Process modeling for quality in order-handled manufacturing system.

Cikotiene, D. ; Bargelis, A.

1. Introduction

Order-handled manufacturing systems (OHMS) involve make to order production operations and customer-tailored end products in the form of capital equipment. Research and practical experience [1] shows that production planning and control procedures can be more difficult to carry out when jobs are produced to order rather than for stock, because the operations are complicated by inherent sources of uncertainty. The objective of an OHMS operation may be defined as the manufacture and delivery of goods of proper design and quantity to customers' specification, with an appropriate guarantee of product quality and prompt delivery at an acceptable cost [2]. Two types of OHMS are considered in theoretical and practical research domain of manufacturing science: 1) with the designing, developing and manufacturing the product and 2) without product development when product manufacturing is only needed. First type of OHMS is more complicated and it rarely occurs because customers often keep new product development in their hands. This research considers the second type of an OHMS in manufacturing of a large number product types and low production volumes.

1.1. Research reasoning

Companies that work applying OHMS approach always feel a strong pressure of customers' inquiries and requirements to product technical data, quality, cost and delivery. The high competition exists among producers to win each order because customers have very big choice in various countries and companies. At the beginning of Global manufacturing (GM) era, a lot of industrial production moved from the USA, Western Europe, Australia and Japan to the developing countries in South-East Asia and Eastern Europe, while in many industrialized nations the hollowing phenomenon of the manufacturing section is observed [3]. A hollow company undertakes itself the functions of marketing, new product development, and delivery. Lithuania is a country of producers when many small and medium enterprises (SMEs) produce various products, their parts and components according to the orders of customers. In biggest part of orders, unfortunately, the product design and development is made by customers and many quality and productivity questions appear to producers. Design for Quality (DFQ) methods [4-6] applied by new product developers in various manufacturing systems are differently implemented and required modeling of some process alternatives for quality and cost.

The consideration of Lithuanian SMEs production results has shown certain quality and low manufacturing cost problems when companies' stakeholders exploiting modern CNC facilities often have product and process quality failures. These failures deal with both the product and process design questions, and order quotation inaccuracies when producers have been very optimistic. No prevention and only small appraisal cost in considered 20 Lithuanian SMEs has been fixed.

This paper reports how process modeling for quality can facilitate and help to accelerate the enterprise business process in a new competitive age avoiding above-mentioned quality and manufacturing cost problems. In this context, some ways achieving the good quality during production - statistical process control at every stage, implementation of prevention and quality appraisal methods in manufacturing operations and foreseen appropriate techniques, resources and quality management are used. Quality improvement processes and calculations also are carried out at business engineering and work stages.

1.2. Literature review on quality cost

There are many research made and publications published related with quality cost. It is identified the efforts between quality cost and value by classifying the quality cost elements into "value added" and "non-value added" grounded on activity based costing (ABC); prevention-appraisal costs are value-added quality costs and failure costs are nonvalue added quality costs [7]. According to the research [8], quality costs are an indicator or a measure of the effectiveness of a quality management system, and the identification of potential failures lead to the recognition of improvement opportunities. The analysis of quality costs and a model for optimum quality costs is presented in research [9]. This model shows the interaction between three types of quality costs: prevention, appraisal and failure. It was stated, when prevention and appraisal costs are increasing then failure costs are going down. This statement was extended in research [10]; failure is the most expensive and prevention is the least expensive quality cost component. Company should not exclusively invest in appraisal because it may lead to unacceptable costs and may affect the company's reputation. It is stated that a quality cost system can be established in an attempt to increase the value of a product and process output, and enhance customer satisfaction. The authors of this research have been defined the relative dependences among quality, appraisal cost plus prevention cost and failure cost for material, machine tool and whole company. Transforming quality cost measurements into product value has been carried out in research [11]. The value of quality improvements is a measure of return on quality investments, which indicates whether the quality improvement efforts gave higher, fair, or lower return. The research methodology on relative changes in utility and cost from time i to the time has been used. It develops and discusses a model of customer value by accommodating its relative nature, and presents a proactive way of measuring quality cost.

Reviewed papers with relative dependences among quality cost and utility mostly in large companies are related. The situation, however, in big variety and low volume production companies, in particular SMEs, is quite other and special tools or techniques for quality cost modeling are necessary at the early stage of new product development or new order engineering. No any recommendations or proposals, unfortunately, what kind of investments to process improvement would match achieving good quality with minimal cost.

The research of this paper is devoted to the process modeling for quality in order-handled manufacturing system and also the forecasting of quality cost for various processes and products when the product is developed and designed by customer. It emphasized the propositions which arise overlapping the product manufacturing cost and quality cost or even latest is neglected. The purpose of this paper is the development of process model for quality and forecasting quality cost which could help to avoid big loses in manufacturing companies. The proposed model is being implemented for the integration of product process planning with manufacturing and quality cost definition at the new order engineering stage.

2. Process modeling for quality

The classification of products, their design features and processes for decreasing uncertainties has been used in this research. Manufacturing system deals business with one or in seldom cases with some product classes because appropriate experience of manufacturing processes, tooling and traditions it has acquired. Quality problems are delicate and tough related with manufacturing processes, employees skill and work motivation, therefore, they can be easier solved in the products and processes on the separate class level when general number of uncertainties is the smallest.

The process modeling for quality on the entire of qualitative indications I of a product G which consists of the lot of original parts P and standard components S is based in the limits of a separate product class level

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

where [F.sub.ji] is the qualitative requirements of the product [G.sub.i] functionality; [E.sub.ik] is the qualitative requirements of the product [G.sub.i] parameters; [A.sub.ip] is the qualitative requirements of the product [G.sub.i] accuracy; n is the number of product [G.sub.i] qualitative indications.

The process modeling task for quality starts with the selection of the original part P work piece, operations and facilities according to the qualitative indications I that are systematized and acquired in the process design knowledge base (KB). The next modeling step is the creation of process alternatives with operations sequence and definition of manufacturing and quality cost. The third modeling step is an estimation of process alternatives and chooses of the best one with minimal cost.

Qualitative requirements [A.sub.jp] of the product [G.sub.i] accuracy depend on the geometrical form and other peculiarities of part design features. Each part P of a product G is expressed as a set of design features D

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

The complexity of each [D.sub.n] is denoted by a set of parameters [A.sub.jp], p = (1, ..., p), e.g., material, geometrical form, dimensions, tolerances, roughness of surfaces and so on. The designer can vary the product structure and functionality combining different numbers of P and S, and different qualitative and quantitative parameters of D. The product design procedure has to be closely related to the process manufacturing cost and also to quality cost. It may be verified at the early product design stage by modeling procedure of manufacturing and quality costs, which is based on the design feature [D.sub.i] structure and qualitative parameters.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The graph theory [12] for transformation of mechanical part drawings' data into digital codes has been used. Typical sheet metal design part is presented in Fig. 1 and its following graph is illustrated in Fig. 2. Sheet metal part consists of four design features [D.sub.t] and appropriate dimensional chains and tolerances. The design features [D.sub.i] of a part are graph's nodes and the dimensions are the edges; edges show the reflexive relations as [D.sub.i] tolerances c1, c2, c3, c4 and irreflexive relations as dimensions C1, C2, C3, C4, C5, C6, C7, C8.

Conversion of [D.sub.i] structure and qualitative parameters for computation of manufacturing and quality costs can be expressed as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

where [D.sub.i] is design feature, i = 1, ..., n; [T.sub.i] is the type of design feature [D.sub.i]; [x.sub.i], [y.sub.i], [z.sub.i] are dimensions of design feature [D.sub.i]; [tx.sub.i], [ty.sub.i], [tz.sub.i] are tolerances of design feature [D.sub.i] dimensions; [K.sub.ij] are design feature [D.sub.i] location requirements in a part, j = 1, ., m; [R.sub.i] is machine tool for design feature [D.sub.i] manufacturing; R[A.sub.ik] is the lot of possible machine tools for design feature [D.sub.i] manufacturing; k = 1, ..., l.

The objective W of process modeling for quality in OHMS can be expressed as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where B is OHMS benefit getting when the product is produced according to customer requirements; H is manufacturing cost; Q is quality cost.

The product manufacturing and quality costs are considered in the integrated manner together with product design by the developed model aiming the biggest benefit. Expected benefit may be checked at the early product design stage or new order engineering stage. The product and process structure is varying if necessary seeking a biggest W value. The producer always must reach the perfect ideal case when denominator of Eq. (5) is going to zero

Ideality = [infinity], when [OMEGA]H = 0 and [OMEGA]Q = 0

Worst case is when W = 0, e.g., product production is impossible because no chances to achieve customers' requirements and denominator of a Eq. (5) greatly exceeds the product value.

Product and process design procedure is a permanent solving of the contradictions among the required best product properties as functionality, quality and desired parameters, and manufacturing and quality costs. In other words, if any product design alternative will satisfy only one requirement, e.g., when designer has achieved the best product functionality, but manufacturing and quality costs are unacceptable then the trade off is appeared and more alternatives are necessary. The designer has to continue the product development procedure and to solve an existing trade off.

The straight tool of solving the above-mentioned problem could be model for quality cost Q at the early new product development or order engineering stage. The first step of this model is forecasting of a product manufacturing cost H. The research carried out in KTU during past twenty years showed very simple and reliable way to forecast product manufacturing cost at the early its development stage according to the product qualitative and quantitative parameters. This method on the separate product class level and each material type is grounded. The decisive role to manufacturing cost of mechanical product and its parts and components has material consumption rate and cost. It is defined on the retrospective analysis of different production processes and operations by the dependencies of material consumption rate and product mass in various Lithuanian companies. Fig. 3 illustrates the sheet metal consumption rate M1 dependency on the sheet metal design products' mass M in Lithuanian company X. The regression equation representing dependency between product's mass M and M1 (Fig. 3) is as follows

M1 = mM + s (6)

where m is the slope of a regression trend line; s is intercept of a regression trend line; the slope and intercept applying Fig. 3 data and standard calculations are defined, m = 1.18 and s = -0.42.

[FIGURE 3 OMITTED]

The values of m and s depend on product and material type, process and company manufacturing traditions. The similar dependences as illustrated in Fig. 3 can be created for any other metal type or profile. Plastics, paints and galvanized also assembling materials consumption are differently defined - according to the conditional consumption norms for coating area or other processing data.

The total manufacturing cost H of a product [G.sub.i] is expressed as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

where H1 is metal consumption, kg; H2 is plastics consumption, kg; H3 is paints and galvanizing materials consumption, kg; H4 is assembling material, kg; n, m, p, r are the number of material types; g1-g4, are the cost in EUR of 1 kg appropriate material; b1 -b4 are coefficients evaluating the cost of workforce, machine tool depreciation and overheads.

The material cost g in various data base (DB) is available to find and parallel the values of various b in companies KB are possible to systematize and acquire. Latter data according products, processes and companies types are classified and KB structure is developed [13].

3. Quality cost modeling

When the manufacturing cost H of a new order is predicted, then the attempt to forecast quality cost as a function of H has been made. It was applied the proposition that quality cost is classified into four categories [14]: prevention, appraisal, internal failure and external failure costs. Taking into account this quality cost classification the kind and size of investments to process development matching a good quality with minimal cost for big variety and low production volume in OHMS manufacturing system has been made. The quality cost Q of product [G.sub.i] can be expressed

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

where Q1 is prevention cost, EUR; Q2 is appraisal cost, EUR; Q3 is internal failure cost, EUR; Q4 is external failure cost, EUR. Prevention quality cost depends on a lot of parameters and can be expressed as an abstraction function

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)

where [x.sub.1] is cost of order review for quality and manufacturing process; [x.sub.2] is cost of a quality audit; [x.sub.3] is preventative maintenance cost; [x.sub.4] is employees training cost.

When developing of a forecasting model to Q1, different influence of various factors used in Eq. (9) on value Q1 was found. Preventative maintenance cost [x.sub.3] has been defined as more decisive to Q1 in OHMS manufacturing system. Applying statistical data of companies and manuals of various machine tools and processes also authors experience, the dependency between [x.sub.3] and total manufacturing cost H of a part has been proposed

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

where [r.sub.1] is correction coefficient estimating a machined part quality by operator; it depends on operation and part type also on the number of design features and their qualitative-quantitative parameters (Table 1).

The costs of order review for quality [x.sub.1], quality audit [x.sub.2] and employees training [x.sub.4] are estimated by correction coefficient [r.sub.2], to the total part manufacturing cost H. The value of [r.sub.2] applying available statistical data of companies' and manuals sources also manufacturing traditions from 0.001 up to 0.005 has been used in this research.

Appraisal quality cost analogously as prevention quality cost can be expressed

Q2=[f.sub.2]([y.sub.1], [y.sub.2], [y.sub.3], [y.sub.4], [y.sub.5]) (11)

where [y.sub.1] is receiving inspection cost; [y.sub.2] is product acceptance cost; [y.sub.3] is inspection labor cost; [y.sub.4] is process control cost; [y.sub.5] is quality control equipment's cost.

Process control cost [y.sub.4] as more decisive for Q2 in OHMS manufacturing system has been defined. Process quality control using variables, means, ranges, charts and samples is carried out. Average of sample measurements is calculated

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

where k is the number of samples size; [[micro].sub.i] is measurements average of i-th sample.

The mean range R is the average of all the sample ranges and may be calculated

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where [R.sub.i] is average range of each sample;

The standard deviation of all population can be calculated applying R value

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (14)

where [d.sub.n] is Hartley constant [6].

Process control cost [y.sub.4], receiving inspection cost [y.sub.1], product acceptance cost [y.sub.2] and inspection labor cost [y.sub.3] are defined employing statistical data by correction coefficient [r.sub.3], to the total manufacturing cost H. The value of [r.sub.3] applying available above mentioned statistical data of various sources fluctuates from 0.007 up to 0.015 in this research.

Part measuring time and cost applying complicated control equipment according to the data of Table 2 is calculated and is added to last-mentioned Q2 cost.

Internal failure quality cost Q3 is expressed as following abstraction function.

Q3=[f.sub.3]([Z.sub.1], [Z.sub.2], [Z.sub.3]); (15)

where [z.sub.1] is downtime cost; [z.sub.2] is reinspection cost; [z.sub.3] is cost of disposal and scrap because defects.

The internal failure cost is increasing when prevention defects are low; appraisal cost also is closely linked with internal failure cost when the latest is high the appraisal cost is high too. It is better to fix defects inside company than get claims from customers. Cost of disposal and scrap because defects [z.sub.3] is more obvious of Q3 and is defined as decisive in this research

[Z.sub.3] = [r.sub.4] B1 (16)

where [r.sub.4] is conditional coefficient estimating the disposal and scrap, [r.sub.4] = 0.03-0.05; B1 is annually (quarterly, monthly) consumption of material, EUR.

Downtime cost [z.sub.1] and reinspection cost [z.sub.2] is defined by correction coefficient [r.sub.5] to the total manufacturing cost H, [r.sub.5] is applied as 0.01 - 0.015 in this research.

External failure quality cost [Q.sub.4] is showed as the following abstraction function

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17)

where [v.sub.1] is customer claims; [v.sub.2] is delivery delay; [v.sub.3] is other external loses.

External failure cost is attempted to show to be quite low, attributed to the high level of appraisal an internal failure cost. Cost of customer claims is more obvious of Q4; the aim of each manufacturer is to strive to keep it in the level of 0.0 - 0.02 of the total manufacturing cost H. Delivery delay cost [v.sub.2] and other external loses [v.sub.3] are very complicated to estimate and they are neglected in this research.

Research based on two Lithuanian SME firms related to the sheet metal design and manufacturing. It referred creation of quality cost estimation methodology in OHMS manufacturing system. The developed methodology is able to estimate and minimize quality cost by proofed manufacturing process and personal understanding of a quality problem.

4. Practical usage of quality cost estimation methodology and achieved results

In this study, quality cost definition methodology in OHMS sheet metal design companies has been tested. The sheet metal design of telecommunication product has been chosen; it consists of 12 plates produced from low carbon galvanized steel and typical part of product in Fig. 4 is shown. Monthly production volume of the product is 500 pieces. Quality cost is available to decrease applying quality control in each phase of product design, manufacturing and delivering; therefore, the product designer has made efforts to use unified design features of product parts - equal sheet metal thickness 2.5 mm and holes diameter 4.6 mm in all twelve parts. Thus the total numbers of holes diameter 4.6 mm is equal to 76. Similarly, it was made also with other design features of product parts including another alternative of part material - to use low carbon steel and painting. Such decision of a product designer has helped manufacturer to simplify process and to decrease the production time and cost.

First step of the developed methodology testing is forecasting of steel consumption applying Eq. (6). The forecasting results are presented in Table 3. Table 4 illustrates the data of forecasted total product manufacturing cost employing Eq. (7); considered product has not plastics and assembling is carried out by customer.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Second step of the test was the definition of process control cost [y.sub.4] as more decisive for appraisal cost Q2 (equation 11); for checking parameter [y.sub.4] was selected Lithuanian sheet metalworking company X, which had the biggest quality problems, because it did neither neglect quality management nor quality cost definition. There were many cases when customer claimed delivered products.

The investigation of claimed product batch with error of the diameter [empty set]4.6[+ or -]0.1 mm is carried out (Fig. 4). Table 5 illustrates the measurement results of 8 claimed plates' samples and calculated [micro], R, and [sigma] values; Fig. 5 shows the diagram of average [micro] diameter [empty set]4.6 [+ or -]0.1 mm, and Fig. 6 shows the diagram of dimension [empty set]4.6 [+ or -]0.1 range values of clamed plates. The average of diameter [empty set]4.6[+ or -]0.1 mm [micro] = 4.8218 (Fig. 5) is so far from tolerance and though average of range R is in the tolerance limits (Fig. 6) the plate batch has been claimed.

The main reasons of defects after careful analysis were detected: 1) though CNC Laser cutting machine tool capability index [C.sub.p] = 1.53 is quite good, but the process capability index [C.sub.pk] = -1.86 is beyond any limits - it means the machine tool is suitable and the reason of errors is a bad process capability; 2) CNC Laser cutting machine operator has used the prepared program of plate machining without any dimensions control after the first part is made; 3) wrong use offset operation of machine tool before machining a new batch of parts; 4) no dimensions control after machining of the whole batch of plates before delivering. Taking into account all mentioned drawbacks of the process the appropriate corrections have been made. Table 6 demonstrates the measurement results of 8 samples produced by corrected process and calculated new [micro], R, and a values; Fig. 7 shows the diagram of average [micro] diameter [empty set]4.6 [+ or -]0.1 mm, and Fig. 8 shows the diagram of dimension [empty set]4.6 [+ or -]0.1 range values of plates produced by corrected process. The average of diameter [empty set]4.6 [+ or -]0.1 mm, [micro] = 4.6068 (Fig. 7) is excellent and also the average of range R ranging is slight (Fig. 8); process capability index after correction became better, [C.sub.pk] = 1.06. The developed methodology was used to the whole products and machines in company X, and employees have been retrained to use it. The importance of human role to quality is also confirmed in research [15].

Third step of the test was checking of forecasting accuracy of a quality cost by equation (8). Quality cost forecasting results are presented in Table 7. The results are given in Euro. The cost of measurement equipment calculating Q2 was neglected because standard simple control tooling has been used. Total quality cost for variant 1 is a 4.8 % while for variant 2 is a 4.65 % of manufacturing cost; it means that total order forecasting cost is equal to 4894 EUR (variant 1) and 4822 EUR (variant 2).

5. Conclusions and further research

Usage of quality cost estimation methodology in Lithuanian industry permits to avoid occurrences of products and process defects already in production stage, which helps to economize materials and other manufacturing resources. The proposed process modeling for quality in order-handled manufacturing system can forecast a best process and quality cost at the early new order engineering stage. Quality cost forecasting is related to manufacturing cost, i.e., knowing the latest cost developed model forecasts percentage proportion of quality cost. It was shown that fairly distributing resources to process prevention and appraisal it is possible to minimize internal and external failure cost.

Employment of suitable quality cost modeling, forecasting and estimation methods enables companies' stakeholders to foresee whether and when quality feature is not correctly situated. Such activities permit to react properly in early stages of new order engineering, production and delivery. It is proved that in OHMS also is available to use statistical process control (SPC) monitoring product quality and maintaining processes to a fixed cost, quality index and delivery deadlines. The aim of the developed methodology and SPC is to get and keep manufacturing process under control.

It was found that quality cost composes approx 4.5-4.8 % of total manufacturing cost in OHMS manufacturing systems, in particular for SMEs. Applying quality prevention strategy, it is possible to decrease this limit to 3.0-3.5 %. The developed methodology has been tested and validated for confirmation of the theoretical consumptions with the industrialists experience in companies.

Future research will focus on the expansion of the investigation various manufacturing processes, machine tool and tooling capabilities aiming to cost minimization and increase the quality indices.

Acknowledgement

This research was partially supported by contract with industry No 8405-2007 "Modeling of estimation productivity and quality for production the mechanical components".

Received August 12, 2008

References

[1.] Barber, K.D., Hollier, R.H. The use of numerical analysis to classify companies according to production control complexity. -Int. J. of Production Research, 1986, 24, no1, p.203-222.

[2.] Shewchuk, J.P., Moodie, C.L. Definition and classification of manufacturing flexibility types and measures. -Int. J. of Flexible Manufacturing Systems, 1998, 10, no 4, p.325-349.

[3.] Hill, T. Manufacturing Strategy: Text and Cases, 1999, Antony Rowe Ltd Chippenham, Wiltshire, GB.-634p.

[4.] Swift, K., Allen, A. Techniques for quality and manufacture. -J. of Engineering Design, 1999, 10, no3, p.81 91.

[5.] Gien, D. Towards to unified representation of quality in manufacturing systems. -Int. J. of Computer Integrated Manufacturing, 1999, 12, no2, p.141-155.

[6.] Stasiskis, A., Bargelis, A., Leibl, P. Modeling of product design for process capability. -Mechanika. -Kaunas: Technologija, 2001, Nr.4(30), p.43-49.

[7.] Tsai, W.H. Quality cost measurement under activity-based costing. -J. of Quality and Reliability Management, 1998, 15, no7, p.719-752.

[8.] Dahlgaard, J.J., Kristensen, K., Kanji, G.K Quality costs and total quality management. -Total Quality Management, 1992, 3, no3, p.211-221.

[9.] Gryna, F.M. Quality and Cost. In Juran J. M. and Godfrey, A. B. (Eds.), Juran's Quality Handbook, 1999, 5th ed.-New York: McGraw-Hill.-748p.

[10.] Omachonu, V.K., Suthummanon, S., Einspruch, N.G. The relationship between quality and quality cost for a manufacturing company. -Int. J. of Quality & Reliability Management, 2004, 21, No3, p.277-290.

[11.] Setijono D., Dahlgaard, J.J. The value of quality improvements. -Int. J. of Quality & Reliability Management, 2008, 25, No3, p.292-312.

[12.] Goodaire, E.G., Parmenter, M.M. Discret Mathematics with Graphs Theory. -New York: Prentice-Hall, Upper Saddle River, 1998.-348p.

[13.] Bargelis, A. Web-based integration for knowledge sharing in hybrid manufacturing system. -10th Commemorative.-Int. Conf. on Productivity and Quality Research ICPQR [electronical source]: February 15-19, 2004, Miami, Florida, U.S.: Proceedings, p.1-11.

[14.] Plunkett, J.J., Dale, B.G. A review of the literature on quality-related cost. -Int. J. of Quality & Reliability Management, 1987, 4, No1, p.40-52.

[15.] Ollikainen, M., Varis, J. Human errors play a remarkable role in sheet metal industry.-Mechanika.-Kaunas: Technologija, 2006, Nr.5(61), p.51-56.

Accepted January 07, 2009

D. Cikotiene *, A. Bargelis **

* Siauliai University, Vilniaus 141, 76353 Siauliai, Lithuania, E-mail: dalia.cikotiene@su.lt

** Kaunas University of Technology, Kqstucio 27, 44312 Kaunas, Lithuania, E-mail: algirdas.bargelis@ktu.lt

Table 1
Correction coefficient [r.sub.1]

Part class Number of [r.sub.1]
 design features D

Sheet metal Up to 5 0.002-0.003
Sheet metal Greater than 5 up to 0.005-0.006
Sheet metal Greater than 31 0.007-0.008
Solid part Up to 3 0.001-0.002
Solid part Greater than 3 up to 0.004-0.008
Solid part Greater than 8 0.009-0.012

Table 2
Part measuring time applying complicated control
equipment

Parameter Index Source of cost

Control equipment MW Control equipment cost
Depreciation per year DP MW/8
Average set up time AS One hour per shift
cost per year
Total control equip- MC DP + AS
ment cost per year
Hours in operation HY 12 x 16 x 8 = 1536
per year
Control equipment MH MC/HY
cost per hour
Part measuring time T Manual
Control equipment MP MH x T
cost per part

Table 3
Metal forecasting results

 Product M1,
Variant mass M, kg kg g1 Material

 1 4.31 4.67 1.00 Galvanized
 steel
 2 4.31 4.67 0.89 Low carbon
 steel

Table 4
Manufacturing cost forecasting results

 Total metal Painting H,
Variant cost, EUR cost, EUR b1 EUR

 1 2335.0 0 2.00 4670.0
 2 2080.0 224.0 2.00 4608.0

Table 5
Plate 1 before process correction, dimension 04.6 [+ or -] 0.1

 Nr. 1 sample 2 sample 3 sample 4 sample

[empty set] 4.6 1 4.78 4.79 4.80 4.81
[+ or -] 2 4.86 4.79 4.80 4.81
0.1 T = 0.2 mm 3 4.78 4.80 4.81 4.82
 4 4.86 4.81 4.82 4.83
 5 4.80 4.82 4.83 4.84
 6 4.81 4.83 4.84 4.85
 7 4.83 4.84 4.85 4.86
[mu] 4.817 4.811 4.821 4.831
R 0.08 0.05 0.05 0.05
[sigma] 0.0315 0.0181 0.0181 0.0181

 Nr. 5 sample 6 sample 7 sample 8 sample

[empty set] 4.6 1 4.78 4.80 4.78 4.81
[+ or -] 2 4.78 4.80 4.79 4.82
0.1 T = 0.2 mm 3 4.78 4.82 4.80 4.83
 4 4.82 4.82 4.81 4.85
 5 4.83 4.86 4.82 4.86
 6 4.84 4.86 4.83 4.85
 7 4.85 4.86 4.84 4.86
[mu] 4.811 4.831 4.810 4.840
R 0.07 0.06 0.06 0.05
[sigma] 0.0285 0.0259 0.0200 0.0185

Table 6
Plate 1 after process correction, dimension [empty set]
4.6 [+ or -] 0.1

 Nr. 9 sample 10 sample 11 sample 12 sample

[empty set] 4.6 1 4.70 4.69 4.68 4.67
[+ or -] 0.1 2 4.70 4.69 4.68 4.67
T = 0.2 mm 3 4.68 4.67 4.66 4.65
 4 4.68 4.67 4.66 4.65
 5 4.60 4.59 4.58 4.59
 6 4.60 4.59 4.58 4.59
 7 4.60 4.60 4.58 4.59
[mu] 4.651 4.643 4.631 4.630
R 0.10 0.10 0.10 0.08
[sigma] 0.0452 0.0437 0.0452 0.0355

 Nr. 13 sample 14 sample 15 sample 16 sample

[empty set] 4.6 1 4.66 4.57 4.56 4.55
[+ or -] 0.1 2 4.66 4.57 4.56 4.54
T = 0.2 mm 3 4.64 4.57 4.56 4.55
 4 4.64 4.67 4.66 4.55
 5 4.58 4.67 4.67 4.63
 6 4.58 4.67 4.66 4.64
 7 4.58 4.57 4.65 4.67
[mu] 4.620 4.613 4.617 4.590
R 0.08 0.10 0.10 0.10
[sigma] 0.0355 0.0495 0.0498 0.0504

Table 7
Quality cost forecasting results

Variant Q1 Q2 Q3 Q4 Q

 1 28.02 32.69 116.75 46.70 224.16
 2 27.65 32.26 108.48 46.08 214.47