A proper process planning can significantly improve a producer’s competitiveness in regard to delivering high-quality and low-cost products with short development-cycle time. Because of process shifting, the produced quality may change during a production run and lead to early product failures. Hence, to compensate for such process shifting, there is a need to determine the optimal resetting cycle before the next setup as well as the initial settings at the beginning of a production run. As the process tolerance is one of the key elements in the production process, determination of the process tolerance must also be considered. Due to the interdependence among decision variables, a model for process planning is proposed to simultaneously determine the initial setting, process tolerance, and resetting cycle, so that the average total cost, in a period of resetting cycle, which includes the setup cost, quality loss, failure cost and tolerance cost, is minimized under process-capability limits, functionality requirements, and conforming rate restrictions.
A certain amount of variation will exist in any production process, regardless of how well it is designed or how carefully it is maintained. This variation is the cumulative effect of many essentially avoidable or unavoidable causes [1]. The variation in quality characteristics usually arises from three sources of error: improper process establishment, operator errors, or defective raw materials. The various errors from improper process establishment will result in poor, inaccurate, and defective parts, including random deviation and systematic deviation from the design target.
During the process design, parameter design determines the process setting, thereby reducing the susceptibility of unit-to-unit variation. The need for further reduction in process variation is generally considered after sensitivity to noise has been minimized. This is related to the process selection, in order to achieve a certain required process capability, namely process tolerance determination. To achieve product functionality, process engineers should specify the process tolerance at a value less than design tolerance to ensure manufacturing feasibility. Because the design tolerance exceeds the process tolerance, additional space for process distribution provides for a possible shift within the specification limits. The process mean may be set at various positions within the specification limits for further quality improvement and cost reduction. That is, the process mean and process tolerance are two decision variables that have to be determined simultaneously because of the dependence existing between the mean and tolerance values during process planning [2] and [3]. In other words, a simultaneous determination of the process mean and process tolerance for a true optimization of process planning is necessitated. However, previous research only focuses on process mean and process tolerance determination under the situation that process shifting does not exist during the production process.
It is possible that a shifting process may occur during the production process. For example, in metal cutting operations, the machining tool is subject to both wear and random shocks. If modification for process shifting is not made during a production run, the risk of product failure increases and the quality of product performance decreases, resulting in a large proportion of non-conforming items [4], [5], [6], [7] and [8]. For modification, the process mean is adjusted to an initial setting with additional setup cost to compensate for the process shifting over the resetting cycle. In regard to the shifting process, Jeang et al. also developed a time-based tolerance design model that considers component deterioration due to wear, when designing the product’s life application [9]. However, the relevant previous works mainly focused on finding the optimal process mean and process tolerance independently with the optimal use time (production run length) for a deteriorating process. As pointed out in the above discussion, a simultaneous determination of the process mean and process tolerance is required for true process optimization. In these regards, Jeang further developed a concurrent optimization of a time-based parameter and tolerance design for an assembly [8]. Thus, there is a motivation to extend a time-based parameter and tolerance design for an assembly to a time-based parameter and tolerance design for process planning in this study.
The loss function is an expression which estimates the cost of quality value versus target value and the variation in product characteristics in terms of monetary loss due to product failure in the view of the consumer [10] and [11]. Quality-related production costs usually increase as the value of the process tolerance becomes tighter, due to the need for more refined and precise operations as the output ranges are reduced. Generally, a low quality loss (good quality) implies a high quality-related production cost (tight tolerance) and a high quality loss (poor quality) indicates a low quality-related production cost (loose tolerance) [12]. Other than quality loss and tolerance cost, there is a possibility that failure costs may occur when the quality values fall outside the specification limits.
In addition, due to process shifting, the process mean is reset at the end of the resetting cycle with a given setup cost, which may influence the appropriate tolerance value being selected. Hence, the quantitative analysis model should minimize the average total cost, for the period of the resetting cycle, and contain the setup cost, quality loss, failure cost, and tolerance cost, with the initial setting, process tolerance, and resetting cycle to be simultaneously determined for further quality improvement and cost reduction.
This paper is written in eight sections. Section 1 is the introduction; Sections 2, 3, 4 and 5 describe the related background information employed for reference in this research; Section 6 presents the model development; Section 7 provides an application; and a summary is given in Section 8. Appendix A proves the dependence between process mean and process tolerance. Appendix B presents the formulation of conforming rate requirements.
