Statistics for Management, Operations, and Operations Research

SECTION A – STATISTICS: CONCEPTS & DESCRIPTIVE ANALYSIS

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1. Statistics in management is primarily used to:
A. Replace intuition with quantitative analysis
B. Eliminate human judgment
C. Avoid decision-making
D. Only summarize data
Answer: A
Explanation: Statistics brings objectivity and helps managers make rational decisions based on numerical evidence.*

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2. Which of the following is not a function of statistics?
A. Data presentation
B. Forecasting
C. Moral judgment
D. Data collection
Answer: C
Explanation: Statistics is factual and quantitative; moral judgment is outside its scope.*

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3. Descriptive statistics involves:
A. Summarizing and presenting data
B. Drawing inferences
C. Testing hypotheses
D. Estimating parameters
Answer: A

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4. The process of drawing conclusions about a population based on sample data is called:
A. Inferential statistics
B. Descriptive statistics
C. Enumeration
D. Classification
Answer: A

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5. Which of the following scales has a true zero?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Answer: D
Explanation: Ratio scale includes an absolute zero, allowing ratio comparisons (e.g., weight, income).*

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6. In a normal distribution, mean = median = mode.
Answer: True
Explanation: Normal distribution is symmetric; all measures of central tendency coincide.*

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7. Which is the most affected by extreme values?
A. Median
B. Mode
C. Mean
D. Geometric mean
Answer: C

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8. The measure that divides data into 100 equal parts is called:
A. Percentiles
B. Quartiles
C. Deciles
D. None
Answer: A

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9. If Mean = 50 and SD = 5, what is the coefficient of variation (CV)?
A. 10%
B. 5%
C. 15%
D. 20%
Answer: A

$$CV=\frac{\sigma }{\bar{X}}\times 100=\frac{5}{50}\times 100=10\mathrm{\%}$$

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10. For skewed data, which measure is most appropriate?
A. Median
B. Mean
C. Mode
D. Range
Answer: A
Explanation: Median is less affected by extreme values and better represents central tendency.*

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🔹 SECTION B – DISPERSION & PROBABILITY DISTRIBUTIONS

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11. The square root of variance gives:
A. Mean deviation
B. Standard deviation
C. Coefficient of variation
D. Range
Answer: B

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12. A low coefficient of variation indicates:
A. High consistency
B. High variability
C. Instability
D. None
Answer: A

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13. In a binomial distribution, mean = np. If n = 10 and p = 0.3, mean = ?
A. 3
B. 7
C. 10
D. 5
Answer: A

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14. For Poisson distribution, variance = ?
A. Mean
B. np(1−p)
C. n²p
D. None
Answer: A

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15. The shape of a normal distribution curve is:
A. Bell-shaped and symmetric
B. Positively skewed
C. Negatively skewed
D. Uniform
Answer: A

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16. In a normal distribution, 95.45% of data lies within:
A. ±1σ
B. ±2σ
C. ±3σ
D. ±4σ
Answer: B

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17. The total area under a probability density curve equals:
A. 1
B. 0
C. 100
D. Mean value
Answer: A

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18. The expected number of occurrences in Poisson distribution is represented by:
A. m or λ
B. σ²
C. n
D. p
Answer: A

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19. Exponential distribution is used to model:
A. Waiting or service time
B. Number of trials
C. Income distribution
D. None
Answer: A

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20. If two events A and B are independent, then $P(A\cap B)=?$
A. $P(A)+P(B)$
B. $P(A)\times P(B)$
C. $P(A)-P(B)$
D. $1-P(A)$
Answer: B

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🔹 SECTION C – SAMPLING AND QUESTIONNAIRE DESIGN

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21. Sampling is used because:
A. Studying the whole population is costly and time-consuming
B. Complete enumeration is impossible
C. Both A and B
D. None
Answer: C

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22. Sampling error arises due to:
A. Observing only a part of population
B. Faulty data recording
C. Incorrect coding
D. None
Answer: A

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23. In stratified sampling, the population is divided into:
A. Homogeneous groups (strata)
B. Heterogeneous groups
C. Random clusters
D. None
Answer: A

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24. Systematic sampling involves:
A. Selecting every kth item from a list
B. Random selection
C. Dividing into strata
D. None
Answer: A

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25. Snowball sampling is especially useful for:
A. Hidden or hard-to-reach populations
B. Large homogeneous populations
C. Statistical inference
D. None
Answer: A

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26. The first step in questionnaire design is:
A. Defining objectives
B. Drafting questions
C. Testing
D. Editing
Answer: A

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27. Which type of question allows freedom in answering?
A. Open-ended
B. Closed-ended
C. Dichotomous
D. Multiple choice
Answer: A

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28. A biased questionnaire results in:
A. Invalid data
B. Accurate results
C. Efficient sampling
D. None
Answer: A

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29. The purpose of pilot testing a questionnaire is:
A. To identify and correct errors before final use
B. To collect final data
C. To test reliability only
D. None
Answer: A

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30. The most common non-probability sampling used in marketing surveys is:
A. Convenience sampling
B. Stratified sampling
C. Random sampling
D. Systematic sampling
Answer: A

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🔹 SECTION D – HYPOTHESIS TESTING

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31. The null hypothesis (H₀) assumes:
A. No significant difference exists
B. A difference exists
C. Sample is biased
D. None
Answer: A

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32. The level of significance is:
A. Probability of committing Type I error
B. Probability of Type II error
C. Power of test
D. None
Answer: A

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33. Type I error occurs when:
A. True H₀ is rejected
B. False H₀ is accepted
C. False H₁ is accepted
D. Both A and C
Answer: A

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34. Which test is suitable for small samples with unknown variance?
A. t-test
B. Z-test
C. F-test
D. χ² test
Answer: A

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35. Z-test is used when:
A. Population variance is known
B. Sample size is large (n>30)
C. Both A and B
D. None
Answer: C

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36. Chi-square test is applied to:
A. Qualitative or categorical data
B. Continuous data
C. Large numerical datasets
D. None
Answer: A

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37. F-test is used to compare:
A. Two variances
B. Two means
C. Two proportions
D. Two correlations
Answer: A

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38. In hypothesis testing, “p-value” indicates:
A. Probability of obtaining test statistic at least as extreme as observed
B. Mean of data
C. Sample size
D. None
Answer: A

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39. A two-tailed test is used when:
A. Deviation can occur in either direction
B. Deviation occurs only on one side
C. Data are nominal
D. None
Answer: A

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40. The decision to reject H₀ is made when:
A. p-value < α
B. p-value > α
C. Mean difference = 0
D. None
Answer: A

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🔹 SECTION E – CORRELATION & REGRESSION

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41. Karl Pearson’s correlation coefficient measures:
A. Strength and direction of linear relationship
B. Cause-effect relationship
C. Non-linear association
D. None
Answer: A

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42. If r = +1, the two variables are:
A. Perfectly positively correlated
B. Perfectly negatively correlated
C. Unrelated
D. None
Answer: A

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43. If correlation between X and Y is zero, it means:
A. No linear relationship
B. Independent variables
C. Non-linear relation exists
D. None
Answer: A

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44. Regression analysis helps in:
A. Predicting one variable from another
B. Comparing means
C. Sampling
D. None
Answer: A

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45. The slope (b) in regression equation $Y=a+bX$ indicates:
A. Change in Y per unit change in X
B. Mean of Y
C. Intercept
D. None
Answer: A

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46. If r = 0.8, coefficient of determination $r^2=?$
A. 0.64
B. 0.8
C. 1.6
D. 0.4
Answer: A

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47. In multiple regression, number of independent variables is:
A. More than one
B. One
C. Two only
D. None
Answer: A

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48. Regression coefficient can be negative.
Answer: True

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49. Correlation implies causation.
Answer: False
Explanation: Correlation shows association, not cause-effect relationship.*

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50. Spearman’s rank correlation is suitable for:
A. Ordinal data
B. Ratio data
C. Interval data
D. None
Answer: A

SECTION F – OPERATIONS MANAGEMENT

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51. Operations Management primarily deals with:
A. Conversion of inputs into outputs efficiently
B. Marketing of products
C. Accounting for profit
D. Setting financial goals
Answer: A
Explanation: Operations Management focuses on optimizing production and service processes to deliver value.*

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52. The main objective of Operations Management is:
A. Increase efficiency and effectiveness
B. Maximize advertising
C. Minimize competition
D. None
Answer: A

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53. Which of the following is not a function of Operations Management?
A. Product design
B. Plant layout
C. Inventory control
D. Stock valuation
Answer: D

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54. Productivity is defined as:
A. Output / Input
B. Input / Output
C. Profit / Cost
D. Cost / Revenue
Answer: A

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55. A major decision area in Operations Management includes:
A. Facility location
B. Promotion mix
C. Financial investment
D. Tax planning
Answer: A

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56. Facility location decision is critical because:
A. It affects cost, accessibility, and efficiency
B. It changes daily
C. It has no long-term impact
D. None
Answer: A

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57. The process layout is most suitable for:
A. Job production
B. Mass production
C. Continuous production
D. None
Answer: A
Explanation: In job production, different processes are grouped by function (e.g., hospital, repair shop).*

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58. Product layout is ideal when:
A. Volume is high and variety is low
B. Volume is low and variety is high
C. Demand is uncertain
D. None
Answer: A

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59. A fixed-position layout is used in:
A. Shipbuilding and construction projects
B. Assembly lines
C. Textile manufacturing
D. None
Answer: A

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60. “Cellular Layout” combines advantages of:
A. Process and Product Layout
B. Job and Project Layout
C. Fixed and Functional Layout
D. None
Answer: A

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SECTION G – ENTERPRISE RESOURCE PLANNING (ERP)

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61. ERP stands for:
A. Enterprise Resource Planning
B. Enterprise Research Process
C. Efficient Resource Planning
D. None
Answer: A

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62. ERP is best described as:
A. An integrated information system covering all functional areas
B. A financial planning tool
C. A marketing strategy
D. A manufacturing technique
Answer: A

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63. The core modules of ERP typically include:
A. Finance, HR, Production, SCM, CRM
B. Advertising and Design
C. Tax and Audit
D. None
Answer: A

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64. Which of the following is an ERP vendor?
A. SAP
B. Oracle
C. Microsoft Dynamics
D. All of the above
Answer: D

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65. A major challenge in ERP implementation is:
A. Resistance to change
B. System integration
C. High cost
D. All of the above
Answer: D

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66. ERP improves decision-making by:
A. Providing real-time data and integrated reports
B. Isolating departments
C. Reducing transparency
D. None
Answer: A

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67. The first step in ERP implementation is:
A. Requirement analysis and planning
B. Testing
C. Data migration
D. Training
Answer: A

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68. One of the main benefits of ERP is:
A. Reduced redundancy and duplication of data
B. Increased manual work
C. Fragmented systems
D. None
Answer: A

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69. ERP integrates:
A. Information across departments
B. Competitors’ data
C. Market research
D. None
Answer: A

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70. ERP’s biggest advantage in supply chain management is:
A. Visibility of inventory and orders
B. Advertisement design
C. Labour reduction
D. None
Answer: A

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🔹 SECTION H – SCHEDULING, SEQUENCING & MONITORING

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71. Scheduling refers to:
A. Determining when and in what order jobs are performed
B. Assigning machines to workers
C. Estimating production cost
D. None
Answer: A

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72. Loading is:
A. Assigning jobs to specific machines or departments
B. Recording sales
C. Maintenance activity
D. None
Answer: A

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73. Sequencing is about:
A. Deciding priority of jobs
B. Setting targets
C. Estimating time
D. None
Answer: A

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74. The rule “SPT” in sequencing means:
A. Shortest Processing Time
B. Standard Production Target
C. Sequential Process Time
D. None
Answer: A

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75. Monitoring in production control ensures:
A. Adherence to schedule and corrective actions
B. Pricing policy
C. Quality audit only
D. None
Answer: A

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76. “Dispatching” in production control refers to:
A. Issuing work orders to start operations
B. Planning demand
C. Procurement
D. None
Answer: A

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77. Which of the following minimizes average job flow time?
A. SPT rule
B. FCFS rule
C. EDD rule
D. LPT rule
Answer: A

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78. A Gantt chart is used for:
A. Scheduling and progress tracking
B. Statistical analysis
C. Regression analysis
D. None
Answer: A

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79. Bottleneck operations are:
A. Work centers limiting system capacity
B. Unused machines
C. Idle resources
D. None
Answer: A

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80. Effective scheduling results in:
A. Improved utilization, reduced idle time, timely delivery
B. Increased cost
C. Delayed production
D. None
Answer: A

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SECTION I – QUALITY MANAGEMENT

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81. Quality means:
A. Fitness for intended purpose
B. High cost
C. Luxury
D. None
Answer: A

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82. Statistical Quality Control (SQC) uses:
A. Control charts
B. Inventory models
C. Demand forecasting
D. None
Answer: A

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83. Total Quality Management (TQM) emphasizes:
A. Continuous improvement and customer satisfaction
B. Inspection only
C. Reduction in workforce
D. None
Answer: A

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84. Kaizen refers to:
A. Continuous small improvements
B. Employee layoffs
C. Major innovation
D. None
Answer: A

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85. Benchmarking means:
A. Comparing performance with best practices
B. Copying competitors blindly
C. Auditing accounts
D. None
Answer: A

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86. Six Sigma aims at:
A. Reducing defects to less than 3.4 per million opportunities
B. Achieving 100% output
C. Increasing production cost
D. None
Answer: A

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87. The DMAIC cycle stands for:
A. Define, Measure, Analyze, Improve, Control
B. Develop, Manage, Audit, Implement, Correct
C. None
Answer: A

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88. ISO 9000 is related to:
A. Quality management system standards
B. Environmental norms
C. Cost control
D. None
Answer: A

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89. A Pareto chart identifies:
A. Major causes contributing most to problems (80/20 rule)
B. Average performance
C. Random variation
D. None
Answer: A

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90. Control limits in control charts are set at:
A. ±3σ
B. ±1σ
C. ±2σ
D. None
Answer: A

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SECTION J – OPERATIONS RESEARCH (OR)

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91. Operations Research is:
A. Application of scientific methods to decision-making
B. Human resource study
C. Market analysis
D. None
Answer: A

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92. Objective of Operations Research is:
A. Optimization of limited resources
B. Cost increase
C. Sales increase only
D. None
Answer: A

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93. The transportation model aims to:
A. Minimize cost of shipping goods between sources and destinations
B. Forecast demand
C. Schedule maintenance
D. None
Answer: A

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94. The initial feasible solution in transportation problems can be found by:
A. North-West Corner, Least Cost, VAM
B. Linear Regression
C. PERT
D. None
Answer: A

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95. Queuing theory deals with:
A. Waiting lines and service systems
B. Inventory planning
C. Facility layout
D. None
Answer: A

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96. Arrival rate (λ) and service rate (μ) are parameters in:
A. Queuing model
B. Regression model
C. Inventory model
D. None
Answer: A

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97. Decision theory helps in:
A. Selecting best alternative under risk or uncertainty
B. Marketing segmentation
C. Labour planning
D. None
Answer: A

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98. In PERT, expected time is calculated as:

$$t_e=\frac{a+4m+b}{6}$$

A. True
B. False
Answer: A

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99. Critical path in CPM represents:
A. Longest path determining project duration
B. Shortest path
C. Average path
D. None
Answer: A

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100. Slack time indicates:
A. Maximum delay possible without affecting project completion
B. Idle labour
C. Cost overrun
D. None
Answer: A

Statistics for Management, Operations, and Operations Research

PART 1: STATISTICS FOR MANAGEMENT

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1. Concept and Scope

Statistics is both a science and an art of collecting, classifying, presenting, analyzing, and interpreting numerical data to aid rational decision-making under uncertainty.

It provides quantitative foundations for managerial functions such as planning, control, and forecasting.

Branches of Statistics

1. Descriptive Statistics – summarizing data through tables, charts, and averages.

2. Inferential Statistics – drawing conclusions about populations from samples using probability theory.

Role of Statistics in Management

• Marketing: Market surveys, consumer behaviour analysis.

• Finance: Portfolio risk analysis, stock price movements.

• Production: Quality control, forecasting demand.

• HR: Wage analysis, performance evaluation.

• Operations: Scheduling, process optimization.

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2. Data and Its Types

A. Based on Source

• Primary Data: Collected first-hand for a specific study (surveys, interviews).

• Secondary Data: Collected earlier for another purpose (reports, journals, databases).

B. Based on Nature

• Qualitative (Attribute): Categorical (e.g., gender, brand preference).

• Quantitative (Variable): Numeric (e.g., income, profit).

C. Based on Measurement Scale

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🟩 3. MEASURES OF CENTRAL TENDENCY

Central tendency expresses the “typical” or “representative” value of a dataset.

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A. Arithmetic Mean

$$\bar{X}=\frac{\sum X}{N}$$

For grouped data:

$$\bar{X}=\frac{\sum fX}{\sum f}$$

Merits: Simple, algebraically tractable.
Limitations: Affected by extreme values.

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B. Median

The middle value when data are arranged in order.

$$\text{Median}=L+\frac{(\frac{N}{2}-CF)}{f}\times h$$

• Less affected by outliers.

• Appropriate for skewed data.

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C. Mode

Most frequent value.
For grouped data:

$$\text{Mode}=L+\frac{(f_1-f_0)}{(2f_1-f_0-f_2)}\times h$$

Used for qualitative data like brand or color preference.

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D. Relationship among Mean, Median, and Mode

$$\text{Mode}=3(\text{Median})-2(\text{Mean})$$

Useful for estimating one measure from the other two.

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🟩 4. MEASURES OF DISPERSION

Dispersion measures how values deviate from the average — indicating consistency or risk.

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Example:
Dataset A: Mean = 50, SD = 10 → CV = 20%
Dataset B: Mean = 80, SD = 16 → CV = 20%
→ Both have equal relative variability.

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🟩 5. PROBABILITY AND PROBABILITY DISTRIBUTIONS

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A. Concept of Probability

Probability quantifies the likelihood of occurrence of an event.

$$P(A)=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$$

Range: 0 ≤ P(A) ≤ 1

• P(A) = 1: Certain event

• P(A) = 0: Impossible event

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B. Rules of Probability

1. Addition Rule:
   If A and B are mutually exclusive,

   $$P(A\cup B)=P(A)+P(B)$$

2. Multiplication Rule:
   For independent events,

   $$P(A\cap B)=P(A)\times P(B)$$

3. Conditional Probability:

   $$P(A\mathrm{\mid }B)=\frac{P(A\cap B)}{P(B)}$$

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C. Probability Distributions

(1) Binomial Distribution

Discrete distribution used for number of successes in n independent trials.

$$P(X=x)=\left(\genfrac{}{}{0px}{}{n}{x}\right)p^x(1-p{)}^{n-x}$$

• Mean = np

• Variance = np(1−p)

Example: Probability of 3 defective bulbs out of 10 when defect rate = 0.1.

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(2) Poisson Distribution

For rare events (e.g., accidents per day).

$$P(X=x)=\frac{e^{-m}{m}^x}{x!}$$

• Mean = Variance = m

Used when n → large, p → small, and np = constant.

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(3) Normal Distribution

Continuous, bell-shaped curve.

$$f(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{(x-\mu {)}^2}{2{\sigma }^2}}$$

Properties:

• Symmetrical about mean.

• 68.26% within ±1σ, 95.45% within ±2σ, 99.73% within ±3σ.
  Used in hypothesis testing and control charts.

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(4) Exponential Distribution

Used to model time between events (e.g., waiting time).

$$f(x)=\lambda e^{-\lambda x},x\ge 0$$

Mean = 1/λ
Variance = 1/λ²

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🟩 6. DATA COLLECTION AND QUESTIONNAIRE DESIGN

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Data Collection

• Primary: Through direct observation, survey, or experimentation.

• Secondary: Government reports, journals, internet sources.

Questionnaire Design

1. Define objectives

2. Select information to collect

3. Choose question type:

   • Open-ended (qualitative insights)

   • Closed-ended (quantitative analysis)

4. Logical sequencing (easy → complex)

5. Pilot testing and revision

Common Mistakes: Ambiguous wording, double-barreled questions, poor scaling.

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🟩 7. SAMPLING THEORY

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A. Basic Concepts

• Population (Universe): Entire group under study

• Sample: Representative subset

• Sampling Unit: Element from which data is collected

B. Steps in Sampling Process

1. Define population

2. Select sampling frame

3. Decide sample size

4. Choose technique

5. Collect and analyze

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C. Probability Sampling Techniques

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D. Non-Probability Sampling Techniques

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🟩 8. HYPOTHESIS TESTING

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A. Key Definitions

• Parameter: Numerical summary of population (μ, σ²).

• Statistic: Calculated from sample (x̄, s²).

Goal: Use sample data to infer about population.

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B. Hypothesis Types

• Null Hypothesis (H₀): No significant difference.

• Alternative Hypothesis (H₁): Significant difference exists.

Errors:

• Type I (α): Rejecting true H₀

• Type II (β): Accepting false H₀

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C. Testing Steps

1. Formulate H₀ and H₁

2. Choose significance level (α = 0.05 or 0.01)

3. Choose appropriate test statistic (Z, t, F, χ²)

4. Compute test statistic

5. Compare with critical value

6. Draw conclusion

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D. Parametric Tests

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E. Non-Parametric Test

Chi-Square (χ²) Test:

$${\chi }^2=\sum \frac{(O-E{)}^2}{E}$$

Used for testing independence or goodness of fit.

Example: Relationship between gender and brand preference.

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🟩 9. CORRELATION AND REGRESSION

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A. Correlation

Measures strength and direction of linear relationship.

Karl Pearson’s Coefficient (r):

$$r=\frac{\mathrm{\Sigma }(X-\bar{X})(Y-\bar{Y})}{\sqrt{\mathrm{\Sigma }(X-\bar{X}{)}^2\mathrm{\Sigma }(Y-\bar{Y}{)}^2}}$$

Range: -1 to +1
r = +1 → Perfect positive
r = -1 → Perfect negative

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B. Rank Correlation (Spearman’s ρ)

$$\rho =1-\frac{6\mathrm{\Sigma }{D}^2}{n(n^2-1)}$$

Used when data are ordinal (ranks).

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C. Regression Analysis

Used to predict value of dependent variable (Y) from independent variable (X).

Simple Linear Regression:

$$Y=a+bX$$

where
$b=\frac{\mathrm{\Sigma }(X-\bar{X})(Y-\bar{Y})}{\mathrm{\Sigma }(X-\bar{X}{)}^2}$

Multiple Regression:
$Y=a+b_1{X}_1+b_2{X}_2+\mathrm{.}\mathrm{.}\mathrm{.}+b_n{X}_n$

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🟩 10. OPERATIONS MANAGEMENT

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A. Concept

Operations Management deals with conversion of inputs (materials, labour, capital, information) into outputs (goods/services) efficiently.

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B. Functions

• Product design & process selection

• Plant layout and facility location

• Capacity planning

• Scheduling and inventory control

• Maintenance and quality management

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C. Objectives

1. Improve productivity

2. Optimize resources

3. Ensure quality and timely delivery

4. Minimize cost

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🟩 11. FACILITY LOCATION AND LAYOUT

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Facility Location

The strategic decision of choosing where to situate production or service facilities.

Quantitative Methods:

• Centre of Gravity Method: minimizes transport cost

• Break-even Analysis: compares fixed and variable cost by site

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Plant Layout

Arrangement of machines, departments, or work areas.

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🟩 12. ENTERPRISE RESOURCE PLANNING (ERP)

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A. Concept

ERP integrates core business functions through a central database.

ERP Modules:

1. Finance

2. HR

3. Production

4. SCM

5. CRM

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B. ERP Implementation Steps

1. Project planning

2. Requirement analysis

3. System design & customization

4. Data migration

5. Training

6. Testing & Go-live

Benefits: Integration, transparency, faster reporting.
Challenges: High cost, change resistance, data migration errors.

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🟩 13. PRODUCTION SCHEDULING AND CONTROL

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A. Loading: Assigning jobs to machines.

B. Scheduling: Determining when and in what sequence jobs are processed.

C. Sequencing: Prioritizing jobs (rules: FCFS, SPT, EDD).

D. Monitoring: Tracking progress, revising schedules.

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🟩 14. QUALITY MANAGEMENT

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A. Quality Concepts

Quality = fitness for purpose.
Quality management ensures that output meets customer expectations.

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B. Statistical Quality Control (SQC)

Uses control charts (mean, range, p-chart, c-chart) to monitor process variation.

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C. Total Quality Management (TQM)

An organization-wide philosophy emphasizing continuous improvement and customer satisfaction.

Principles:

1. Customer orientation

2. Continuous improvement (Kaizen)

3. Employee involvement

4. Scientific decision-making

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D. Quality Tools

• Control Charts

• Fishbone Diagram (Ishikawa)

• Pareto Analysis (80/20 Rule)

• Check Sheets, Histograms, Scatter Diagrams

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E. Kaizen

Continuous small improvements involving all employees.

F. Benchmarking

Comparing performance with best-in-class organizations.

G. Six Sigma

A disciplined methodology targeting defect reduction to 3.4 defects per million opportunities (DPMO).
Focuses on DMAIC cycle – Define, Measure, Analyze, Improve, Control.

H. ISO 9000 Series

Global quality management system standards (documentation, process control, auditing).

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🟩 15. OPERATIONS RESEARCH (OR)

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Definition

Operations Research applies scientific and mathematical models to managerial decision-making for optimization of limited resources.

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Applications:

• Production scheduling

• Inventory control

• Transportation and distribution

• Network planning

• Queuing and service design

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A. Transportation Problem

Objective: Minimize total cost of shipping goods.

$$Z=\sum _{i=1}^m\sum _{j=1}^n{C}_{ij}{X}_{ij}$$

Methods:

1. Initial solution → North-West Corner, Least Cost, Vogel’s Approximation (VAM).

2. Optimality test → MODI method.

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B. Queuing Theory

Studies waiting line systems.

Parameters:
λ = Arrival rate, μ = Service rate
System utilization: ρ = λ / μ
Objective → minimize waiting cost + service cost.

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C. Decision Theory

Used when decisions must be made under risk or uncertainty.

Criteria:

• Maximax (optimistic)

• Maximin (pessimistic)

• Minimax regret (Savage)

• Expected monetary value (probabilistic)

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D. PERT / CPM (Project Scheduling)

PERT Expected Time:

$$t_e=\frac{a+4m+b}{6}$$

Variance $={\left(\frac{b-a}{6}\right)}^2$

Critical Path: Longest path through network; determines project duration.
Slack Time: $LST-EST$ → available delay time.