(a) A newly constructed house can collapse due to fault in its design. It can also collapse even if it does not have a design…

(a) Let F = event that the design is faulty, N = event that there is no design fault, and C = event that the house collapses. By Bayes’ theorem, we first find P(C), the total probability that the house collapses.

Given: P(F) = 0·1, so P(N) = 1 − 0·1 = 0·9. P(C|F) = 0·95. P(C|N) = 0·45.

Using the theorem of total probability: P(C) = P(C|F)P(F) + P(C|N)P(N) = 0·95 × 0·1 + 0·45 × 0·9 = 0·095 + 0·405 = 0·500.

Now applying Bayes’ theorem: P(F|C) = P(C|F)P(F) / P(C) = (0·95 × 0·1) / 0·500 = 0·095 / 0·500 = 0·190.

Final answer: The probability that the collapse is due to a fault in design is 0·19, i.e. 19%.

(b) A knowledge-based expert system (KBES) is a computer-based information system that uses a stored body of knowledge and a set of inference rules to imitate the problem-solving and decision-making ability of a human expert in a narrow domain. Its main components are the knowledge base, inference engine, working memory, knowledge-acquisition module, explanation facility, and user interface. The knowledge base contains facts, heuristics, rules of thumb, and domain-specific relationships. The inference engine applies logical rules to the facts to derive conclusions or recommendations. Unlike conventional programs, a KBES separates knowledge from the control mechanism, so it can be updated as expert knowledge improves.

Major applications of KBES in business include:

• Financial decision-making: credit appraisal, loan approval, risk assessment, portfolio selection, bankruptcy prediction, and fraud detection.
• Insurance: underwriting, claim settlement, policy pricing, and risk classification.
• Customer service: help desks, complaint diagnosis, troubleshooting, and automated advisory systems.
• Manufacturing: fault diagnosis, preventive maintenance, process control, quality assurance, and production scheduling.
• Marketing and sales: customer profiling, product recommendation, pricing support, and sales forecasting.
• Human resource management: candidate screening, job matching, training needs diagnosis, and performance advisory systems.
• Accounting and auditing: tax planning, audit risk assessment, internal control evaluation, and compliance checking.
• Strategic management: scenario analysis, competitive intelligence, and decision support under uncertainty.

KBES improves consistency, preserves expert knowledge, reduces dependence on scarce experts, shortens decision time, and supports training. Its limitations include high knowledge-acquisition effort, difficulty in handling novel situations, maintenance cost, and inability to replace human judgement in unstructured problems.

(c) The traditional distinction between manufacturing and service operations rests on certain fundamental differences. Goods are tangible, storable, transportable, and often produced before consumption. Services are intangible, perishable, inseparable from the provider, heterogeneous, and usually consumed while produced. In manufacturing, customer contact is low, production can be decoupled from consumption, inventory can buffer demand, quality can be inspected before delivery, and productivity is easier to measure. In services, customer participation is high, production and consumption coincide, capacity cannot be stored, variability is greater, and quality depends heavily on front-line employees and customer behaviour.

However, the statement that the difference between management of manufacturing and service operations is reducing is largely valid today. Several forces have narrowed the gap:

• Servitization: Manufacturers increasingly add after-sales service, maintenance, leasing, analytics, and product-service systems, making their operations more service-like.
• Industrialisation of services: Service firms now use standardisation, automation, self-service technology, modularisation, and mass customisation, making their operations more factory-like.
• Information technology: Digital platforms, ERP, CRM, IoT, and AI allow real-time coordination, remote diagnosis, and customisation in both sectors.
• Quality management: TQM, Six Sigma, and lean principles are now applied in hospitals, banks, retail, and government as well as factories.
• Customer focus: Manufacturers design products around customer experience, while service firms design processes around customer journeys.
• Capacity and demand management: Both sectors use scheduling, yield management, queuing theory, and demand forecasting.
• Measurement: Both now use productivity, cost, quality, cycle time, and customer satisfaction metrics, though service measurement remains harder.

Still, the convergence is not complete. Services cannot be inventoried, customer-induced variability remains high, and many personal services require physical presence and emotional labour. Therefore, the distinction is not disappearing but shifting from a goods-versus-services dichotomy to a goods-service continuum. Managers must combine manufacturing-efficiency tools with service-oriented flexibility and customer responsiveness.

(d) Since the same eleven police personnel are measured before and after training, the data are paired. The appropriate test is the paired t-test for small samples. Let d = Test 2 marks − Test 1 marks. A positive mean difference would indicate benefit from training.

Hypotheses: H₀: μd = 0, i.e. training produced no improvement. H₁: μd > 0, i.e. the police personnel benefited from training.

The differences are: 1, −1, 3, −3, 2, 2, 2, 3, 0, 4, −2.

Number of pairs n = 11. Σd = 1 − 1 + 3 − 3 + 2 + 2 + 2 + 3 + 0 + 4 − 2 = 11. Mean difference d̄ = Σd / n = 11 / 11 = 1.

Now compute Σd²: 1² + (−1)² + 3² + (−3)² + 2² + 2² + 2² + 3² + 0² + 4² + (−2)² = 1 + 1 + 9 + 9 + 4 + 4 + 4 + 9 + 0 + 16 + 4 = 61.

Sample variance: s² = [Σd² − (Σd)²/n] / (n − 1) = [61 − 11²/11] / (11 − 1) = [61 − 121/11] / 10 = [61 − 11] / 10 = 50 / 10 = 5.

So s = √5 ≈ 2·2361.

Standard error: SE = s / √n = √5 / √11 = √(5/11) ≈ 0·6742.

Paired t-statistic: t = d̄ / SE = 1 / √(5/11) = √(11/5) ≈ 1·483.

Degrees of freedom = n − 1 = 10. At 5% level of significance for a one-tailed test, the critical value is t₀.₀₅,₁₀ = 1·812.

Since calculated t = 1·483 < 1·812, we fail to reject H₀. The result is not significant at the 5% level. If a two-tailed test were used, the critical value would be 2·228, and the conclusion would still be the same.

Final answer: The marks do not give sufficient statistical evidence at the 5% level that the police personnel benefited from the training. The test assumes paired observations, independent differences, and approximate normality of the differences.

(e) Material Requirements Planning (MRP) is a computer-based production planning and inventory control system used mainly for dependent-demand items. It translates the Master Production Schedule (MPS) into detailed requirements for raw materials, components, and sub-assemblies needed to produce finished products on time.

The main objectives of MRP are:

• Ensure that materials and components are available when required for production.
• Ensure that finished products are available to meet customer delivery schedules.
• Maintain the lowest possible inventory levels without causing stock-outs.
• Plan and control manufacturing activities, purchase orders, and delivery schedules.
• Reduce production delays, idle time, and expediting costs.
• Improve capacity utilisation and production efficiency.
• Provide valid priorities and schedules for shop-floor and purchase operations.
• Improve customer service through reliable delivery performance.

An MRP system achieves these objectives through the following logic:

• Master Production Schedule: It states what end products are required, in what quantity, and by when.
• Bill of Materials (BOM): It shows the structure of each product, listing all components, sub-assemblies, and raw materials needed.
• Inventory Records File: It provides current stock on hand, scheduled receipts, lead times, lot-sizing rules, and safety stock.
• Explosion: MRP explodes the MPS through the BOM to calculate gross requirements of each dependent-demand item at each level.
• Netting: It subtracts available inventory and scheduled receipts from gross requirements to obtain net requirements.
• Lot sizing: It converts net requirements into planned order quantities using rules such as lot-for-lot, economic order quantity, or periodic order quantity.
• Lead-time offsetting: It schedules planned order releases backward from required dates using lead times.
• Planned orders: It generates planned order receipts and planned order releases for purchasing and production.
• Exception reports: It highlights shortages, delays, excess inventories, and schedule conflicts so managers can act.
• Capacity Requirements Planning: It checks whether the planned orders are feasible with available capacity and feedback is sent to the MPS.
• Feedback and rescheduling: Actual production, purchases, and inventory changes update the system continuously.

Thus, MRP integrates demand, product structure, inventory, and lead-time information to ensure the right materials are available at the right time, in the right quantity, while minimising inventory and improving delivery performance. Its effectiveness depends on accurate MPS, BOM, inventory data, lead times, and disciplined updating.