Determination of the Functional Model The Value and Cost Weighting of the Functions Iteration

The construction of the diagram, the value and cost weighting of the functions is presented. Based on the values for coordinates xi and yi presented in table 9 the diagram of figure 15 is plotted. Calculations are made with the smallest squares method.

The parameters have the following computed values: a = 0,99, α = 44,7 o_{, S = 92,62, S' = 0.} Table 9 provides the necessary values for constructing the following types of diagrams: • Diagram of the value weighting of the functions (identical to the diagram of fig. 3), • Diagram of the cost weighting of the functions (fig. 14),

• Diagram of the value and cost weighting of the functions (fig. 15). Figure 14 shows the ranking of the functions by their functional cost.

An analysis of the diagram of figure 15 shows that functions F1 and F7 are located above the regression lines, indicating high costs, not justifiable in relation to the value.

In the diagram of figure 15 can be seen following straight:

• The straight of equation y = x (first bisector), straight mediating share in value and cost functions, show the ideal situation of proportion to the two weights, the value and cost weighting of the functions

• The straight of regression equation y = 0,9652 * x + 0,2673, approximates arrangement of points, show the real situation of proportion to the two weights, the value and cost weighting of the functions. The R – squared value on chart is R = 0, 7984, two times

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higher than in the first iteration. This shows a large group of points of the two straight regressions.

Analyzing the diagram in figure 15 shows that some functions are above the regression lines, this attests to high costs, unreasonable in relation to value.

These aspects allow the assumption that these functions are deficient, hence the solutions to be identified are to focus on those assemblies, parts, materials and technological operations that contribute, within the general structure of the product, to the achievement of these functions.

In the second iteration of the Value engineering study will provide the functional model of this roll crusher, to see the deficient functions.

These functions are:

• The function F4, provides support of crusher; to achieve this function have the highest participation the shaft support, the frame part of the crusher,

• The function F7, ensure uniformity of movement; to achieve this function have the highest participation the flywheel of crusher.

Table 8 The cost weighting of the functions (*Y coordinate, ** monetary units)

Parts Cost part* * Functions _Cost part** F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 1-Engine 100_% 20 5 15 30 10 20 100 700 140 0 0 35 105 210 70 140 0 0 0 700 2-Gear 100_% 10 50 5 5 10 5 10 5 100 n-... 0 Total cost 2700 536 291 228 353 290 315 323 219 75,9 42,8 22,6 2700 Ratio 0,19 0,10 0,08 0,13 0,10 0,11 0,12 0,08 0,02 0,01 0,00 1 *Cost of functions % 19,9 10,8 8,47 13,1 10,7 11,7 12 8,14 2,81 1,59 0,84 100

Table 9 Computational elements (*the smallest squares method-SSM) for plotting the diagrams

*SSM - C.E. = Computational elements; **S = Σ(Y i - a*Xi)2; ***S'=Σ(2*a*(Xi)2 –2*Xi*Yi)

11. Conclusions

In two iterations of Value engineering study one component of roll crusher, the cylinder who contribute at the function F1 (ensure material crushing) was redesign and optimized:

1. from engineering viewpoint:

• from variant of cylinder of figure 16 consists of 20 parts, one complicated part (many components, mechanical machining, turning of metal parts complicated, long and very

*SSM C.E. Functions _Total value F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 X i 16,7 15,2 13,6 12,1 10,6 9,09 7,58 6,06 4,55 3,03 1,52 100 Y i 19,9 10,8 8,47 13,1 10,7 11,7 12 8,14 2,81 1,59 0,84 100 (X i)2 277,8 229,6 186 146,9 112,5 82,64 57,39 36,73 20,66 9,182 2,295 1161, 6 X i * Y i 331,3 163,5 115,5 158,5 114 106,2 90,62 49,33 12,78 4,809 1,271 1148 **S 11,62 17,48 25,04 1,212 0,071 7,295 20,03 4,62 2,819 1,981 0,433 92,61 ***S' -113 126,7 136,5 -26,6 -5,65 -49,1 -67,8 -26,0 15,26 8,531 1,995 0

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expensive, etc.) to the variant F18 (fig. 17) or to the variant F127 (fig.18) or to the variant F128 consists of 2 components (mechanical machining, turning of metal parts simple, short and less expensive than the cylinder of fig. 16, etc.).

2. from the economic viewpoint:

• the cost of function F1 decrease from 640 monetary units, representing 20 %, in the first iterations of Value engineering study (fig. 5, tables 4, 5) to 573 monetary units, representing 19,9 % in the second iterations of Value engineering study, decrease with 0,49 %, (fig. 15, table 9),

• the cost of roll crusher decrease from 450 monetary units (fig. 5, table 4), to 300 monetary units (fig. 14, table 8).

• Looking at the diagrams in Figures 5 and 15 shall conclude at first sight they are pretty similar and did not change anything. It is only at first sight.

Looking more closely diagrams, and tables 4 and 8 can be observed the following:

1 - Product costs decreased from 3205 monetary units in the first iteration at 2700 monetary units in the second iteration, a decrease of 15%,

Figure 15 The value and cost weighting of the functions

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2 - F1 cost function decreased to 640 monetary units in the first iteration to 536 monetary units in the second iteration, a reduction of 16%

3 - F4 function cost decreased from 451 monetary units in the first iteration to 353 monetary units in the second iteration, a decrease of 21,9%

4 - F7 function cost decreased to 437 monetary units in the first iteration to 323 monetary units in the second iteration, a decrease of 26%.

These values explain the close percentages in the two iterations:

1 - Percentage of function F1 20% in the first iteration and 13% in the second iteration, 2 - Percentage of function F4 14% in the first iteration and 19,9% in the second iteration, 3 - Percentage of function F7 13,6% in the first iteration and 12% in the second iteration, This reduction of the cost is upon the following articles: design, type of material, quantity of material from cylinder, machining mode, how to repair after working.

In the next iterations of Value engineering study are analyzed other functions above the regression straight line, y = x (for example F4) and their cost reduced, then the regression lines are re-plotted and the functions relocated above them are noted; these functions too are analyzed in view of reducing their cost, followed by the re-plotting of the regression lines, etc.,

At the end of the Value engineering study the points are aligned as perfectly as possible along the straight line y = a * x, with a tilt of 45o_{, this is the optimal situation, the values} weighting of functions and the functions cost weighting are equal.

References

1 Value engineering, Available from: http://en.wikipedia.org/wiki/Value_engineering, Accessed:

26.10.2011