(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) Probability that the collapse is due to a design fault

Let F be a faulty design, N no fault and C a collapse. P(F) = 0·1, P(N) = 0·9, P(C|F) = 0·95, P(C|N) = 0·45.

Total probability: P(C) = 0·95 × 0·1 + 0·45 × 0·9 = 0·095 + 0·405 = 0·500.

Bayes’ theorem: P(F|C) = P(C|F)P(F) / P(C) = 0·095 / 0·500 = 0·19.

So there is a 19% chance that the collapse was due to faulty design. Although faulty designs collapse far more often, most houses are not faulty, so most collapses come from sound designs.

(b) Knowledge-based expert systems

A knowledge-based expert system (KBES) is a computer system that stores the knowledge of human experts in a narrow field and uses inference rules to reach conclusions or advice as an expert would. Its parts are a knowledge base of facts and heuristics, an inference engine that applies rules (forward or backward chaining), working memory, a knowledge-acquisition module, an explanation facility and a user interface. Knowledge is kept separate from control logic, so it can be updated.

Business applications:

• Finance: credit appraisal, loan approval and fraud detection.
• Insurance: underwriting and claims settlement.
• Manufacturing: fault diagnosis, maintenance and scheduling. Classic examples are XCON at Digital Equipment for configuring computers and MYCIN-style diagnostics.
• Customer service: help desks and troubleshooting.
• Marketing: product recommendation and pricing support.
• HR and audit: candidate screening, tax planning and audit risk.

Expert systems give consistent advice, preserve scarce expertise and train staff, but knowledge acquisition is costly and they handle novel situations poorly.

(c) Convergence of goods and service operations

Fundamental differences: goods are tangible, storable and made before consumption, so inventory buffers demand, contact with customers is low and quality can be inspected before delivery. Services are intangible, perishable, produced and consumed together, and variable, so capacity cannot be stored, customers take part, and quality depends on front-line staff.

Why the gap is narrowing:

• Servitization: manufacturers sell maintenance, leasing and data services (aircraft engines sold "by the hour").
• Industrialised services: standard processes, automation and self-service, as in fast-food chains and online banking.
• Shared tools: lean, Six Sigma, TQM, ERP and analytics are used in hospitals and banks as well as factories.
• Shared problems: demand forecasting, yield management, queuing and customer experience matter in both.

Limits: services still cannot be stored, customer-caused variability stays high, and many services need presence and emotional labour. The distinction is becoming a goods-service continuum rather than disappearing.

(d) Did the training help? Paired t-test

The same 11 people were tested twice, so a paired t-test applies. Let d = Test 2 − Test 1.

H₀: μd = 0 (no improvement). H₁: μd > 0 (improvement), a one-tailed test.

Differences: 1, −1, 3, −3, 2, 2, 2, 3, 0, 4, −2. Σd = 11, so d̄ = 11/11 = 1. Σd² = 61, so s² = [61 − 11²/11]/10 = 50/10 = 5 and s = √5 ≈ 2·236. SE = s/√n = √(5/11) ≈ 0·674. t = d̄/SE = 1/0·674 ≈ 1·483, with 10 degrees of freedom.

The one-tailed critical value at 5% for 10 df is 1·812. Since 1·483 is below 1·812, H₀ is not rejected. The marks do not show at the 5% level that the training helped. The test assumes the differences are roughly normal.

(e) Objectives of MRP and how it achieves them

Material Requirements Planning converts the Master Production Schedule into time-phased requirements for dependent-demand items.

Objectives: have materials available when needed, meet delivery dates, keep inventory low, plan purchase and production orders, cut delays and expediting, and set valid priorities.

How MRP achieves them:

• Inputs: the Master Production Schedule (what, how many, when), the Bill of Materials (product structure) and inventory records (stock, scheduled receipts, lead times).
• Explosion: gross requirements of each component are derived from the schedule through the bill of materials.
• Netting: stock on hand and scheduled receipts are subtracted to give net requirements, which keeps inventory low.
• Lot sizing: net requirements become order quantities (lot-for-lot or economic order quantity).
• Lead-time offsetting: order releases are scheduled back from need dates, so materials arrive on time.
• Outputs: planned order releases, exception reports on shortages or excess, and rescheduling notices that keep priorities valid.
• Capacity check: capacity requirements planning tests feasibility, and MRP II and ERP extend the logic to finance and capacity.

MRP depends on accurate schedules, bills of materials, inventory records and lead times.