Capability Index Making using Economic Process for Product Design and Process Planning Economic Process Methods

“Process capability index — real-time quality status 􏰔 production cost — off-line — tolerance cost function, concurrent product design”


In recent years, as the concept of concurrent engineering has become widely accepted, design engineers hope to achieve simultaneous product design and pro- cess planning, side by side, at an early stage of product development [1]. The goals are: to shorten the time span required for introducing the new product onto the mar- ket and to attain the lowest production cost and premium product quality. Hence, what is needed is a way to measure the degree of the producer’s process capabil- ity, in satisfying the customer’s quality requirement. More importantly, a growing number of producers include this measurement value in their purchase contracts with customers, as a documentation requirement [2]. One such measurement is the process capability index (PCI).

The process capability index (PCI) is a value which reflects real-time quality status. The PCI acts as the reference for real-time monitoring that enables process controllers to acquire a better grasp of the quality of their on site processes [3, 4]. Although the PCI is considered as one of the quality measurements employed during on-line quality management, several authors have pointed out that the PCI should be addressed at the beginning of the design stage rather than at the production stage, where process capability analysis is typically done [Shina, 1995]. For the sake of convenience, let us call the PCI for the former one, off-line PCI, and the latter one, on-line PCI. The on-line PCI has realized process mean and process variance that are obtained from the existing process. Conversely, the off-line PCI has the process mean and process variance as two unknown variables, which the product designer and process planner would have to determine. When cost is not considered as a factor for off-line PCI analysis; normally the process planners would do their best to set the process mean close to the design target, and minimize the process variance to the process limit. Because the additional cost incurred for tightening the variance is not considered, obviously, the establishment of mean and variance values will result in a high PCI scale [6]. Thus, a PCI expression which contains cost factors for an Off-line application is developed.

The PCI value is typically defined as the ability to carry out a task or achieve a goal. The controllable factors are the process mean and process variance [7]. The deviation between process mean and design target can be reduced by locating the process mean close to the design target without additional cost being incurred. The process variance can be lowered by tightening the process tolerance, with extra cost incurred. In case the conventional on-line PCI is used for process capability analysis during the product and process designs, designer engineers naturally intend to raise the PCI value by locating the process mean near the target value, and by reducing the tolerance value to ensure a better product quality. However, simply increasing the PCI value can easily create additional and unnecessary production costs that result from extra efforts and expensive devices for ensuring tolerance control. Hence, there is a need to balance customer demands for quality and pro- duction costs. In this regard, the off-line PCI value is introduced, in consideration of quality loss and production cost, simultaneously in this research. The quality loss is expressed by quality loss function, and the production cost is represented by tolerance cost function. Then, this new PCI expression can be used as linkage for concurrent product design and process planning, prior to actual production. The rationale will be discussed in the latter sections.

Process Capability Indices (PCI)

Fig. 1. The Distribution for process A, B and C
Table 1. PCI values for processes A, B, and C

Single Quality Characteristic

Table 2. Various CPMC when CPM is 1.2

Multiple Quality Characteristics

Fig. 2. A DC differential amplifier
Table 3. The numerical results of example 2

In Conclusion



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