ECE 269 VLSI System Testing Krish Chakrabarty Lecture 3 Test Economics ECE 269 Krish Chakrabarty 1 Lecture 3 Test Economics ECE 269 Economics defined Costs Production Benefit cost analysis Economics of design for testability DFT Quality and yield loss Summary Krish Chakrabarty 2 1 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 ECE 269 Krish Chakrabarty 3 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 ECE 269 Krish Chakrabarty 4 2 Costs Fixed cost Variable cost Total cost Average cost Example Costs of running a car Fixed cost 25 000 Variable cost 20 cents mile Total cost 25 000 0 2x Average cost 25 000 0 2 x ECE 269 Purchase price of car Gasoline maintenance repairs For traveling x miles Total cost x Krish Chakrabarty 5 Simple Cost Analysis Case 1 10 000 miles yr 12 500 resale value after 5 years 25 000 12 500 Average cost 0 2 45 cents mile 50 000 Case 2 10 000 miles yr 6 250 resale value after 10 years 25 000 6 250 Average cost 0 2 38 75 cents mile 100 000 Case 3 10 000 miles yr 0 resale value after 20 years 25 000 0 Average cost 0 2 32 5 cents mile 200 000 ECE 269 Krish Chakrabarty 6 3 Cost Analysis Graph 100 tal To st co Fixed cost 25 000 20 000 50 Average cost ble ria a V st co 0 0 50k 100k 150k Average Cost cents Fixed Total and Variable Costs 40 000 0 200k Miles Driven ECE 269 Krish Chakrabarty 7 Production Inputs x Labor land capital enterprise energy x may include both fixed and variable costs Production output Q f x Average product Q x Marginal product dQ dx ECE 269 Krish Chakrabarty 8 4 Law of Diminishing Returns Output Q x 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 Krish Chakrabarty ECE 269 9 Technological Efficiency Technological efficiency Q x where x variable cost To maximize tech Efficiency 1 dQ Q 0 x dx x 2 or Tech Eff 1 0 0 5 0 0 ECE 269 Q dQ x dx Max tech eff Q x dQ dx Input Resources x Krish Chakrabarty 10 5 Economic Efficiency Maximum economic efficiency minimizes the total average cost X Q where X is the total fixed variable cost Maximum economic efficiency is achieved when total average cost equals the marginal cost X Q dX dQ For average cost marginal cost Take variable cost to maximize technological efficiency Take total cost to maximize economic efficiency Krish Chakrabarty ECE 269 11 Maximum Efficiencies Costs Max economic efficiency With actual fixed cost Average cost X Q Max tech efficiency Marginal cost dx dQ With zero fixed cost assumed Input resources ECE 269 Krish Chakrabarty 12 6 Mass Production Production can be increased at a faster rate than the increase of inputs This is known as increasing returns to scale Some reasons for increasing returns to scale Technological factors Specialization Only some inputs are increased If increase of inputs continues eventually the law of diminishing returns applies ECE 269 Krish Chakrabarty 13 Benefit Cost Analysis Benefits Savings in manufacturing costs capital and operational and time reduced wastage automation etc Costs Extra hardware training of personnel etc Benefit cost ratio Annual benefits B C ratio 1 Annual costs ECE 269 Krish Chakrabarty 14 7 Economics of Design for Testability DFT Consider life cycle cost DFT on chip may impact the costs at board and system levels Weigh costs against benefits Cost examples reduced yield due to area overhead yield loss due to non functional tests Benefit examples Reduced ATE cost due to selftest inexpensive alternatives to burn in test Krish Chakrabarty ECE 269 15 Benefits and Costs of DFT Level Design and test Fabrication Manuf Test Chips Boards System Maintenance test Diagnosis and repair Service interruption Cost increase Cost saving Cost increase may balance cost reduction ECE 269 Krish Chakrabarty 16 8 Summary Economics teaches us how to make the right trade offs It combines common sense experience and mathematical methods The overall benefit cost ratio for design test and manufacturing should be maximized one should select the most economic design over the cheapest design 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 ECE 269 Krish Chakrabarty 17 9
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