Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 31 Lecture 3 Test Economics n Economics defined n Costs n Production n Benefit - cost analysis n Economics of design-for-testability (DFT) n Quality and yield loss n Summary

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 32 The Meaning of Economics Economics is the study of how men choose to use scarce or limited productive resources (land, labor, capital goods such as machinery, and technical knowledge) to produce various commodities (such as wheat, overcoats, roads, concerts, and yachts) and to distribute them to various members of society for their consumption. -- Paul Samuelson

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 33 Engineering Economics Engineering Economics is the study of how engineers choose to optimize their designs and construction methods to produce objects and systems that will optimize their efficiency and hence the satisfaction of their clients.

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 34 Costs n Fixed cost n Variable cost n Total cost n Average cost Example: Costs of running a car Fixed cost Variable cost Total cost Average cost $25, cents/mile $25, x $ ───── ,000 x Purchase price of car Gasoline, maintenance, repairs For traveling x miles Total cost / x

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 35 Simple Cost Analysis Case 1: 10,000 miles/yr, $12,500 resale value after 5 years Average cost = $ ────────── = 45 cents/mile 25, ,500 50,000 Case 2: 10,000 miles/yr, $6,250 resale value after 10 years Average cost = $ ───────── = cents/mile Case 3: 10,000 miles/yr, $0 resale value after 20 years Average cost = $ ─────── = 32.5 cents/mile 25, , ,000 25, ,000

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 36 Cost Analysis Graph 40,000 25,000 20, k150k100k 50k Miles Driven Fixed, Total and Variable Costs ($) Average Cost (cents) Total cost Fixed cost Variable cost Average cost

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 37 Production n Inputs (X): Labor, land, capital, enterprise, energy (X may include both fixed and variable costs) n Variable costs (x) n Production output, Q = f (x) n Average product, Q / x n Marginal product, dQ / dx n Total Average cost, X / Q

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 38 Law of Diminishing Returns If one input of production is increased keeping inputs constant, then the output may increase, eventually reaching a point beyond which increasing the inputs will cause progressively less increase in output. Input Resources, x Output, Q(x)

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 39 Technological Efficiency Technological efficiency = Q/x where x = variable cost d Q 1 dQ Q Q dQ ── ─ = 0; ─ ── ─ ── = 0 or ── = ── dx x x dx x 2 x dx To maximize tech. Efficiency: Input Resources, x Tech. Eff Max. tech. efficiency Q/x dQ/dx

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 310 Economic Efficiency n Maximum economic efficiency minimizes the total average cost X /Q, where X is the total (fixed + variable) cost. n Maximum economic efficiency is achieved when total average cost equals the marginal cost, X /Q = dX /dQ. n For average cost = marginal cost n Take variable cost to maximize technological efficiency n Take total cost to maximize economic efficiency

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 311 Maximum Efficiencies Marginal cost, dx/dQ Average cost, X/Q For zero fixed cost For actual fixed cost Max. tech. efficiency Max. economic efficiency Input resources Costs

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 312 Mass Production n Production can be increased at a faster rate than the increase of inputs. This is known as increasing returns to scale. n Some reasons for increasing returns to scale n Technological factors n Specialization n Only some inputs are increased n If increase of inputs continues, eventually the law of diminishing returns applies.

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 313 Benefit-Cost Analysis n Benefits: Savings in manufacturing costs (capital and operational) and time, reduced wastage, automation, etc. n Costs: Extra hardware, training of personnel, etc. n Benefit/cost ratio Annual benefits B/C ratio = ───────────── > 1 Annual costs

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 314 Example: A PCB Repair Shop n Average cost of repair = $350, includes Cost of diagnostic test= $300 Cost of replacement chip= $ 10 Cost of assembly and test= $ 40 n Failure data for 100 chips on PCB Chip A failure rate= 90% Chip B failure rate= 90% Collective failure rate for chips A and B = – 0.81 = 0.99

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 315 PCB Repair Strategies n Strategy 1 Diagnose the faulty PCB Replace faulty chip and test n Strategy 2 Replace chips A and B Test n Pass → Done n Fail – Diagnose the faulty PCB – Replace faulty chip and test

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 316 PCB Repair Strategies Faulty PCB Apply diagnostic Test Cost = $300 Replace faulty Chip and test Cost = $50 Faulty PCB Replace chips A and B and test Cost = $60 Replace faulty Chip and test Cost = $50 PCB passes Test? Apply diagnostic Test Cost = $300 Repair completed Av. Cost = $63.50 Repair completed Av. Cost = $ Yes Prob=0.99 No Prob=0.01 Strategy 1 Strategy 2

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 317 Economics of Design for Testability (DFT) n Consider life-cycle cost; DFT on chip may impact the costs at board and system levels. n Weigh costs against benefits n Cost examples: reduced yield due to area overhead, yield loss due to non-functional tests n Benefit examples: Reduced ATE cost due to self-test, inexpensive alternatives to burn-in test

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 318 Benefits and Costs of DFT Design and test + / - Fabri- cation + Manuf. Test - Level Chips Boards System Maintenance test - Diagnosis and repair - Service interruption - + Cost increase - Cost saving +/- Cost increase may balance cost reduction

Copyright 2001, Agrawal & BushnellVLSI Test: Lecture 319 Summary n Economics teaches us how to make the right trade-offs. n It combines common sense, experience and mathematical methods. n The overall benefit/cost ratio for design, test and manufacturing should be maximized; one should select the most economic design over the cheapest design. n A DFT or test method should be selected to improve the product quality with minimal increase in cost due to area overhead and yield loss.