Abstract
Quality risks determined by inspection economies represent a difficult controllable variable in complex manufacturing environments. Planning a quality strategy without being able to predict its effectiveness in all the stations of a system might eventually lead to a loss of time, money and resources. The use of one station to regularly select the samples for a production segment introduces relevant complexities in the analysis of the available quality measurements when they are referred to the other stations in that segment. The multiple streams of product through the parallel machines of the stations and the cycle time randomness, responsible for variation of the item sequence order at each production step, nullify the regularity of the sampling patterns at the machines of the non-sampling stations. This work develops a fundamental model which supports the prediction of the ‘quality risk’, at a given machine in the non-sampling stations, associated with a particular sampling policy for a multi-product, multi-stage, parallel processing manufacturing system subjected to sequence disorder and multiple stream effects. The rationale on which the model is based and successful applications of the model, to scenarios structurally different from those used for its development, give confidence in the general validity of the model here proposed for the quality risk prediction at non-sampling station machines.
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Acknowledgements
This research has been funded by an Enterprise Ireland Innovation Partnership Scheme under the Government of Ireland’s National Development Plan 2007–2013 and the European Union Structural Funds.
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Appendix
Appendix
The main effects plot for the mean time between samples reveals that all the three factors considered in the analysis, which are the line speed, the line configuration and the sampling intervals, impact this performance measure (Fig. 14(a)). The sampling interval proves the most affecting factor; the larger the sampling interval (level 1), the lower the sampling frequency, hence, the higher the mean time between samples. An enlarged line configuration (level 1) determines an increase in the mean time between samples at a machine level as the same number of items, both sampled and unsampled, is spread across a greater number of machines.
Main effects & Interaction plots for the Mean Time Between Samples (MTBSs) & the Number of Consecutive Unsampled Items (NCUIs)
The impact of the line speed on the mean time between samples is ascribable to the potential influence that variations of the line speed can have on the inter-arrival time at a station level. Whenever the inter-arrival time is affected by variations of the line speed (e.g. in scenarios 3 and 4), then the mean time between samples will vary. The increase in the line speed for scenarios 3 and 4 is obtained by reducing the inter-arrival time of all the products in the segment; this necessarily means an increase of the time between samples as they arrive slower at each station and, as a consequence, at each machine. This observation on the line speed is confirmed by the results shown in the interaction plot for the mean time between samples (Fig. 14(b)). The line speed presents an impact on the mean time between samples only for the low level of the line configuration; for the original line configuration (level −1) the increase in line speed is obtained by reducing the inter-arrival time so that the inventory level in the segment could be reduced (scenarios 3 and 4). In the enlarged configuration (level 1), the line speed does not impact the mean time between samples. Figure 14(b) also suggests that the sampling interval does not interact with the other two factors. The factorial plots for the number of items between consecutive samples suggest that the sampling interval is the only affecting factor (Fig. 14(c)). The mean number of items between samples at a machine reduces when the sampling intervals are smaller; this means that the products are sampled more frequently. No interaction between the factors is detected (Fig. 14(d)).
The plots reported in this Appendix refer to the responses obtained at the machines of the first production station in the segment. The different cross flows observed at the different stations prevent considering the output data pertaining to the different stations as replications of the experimental plan. Similar results, to the ones shown here, were obtained for the other non-sampling stations.
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Rotondo, A., Young, P. & Geraghty, J. Quality risk prediction at a non-sampling station machine in a multi-product, multi-stage, parallel processing manufacturing system subjected to sequence disorder and multiple stream effects. Ann Oper Res 209, 255–277 (2013). https://doi.org/10.1007/s10479-012-1145-y
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DOI: https://doi.org/10.1007/s10479-012-1145-y