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Detailer. Makes detailed drawings of parts from layout under instructions of layout man or designer. Shows dimensions, materials to be used, heat-treating data, and other necessary information. Makes drawings to scale. Completes simple tool or die drawings. Makes alterations, and details simple fixtures for layout. Must acquire knowledge of machinery, materials, machine surfaces, and tolerances. Works under instructions of layout man, designer or group leader. Must be able to read mechanical prints and layouts.

Layout Man. Makes complete and comprehensive drawings from specifications or notes furnished by designer, often completing designs; may do some designing of details not completely developed by designer. Must have considerable knowledge of manufacturing processes and their limtiations and may make stress analyses. Works under direction of designer or supervisor.

Process Engineer and Tool Planner. Determines specifications of methods to be used in the manufacture of products, including equipment specifications and tool requirements.

Process Man. Has the same knowledge requirements as a tool, die, or machine designer as well as a knowledge of operations cost and of the relevant aspects of time and motion study. Devises methods and procedures in proper sequence for the manufacture of all parts in product production, coordinates production with methods, analyzes component parts of products, and determines necessary machine and tool equipment. Determines locating points, sets up special sequences, and lists necessary machines. Devises methods in terms of quantity to be produced. May prepare detailed job breakdown for project budget, with minimum assistance and direction from supervisor.

Die Cast or Moldmaker. Builds, remodels, maintains and tries out all types of dies used in die casting. Lays out work from blueprints, makes templates, and determines the sequence of work operations. Operates the basic machines of the trade and uses all types of hand tools and precision measuring instruments. Understands the working properties of common metals and alloys. Performs such work as is necessary to make a die, taking into consideration that these dies are subjected to high temperature and pressure, that the surfaces of the completed product must have a smooth finish, and that special calculations must be made for gates, vents, shrinks, and drafts. Performs on bench all types of fitting, finishing, and assembling of parts. Has knowledge of shop mathematics and blueprints; should have knowledge of the properties of the metals cast. Makes plaster models and frequently makes wax or sulphur casts. In general, the job requires a formal apprenticeship training of 8000 hours as a diemaker.

Gagemaker. Builds, repairs, and maintains various types of precision gages used to check accuracy of machined work; plans layout work and

makes necessary templates from blueprints or drawings to determine the sequence of work operations; uses a variety of gagemaker's hand tools, precision instruments, and other related equipment; understands the working properties of common metals and alloys; has knowledge of shop mathematics; performs on the bench all types of fittings, assembles and laps parts to prescribed tolerances and allowances related to gage making; has knowledge of cutting properties of laps, abrasives, and lubricants. In general, the work requires 8000 hours of formal apprenticeship training as a Toolmaker.

Tool Pantograph Operator. Is skilled in setup and operation of pantograph engraving machine used to reproduce lettering or designs from templates, models, or plates in various ratios on tools, dies, and patterns. Reproduction is accomplished by manually following master with tracer point connected to the cutting head by series of bars and levers. The ratio of master to reproduction is controlled by adjustment of Pantograph bar connected to tracer point. The operator is able to sharpen cutting tools and locate design or lettering by use of precision measuring instruments. He has knowledge of shop mathematics and understands working properties and strengths of materials used, speeds and feeds, and proper sequence of operations. In general, the job requires a formal apprenticeship training of 8000 hours as a Tool and Die Maker.

Tool and Die Welder. Must perform all types of tool and die welding. Welds tool dies, jigs, and fixtures in all positions. Welds machine steel, tool steel, and the various alloys used in the tool or die trade, including brazes and silver solders. Uses a variety of welding equipment such as arc, acetylene, argon gas, and atomic welding. Should know hardness tests such as Rockwell and Brinell. Should know which rods to apply to produce a cutting or wearing surface upon receiving information from tool or die maker. Must be able to produce dense welds free from pits and blow holes. The job requires a knowledge of elementary metallurgy, especially heat-treating and flame hardening. An apprenticeship of 8000 hours is required.

Tool Hardener. Is skilled in operation of various types of furnaces. Alters the physical qualities or structure of metals or alloys by controlled heating and cooling to obtain desired physical characteristics. Must have knowledge of physical qualities such as shrinkage and expansion of metals and alloys. Understands hardening, tempering, drawing, annealing, normalizing, carburizing, casehardening, cyaniding, etc. Understands straightening and use of arbor presses. Must have knowledge of Rockwell and Brinell testing machines, etc. Should be familiar with gas and electric furnaces, proper quenching methods, and various types of coolants. Must have some knowledge of shop mathematics, physics, chemistry, and metallurgy. A formal apprenticeship training is generally required.

Appendix B

OUTPUT: 1975 AND 1980*

The adaptation of new technological processes necessarily implies, to the individual businessman, large outlays for production equipment. Such expenditures will not be made unless the anticipated demand for his product is sufficient to use the capacity created by the new equipment. On the other hand, since the labor force in the tool and die industry is highly skilled and specialized, there are practical limits to how fast it can be expanded. If the demand for the industry's output should grow rapidly, new methods must be found to make the existing labor force more productive.

For these and other reasons, it is useful to attempt to predict the demand for the industry's output. Before presenting the predictions, certain warnings are in order. First, any defensible prediction must be projected from past evidence. While it is generally reasonable to assume that economic relationships which existed in 1965 will also exist in 1975 or 1980, it is virtually certain that they will have changed to some degree or other. Although economic history does tend to repeat itself, it rarely, if ever, repeats itself precisely.

Second, even if the relationships between the variables should remain precisely the same, our prediction of tool and die demand is only as good as our prediction of what happens to the variables on which it depends. For example, a prediction of the output of the baby food industry depends on successfully predicting the number of jars each baby will consume (the relationship between variables), and on projecting the trend of the birthrate (the independent variable). A researcher might specify the relationship between baby food output and the number of babies perfectly, yet be far off in his prediction because he used incorrect estimates of the future baby population. This admonition is particularly relevant here, since our estimates of the future values of the independent variables were taken from a variety of sources. While they are as reliable as can be realistically expected, they may be substantially in error, for they too are based on projections which may or may not be correct. Hence, our projection is really an estimate which depends on estimates which are based on other estimates. The possible compounding of errors involved in such a procedure requires that one look at this projection with a healthy skepticism.

* This appendix was prepared by William H. Hieronymus, candidate for the Ph.D., Department of Economics, The University of Michigan.

The method of estimation used was the linear multivariate regression analysis. Since this is a standard statistical procedure, no explanation of its advantages and limitations will be undertaken here. However, two special problems presented themselves which warrant some discussion. First, there was a very limited body of data available. A time series of estimated tool and die output for the years 1951-65 was shown in Chapter One. Data for earlier years was unavailable, and even if it were available, it would be of questionable usefulness. Hence, we had only 15 observations, or 15 "degrees of freedom," to work with. This greatly limited the number of variables which could be used in our regression equations. The number of independent variables was therefore arbitrarily limited to five per equation.

Second, as shown in Chapter One, tool and die output has varied quite sharply over the business cycle. For this reason, there is no single variable with which it is closely and systematically associated. For example, the relationship between tool and die value added by manufacture and value added by manufacture is illustrated in Figure B-1. It is obvious that the relationship is not a very close one.

Of the several alternative forms of the regression equation, the one which yielded the best "fit" to the data made use of the following independent variables: value added by manufacture, output of the automobile industry, defense expenditures, plant and equipment expenditures, and a time trend. Value added by manufacture serves as our long-run trend variable; the other variables essentially serve the function of "explaining" the deviation of tool and die output from its average ratio to value added by manufacture.

Of the several alternative formulations, the following one gave the best fit:

T1.0751 + .0122 VAM + .01287D

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= value added by manufacture in the tool and die industry (SIC 3544).

VAM = value added by manufacture, the output of the entire manu

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= value added by manufacture in the automobile industry (SIC 3717, motor vehicles and parts).

= time, an index where 1951 = 1, 1952 = 2, etc. All data are in constant dollars (1957-59 = 100).1

1 T was constructed as explained in Appendix C. The values used are those which appear in Table I-1, deflated for price changes. All other data are from Department

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FIGURE B-1. Relationship of Tool and Die Output and Value Added by Manufacture.

The equation "explained" 89.26% of the variance in tool and die output, a quite satisfactory result considering the pronounced cyclical fluctuations of tool and die output. The bulk of the unexplained variance comes from the equation's having failed to predict the very large changes in output in 1956, 1958, and 1962. For all other years, the predicted value is within 5% of the actual value.

It would be unwise to take the equation too literally. The question states, for example, that a $1 billion increase in manufacturing output will cause tool and die output to rise by $102.2 million, other things remaining equal. But "other things" would not remain equal-plant and equipment expenditures would increase; so would motor vehicle output. This is simply to say that the variables are intercorrelated, and that the relationships are not as simple as the equation would seem to indicate. In particular, the negative coefficient on A implies that a rise in motor vehicle output would cause tool and die output to fall. Since the auto industry is a major customer of the tool and die industry, this interpretation becomes somewhat absurd. The correct interpretation is that both tool and die, and motor vehicle output are responsive to swings in GNP and that tool and die output is somewhat less responsive to auto

of Commerce statistics. The time series for SIC 3717 comes from the Annual Survey of Manufactures for the appropriate years. The other three time series are from the 1965 edition of Business Statistics, U.S. Dept. of Commerce, 1951-64. 1965 data are from Survey of Current Business, April, 1967.

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