6. Overview of manufacturing system
6.3. Results of stage 3
The objective of this stage was to determine the influence degree of individual risk factors on selected parameters of the production process.
7 simulation models were used for risk evaluation. Each of the subsequent models was built by introducing next risk factors to the base model, with their probability of occurrence. This was aimed at demonstration of growing effect of disturbances on the production process. The following models for risk evaluation were created:
1. Base model – that considers the suggested changes accepted in the stage 1 of the project but does not include any risk factors;
2. DB model – for analysis of disturbances caused by specific customer's require-ments;
3. Delivery model – that includes real delays and shortages of the sheets deliveries;
4. Co-operation model – that analyses risk factors for missing deliveries and de-fective components from co-operating parties;
5. Production model – with real operation times (different from the technological times);
6. Failure model – with statistical down-times of the production line caused by the equipment failures;
7. QI model – that considers statistical production rejects and technological times of their correction, as well as the risk related to planning of quality inspection;
Losses of time (Δti) in individual models caused by risk factors are shown in Fig-ure 5.
Using Equation (10) we may calculate losses in individual areas of production system (simulation models) that are caused by risk factors appearing in those areas.
Those losses for Wtheoret = 138 pieces per 12 weeks and are shown in Table 2.
Table 2. The losses in individual models [pieces per 12 weeks]
S1 S2 S3 S4 S5 S6
8.05 11.5 21.85 26.45 11.5 20.7
1,8 1,0
2,3 1,9
1,0 0,7
0 [weeks] 3
DB Delivery Co-operation Production Failure QI
t1
Δ t2
Δ
t3
Δ
t5
Δ
t4 Δ
t6
Δ
Fig. 5. Losses of time in individual models
For known quantity of losses in individual areas of production system there can be calculated the quantity of risk in individual areas of this production system (the Equa-tion (9)).
The individual areas the risk Ri is calculated and shown in Table 3.
Table 3. The risk individual areas of analysed production system
R1 R2 R3 R4 R5 R6
0.06 0.09 0.18 0.27 0.16 0.35
In the next step, using Equation (11), the total risk (RC) for the representative prod-uct in the analyzed prodprod-uction system can be calculated – Rc = 0.73.
The received value of the total risk (RC) means that with the probability of 0.73 it is not possible to reach the determined goal in the production system, which is produc-tion of 138 pieces per 12 weeks. Figure 6 presents the increases of risk’s level in indi-vidual simulations models. The level of the risk regarding the QI model is equivalent with the total risk (RC) of the whole production system, as it includes all risk factors.
0 0,06
0,14
0,3
0,49
0,58
0,73
0 1
Base DB Delivery operationCo- Production Failure QI Fig. 3. The increases of risk’s level in individual simulations models
Methods of risk evaluation in manufacturing systems 29
The risk’s increases analyzed in simulation models prove that the highest increase of risk is caused by risk factors appearing in production, co-operation and quality control areas.
In order to minimize the total risk level (RC) it is advisable to undertake the effort of the risk reduction in the mentioned above three areas.
The application of the weight coefficients in the described method delivers the pos-sibility to determine the real level of the risk in the system independently from the or-ganizational level of the production system.
The analysed industrial enterprise keeps the security stock of metal sheets and components which covers 3 days of production. Hence the change of time Δti for the area of the metal sheets delivery as well as cooperation is as follows:
1,01
Name of the area
[weeks]
Losses of time in the areas with the stock
t2
Losses of time in the i areas without the stoc
Fig. 7. Variation of time in selected areas of the production system with and without the security stock 0
Figure 7 presents only areas of the production system for which the organizational changes were applied. In other areas Δti are as in the Figure 7. The time changes in the areas with the security stocks, specified as Δ and t2r Δ , determine the real extensiont3r time of the production process. Those periods are proportionally shorter because the security stock decreases the negative influence of risk factors in these areas.
Taking into consideration the data presented in Figure 7 there can be calculated values of the weight coefficients in the area of metal sheet delivery and cooperation according to Equation (12):
67
The values of both weight coefficients can be used in Equation (13). The total risk RC for the representative product is equal to:
69
According to the above calculations the implementation into the production system the security stock that covers 3 days production decrease the risk level of the repre-sentative product by 0.04.
References
[1] Bizon-Górecka J.: Engineering of reliability and risk in enterprise management [in Polish], Printing House of the Organisation Development Centre, Bydgoszcz, 2001.
[2] Bubnicki Z.: The basics of computer systems management [in Polish], Printing House of the Wroclaw University of Technology, Wroclaw, 1993.
[3] Burduk A.: Methodology for applications of simulation models in planning and risk evalua-tion of producevalua-tion processes realizaevalua-tion [in Polish], PhD thesis, Wroclaw, 2004.
[4] Drucker P.F.: The emergency theory of manufacturing, Harvard Business Review, No. 3, 1990.
[5] Durlik I.: Engineering of management. Strategy and design of production systems [in Polish], Printing House Placet, Warszawa, 1995.
[6] Migdalski J.: Reliability engineering [in Polish], Printing House ZETOM, Warszawa, 1992.
[7] Ostrowska E.: Risk of investment projects [in Polish], PWE, Warszawa, 2002.
[8] Wilimowska Z., Wilimowski M.: Art of finance management [in Polish], Printing House of Organisation Development Centre, Bydgoszcz, 2001.
Metody wyznaczania ryzyka w systemach produkcyjnych
W artykule zdefiniowano system produkcyjny zgodnie z teorią systemów, natomiast ryzyko potraktowano jako synonim zawodności. Takie podejście umożliwiło dekompozycję systemu produkcyjnego na obszary i wyznaczenie struktury niezawodnościowej. W artykule przedsta-wiono metodę wyznaczania ryzyka dla szeregowej struktury produkcyjnej i koncepcję współ-czynników wagowych uniezależniających poziom ryzyka od poziomu organizacyjnego syste-mu produkcyjnego. Proponowana metoda wyznaczania ryzyka może być stosowana zarówno przy obliczaniu ryzyka poszczególnych linii produkcyjnych, jak i dla całego przedsiębiorstwa.
Metoda została zweryfikowana w przedsiębiorstwie produkującym ramy wózków do wagonów kolejowych i lokomotyw.
ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING
Vol. IX 2009 No. 3