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Research paper : Toward the integrated optimization of steel plate production process (K. Nishioka et al.)−103−Synthesiology - English edition Vol.5 No.2 (2012) manufacturing lead time (rolling start until manufacturing completion). If component events occur independently, the sum of variance of each independent event equals the sum of variance for the total, which means, if respective variations are determined independently, the standard deviation of the number of spare delivery days is estimated by the following formula:spare days until delivery = (spare days for starting rolling against delivery2 + manufacturing lead time2)1/2where, spare days until delivery: standard deviation of the number of spare days until delivery (manufacturing completion until delivery)spare days for starting rolling against delivery: standard deviation of spare days for starting rolling against delivery date (rolling start until delivery)manufacturing lead time: standard deviation of manufacturing lead time (rolling start until manufacturing completion)The estimated number of spare days of delivery is in good agreement with the past records and the validity of the assumption that each one of the events is independent was TemperingQuenchingNormalizingShot BlastingMarkingWeld repairUSTCoatingGas cutingOLCLSurface grindingA・ⅠA・ⅡA・ⅢA・ⅣA・ⅤA・ⅥB・ⅡB・ⅢB・ⅣB・ⅤB・ⅥC・ⅢC・ⅣC・ⅤC・ⅥD・ⅠD・ⅡD・ⅢD・ⅣD・ⅤD・ⅥE・ⅣE・ⅤE・ⅥF・ⅡF・ⅢF・ⅣF・ⅤF・ⅥG・ⅢG・ⅣG・Ⅴ0123456789Steel type/plate thicknessAverage manufacturing completion(a)steel type:A~Gplate thickness:Ⅰ~ⅥAverage manufacturing ldad time, Hr050100150200250300350400(b)A・ⅠA・ⅡA・ⅢA・ⅣA・ⅤA・ⅥB・ⅡB・ⅢB・ⅣB・ⅤB・ⅥC・ⅢC・ⅣC・ⅤC・ⅥD・ⅠD・ⅡD・ⅢD・ⅣD・ⅤD・ⅥE・ⅣE・ⅤE・ⅥF・ⅡF・ⅢF・ⅣF・ⅤF・ⅥG・ⅢG・ⅣG・ⅤTemperingQuenchingNormalizingShot BlastingMarkingWeld repairUSTCoatingGas cutingOLCLSurface grindingsteel type:A~Gplate thickness:Ⅰ~ⅥSteel type/plate thicknessFig. 5 Average number of processes to be passed and the manufacturing lead time for individual product types(a) Average number of processes to be passed for individual product types(b) Average required completion time for individual product typesconfirmed. Using the formula above we calculated the contribution of each term to the standard deviation of spare delivery days, and revealed that the contribution of the spare days for starting rolling against delivery date to the standard deviation of the number of spare days until delivery and the variation of manufacturing lead time were 70 % and 30 % respectively, and it was confirmed that the former contributed predominantly. Therefore, to reduce the standard deviation of spare delivery days, it is important to narrow down the standard deviation of rolling start timing against the delivery day, which means that for lowering the stock level, it is essential to control the lot size of rolling/ steelmaking casting (see NOTE 2).5.5 Analysis for the contribution of manufacturing lead time – lead time of each processThen, we studied the contribution of each plate manufacturing process to the variation of manufacturing lead time. Assuming that the required completion time of each finishing process is determined independently, the variance of the manufacturing lead time as a whole is expressed in the following formula as the sum of variance of the required

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