone diagram
b. Scatter diagram
c. Box and whisker plat
d. Histogram
40. In a manufacturing company, the machine shop is what kind of customer in relation to the Human
Resource department?
a. Intermediate
b. Hidden
c. External
d. Internal
1. Describe how QFD fits into the overall DFSS process.
2. What is interrelationship Digraph? Explain it with example.
3. Find the area under the standard normal curve between +1.50 standard deviations and +2.50
standard deviations.
4. Define terms related to One-Way ANOVA and interpret their results & data plots.
5. Define & describe the use of Rational Sub grouping.
1. Suppose you are cooking steak for 100 people, & the current approval rating is 75% acceptable.
You want to know the affect of different methods and approaches to see how the overall approval
or “yield” is affected. By using the Full Factorial method explain how the overall approval or
“yield” is affected.
You want to know the affect of different methods and approaches to see how the overall approval
or “yield” is affected. By using the Full Factorial method explain how the overall approval or
“yield” is affected.
2. Interpret Control Charts? Distinguish between common & special causes using rules for
determining stastical control.
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Operations Research
Part One:
1. In case of (<=) inequality, to convert the inequality to an equation, we used to add a slack
variable to the left hand side of the constraint, this slake variable should be:
a. Negative
b. Positive
c. May be positive or negative
d. Zero
2. In a set of m Χ n equations (m<n) the maximum number of corner points is given by…………
3. According to penalty rule for artificial variables, the objective coefficient of the artificial variable represents an appropriate penalty, positive or negative depending on the problem, but the necessary condition required to hold this is, the value should be:
a. ∞
b. 0
c. 1
d. None of the above
4. The cases of the Simplex method in which the value of the variables may increased indefinitely
without change in the constraints is:
a. Degeneracy
b. Alternative optima
c. Unbounded solutions
d. Nonexisting solutions
5. An arc in network model is said to be ‘Directed’ if it allows positive flow in one direction and
a. Negative flow in negative direction
b. Zero flow in negative direction
c. Negative flow in perpendicular direction
d. None of the above
6. PERT stands for……………………………………………………………………………………..
7. In preemptive method for goal programming , the optimum value of a higher priority goal is never degraded by a lower priority goal.(T/F)
8. The column dropping rule does not guarantee the non degradation of higher priority goals.(T/F)
9. The additive algorithm developed by E Balas for solving ILP problems was based on pure binary variables.(T/F)
10. According to inventory model for commodity possession for smooth business operation, Holding cost represents:
a. Price per unit of an inventory item.
b. The fixed charge incurred when an order is placed regardless of its size.
c. The cost of maintaining inventory in stock.
d. None of the above
1. In case of (<=) inequality, to convert the inequality to an equation, we used to add a slack
variable to the left hand side of the constraint, this slake variable should be:
a. Negative
b. Positive
c. May be positive or negative
d. Zero
2. In a set of m Χ n equations (m<n) the maximum number of corner points is given by…………
3. According to penalty rule for artificial variables, the objective coefficient of the artificial variable represents an appropriate penalty, positive or negative depending on the problem, but the necessary condition required to hold this is, the value should be:
a. ∞
b. 0
c. 1
d. None of the above
4. The cases of the Simplex method in which the value of the variables may increased indefinitely
without change in the constraints is:
a. Degeneracy
b. Alternative optima
c. Unbounded solutions
d. Nonexisting solutions
5. An arc in network model is said to be ‘Directed’ if it allows positive flow in one direction and
a. Negative flow in negative direction
b. Zero flow in negative direction
c. Negative flow in perpendicular direction
d. None of the above
6. PERT stands for……………………………………………………………………………………..
7. In preemptive method for goal programming , the optimum value of a higher priority goal is never degraded by a lower priority goal.(T/F)
8. The column dropping rule does not guarantee the non degradation of higher priority goals.(T/F)
9. The additive algorithm developed by E Balas for solving ILP problems was based on pure binary variables.(T/F)
10. According to inventory model for commodity possession for smooth business operation, Holding cost represents:
a. Price per unit of an inventory item.
b. The fixed charge incurred when an order is placed regardless of its size.
c. The cost of maintaining inventory in stock.
d. None of the above
Part Two:
1. What do you understand by ‘Degeneracy’ found in using simplex method?
2. What do know about ‘The Balancing of Transportation Model’? If unbalanced then remedy.
3. Explain ‘Vogel Approximation Model (VAM)’.
4. Explain ‘Dijkstra’s Algorithm’ for routing.
1. The stock of WalMark Stores, Inc., trades on the New York Stock Exchange under the symbol WMS. Historically, the price of WMS goes up with the increase in the Dow average 60% of the time and goes down with the DOW 25% of the time. There is also a 5% chance that WMS will go up when the Dow goes and 10% that it will go down when the Dow goes up.
a) Determine the probability that WMS will go up regardless of the Dow.
a) Determine the probability that WMS will go up regardless of the Dow.
b) Find the probability that probability that WMS goes up given that the Dow is up?
c) What is the probability WMS goes down given that Dow is down?
2. Prove that if the probability P {A/B} = P {A}, then A and B must be independent.
3. Tasco Oil owns a pipeline booster unit that that operates continuously. The time between
breakdowns for each booster is exponential with a mean of 20 hours. The repair time is
exponential with mean 3 hours. In a particular station, two repairpersons attend 10 boosters. The hourly wage for each repairperson is $18. Pipeline losses are estimated to be $30 per broken booster per hour. Tasco is studying the possibility of hiring an additional repairperson.
a) Will there be any cost savings in hiring a third repairperson?
b) What is the schedule loss in dollars per breakdown when the number of repairpersons on duty is two? Three?
4. Cars arrive at a one-bay car wash facility the interarrival time is exponential, with a mean of 10 minutes. Arriving cars line up in a single lane can accommodate at most five waiting cars. If the lane is full, newly arriving cars will go elsewhere. It takes between 10 and 15 minutes, uniformly distributed, to wash a car. Simulate the system for 960 minutes, and estimate the time a car spends in the facility?
1. Define Transportation Model and its variant in brief.
2. Explain in detail Game Theory. Support you answer examples.
2. Explain in detail Game Theory. Support you answer examples.
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