DOI 10.1007/s10845-009-0302-x
Measuring relative performance of wafer fabrication
operations: a case study
Wen-Chih Chen · Chen-Fu Chien
Received: 4 July 2008 / Accepted: 6 July 2009 / Published online: 25 July 2009 © Springer Science+Business Media, LLC 2009
Abstract This paper was motivated by a request to review relative operations performance for various fabrication facili-ties within a leading Taiwanese semiconductor manufacturer. Performance evaluation is important but often controversial. To dispel the controversy, we propose a two-stage fabrication process model to systematically analyze metrics currently adopted, and show that the commonly used wafer-based indi-ces are biased for operations performance. Instead, they should be decomposed into productivity, representing true operations performance, and manufacturability. We suggest the use of data envelopment analysis because of its confirmed linkages to other widely used productivity measures and its overall performance via relative comparisons. The case study illustrates how the two-stage model evaluates and analyzes real-world operations, and the empirical results show the drawbacks of conventional methods.
Keywords Performance evaluation· Fab operations · Semiconductor manufacturing· DEA
Introduction
Since the global semiconductor industry is highly compet-itive, properly utilizing resources to provide products and services is essential for maintaining firms’ competitive edges and survival. Various types of businesses regard relative W.-C. Chen (
B
)Department of Industrial Engineering and Management, National Chiao Tung University, 30010 Hsinchu, Taiwan
e-mail: wenchih@faculty.nctu.edu.tw C.-F. Chien
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, 30013 Hsinchu, Taiwan
performance analysis as a foundational tool for monitoring, diagnosing and improving activities and processes, determin-ing future strategies and suggestdetermin-ing improvements. The per-formance comparison can be inter- or intra-firm. Inter-firm analyses compare different organizations which are not con-trolled or planned by a central decision-maker. In contrast, intra-firm comparison compares units within an organization and the results are monitored and used by the central decision makers. Particularly, intra-firm comparison is used for peri-odic review in the sense of competition and directly related to rewards including future promotion and compensation. Units under evaluation are thus very sensitive to the performance evaluation rules and methods; controversies often arise in response to the poor performance.
This paper was motivated by a request in real setting to evaluate (compare) the operations performance for various wafer fabrication facilities (fabs) within a leading Taiwanese semiconductor manufacturer. The evaluation is an intra-firm comparison, and is directly related to fab managers’ reputa-tions and compensareputa-tions. This paper uses the term fab oper-ations to refer to all activities in a fab that involve consuming resources to provide outputs such as products or services, and excluding finance, sales and technology development. Indeed, fab operations performance significantly interacts with capacity and resource/product allocations; these factors can influence the performance and evaluation result supplies feedback about past decisions. Although the operations per-formance evaluation is important, as addressed, it is contro-versial. Indeed, fab managers often refuse to accept the poor performance evaluation result and question the method. How to conduct a practically proper and convincing performance evaluation is the major challenge.
Performance evaluation processes include defining met-rics and concluding the performance. A performance evalu-ation method should consider: (1) Inclusiveness—it should
consider all aspects of the organization (Beamon 1999); (2) Reflectibility—it should consider only the aspects responsi-ble for the organization, (3) Convergence— it should provide consistent and simple information (Bhargava et al. 1994). Defining appropriate performance metrics and correctly col-lecting values underlie the success of the evaluation pro-cess regarding to inclusiveness and reflectibility. The metrics selected must be sufficient to represent all necessary impor-tant objectives of the target activities, in this paper, fab oper-ations. There are trade-offs among objectives, and they often lead to inconsistent conclusions based on different indices. Thus, it is desirable to establish a single index effectively rep-resenting the overall performance, and then closely analyze the performance index and the possible drivers.
A literature survey reveals several methods for measur-ing equipment performance in semiconductor manufactur-ing. For example, overall equipment efficiency (OEE) is proposed as a comprehensive index for individual equipment performance. See SEMI E079-0200 (SEMI E079-0200), Jeong and Philips(2001) andMuchiri and Pintelon(2008). Since OEE focuses on a single machine, extensions have been created to measure performance in broader, more complex semiconductor manufacturing systems (e.g., Huang et al. 2003; Chien et al. 2007). Nevertheless, they are detailed and bottom-up approaches based on equipments and other relative policies.
Other studies of semiconductor industry performance evaluation look at macro-operational aspects.Leachman and Hodges(1996) provide the first complete benchmarking of the competitive semiconductor manufacturing (CSM) pro-gram; this program includes several of the leading compa-nies around the world. The authors propose seven KPIs: cycle time per wafer layer, line yield, die yield, stepper produc-tivity, direct labor producproduc-tivity, total labor producproduc-tivity, and on-time delivery. Associations between practices and per-formance are also presented. Although it is the first industry-wide benchmarking study with rich data, the performance is based on various KPIs, and the conclusions should be regarded as the correlations between practices and a particu-lar KPI, and not the overall performance.Leachman et al. (2007) extend the studies in CSM program and use data envelopment analysis (DEA) to provide an overall relative efficiency measure. Total wafer starts, number of steppers, direct and indirect headcounts, and clean room size are the inputs, and die output and effective revenue the outputs. How-ever, these two studies are inter-firm comparisons, not for relatively controversial inter-firm evaluation.
This paper aims to evaluate the performance of the fab-rication site for period review, not a single production line or tools. To our experience, practitioners still utilize vari-ous wafer-based KPIs when assessing fab performance. The major hurdle in adopting methods proposed in the literature such as DEA is that early studies do not provide a clear
rationale for the indices selected, and DEA is less intuitive than traditional wafer-based indices. Moreover, to dispel the controversy, it is necessary to develop: (i) a systematic way to express, model and organize performance metrics; (ii) a method to provide consistent performance conclusions. Therefore, this study aims to propose a two-stage fabrica-tion process model that systematically analyzes metrics cur-rently adopted, and show that using wafer-based metrics are problematic since it violates reflectibility. In particular, DEA is employed to compute the overall relative performance, in which we carefully link DEA theory and the currently adopted ratio methods. To estimate the validity of the pro-posed approach, we conducted a case study in real setting to demonstrate how the proposed model assists in diagnos-ing operations and suggestdiagnos-ing improvements. The empirical results also reveal the bias of wafer-based KPIs and how it leads to poor decisions.
The paper is organized as follows. In the next section, we introduce a two-stage model for the fabrication production process. The model gives a clearer picture of fabrication and a better reasoning of the performance metrics. we then intro-duce DEA as the analysis technique and discusses some of the model’s appealing properties. Next we apply the model to a real-world case study followed by conclusion.
Fabrication production process
This section presents a two-stage model to describe (and understand) fabrication production process, and thus a ratio-nale basis to discuss, model and organize essential perfor-mance metrics is provided to dispel the possible controversy. Particularly, we approach the problem by reviewing the all performance ratios including those based on wafer outputs, which are currently adopted. The model shows using wafer-output as a metric violates reflectibility since it also includes the aspect beyond the responsibility of fab operations.
The operations of a fab are the activities and decisions for transforming resources, e.g., labor, equipments, etc., into products (outputs). Productivity describes the resource-output transformation. A “good” production unit, i.e., one with high productivity, can provide more outputs by using fewer resources. Productivity is measured formally using ratios of output to input; in nontechnical contexts, ratios of input to output are also used (e.g., labor hours needed to pro-duce a car). Both measures give identical conclusions with opposite improvement directions. Wafers are the physical final products produced and delivered. In practice, the typical productivity indices adopted, such as labor or equipment pro-ductivity, use total wafers produced as the output. However, the use of this output is questionable and may underestimate fab operations performance.
Productivity headcount equipment space time effective layer Manufacturability wafer out FabProductionProcess Stage1 Stage2
Fig. 1 Fab production process
This paper suggests a two-stage model to describe the transformation process from resources to final products; the model provides a rationale basis to define proper perfor-mance indices. Figure1shows the two-stage process. Stage 1 refers to productivity, the process that provides masking lay-ers (outputs) by consuming labor, capital investments includ-ing equipments and space, and time. The first three resources are commonly found in other studies. Time, which is not as straightforward as the first three, is the total time used in the production corresponding to a particular volume of layers. Given the same level of labor, equipment and space, more layers require more time. Similarly, less labor (equipment) generally requires more time to generate the same required layers, and reveals the substitutability among resources. It is helpful to interpret the output of Stage 1 (number of layer pro-cesses) as a service provided rather than a product. A good performance indicated in Stage 1, namely providing more layers by using fewer resources, suggests that the production process is productive.
Stage 2 is the process of transforming layers to wafers. Different types of wafer products require different numbers of layers and the transformation itself is termed manufactura-bility. Design for manufacturability (DFM) is an engineering concept that includes a set of methodologies for designing products so that they are simple to manufacture. Manufactu-rability derives from both the engineering side (particularly in R&D activities of design or manufacturing, i.e., manufac-turing recipes), and the strategic side (i.e., allocating prod-ucts to specific fabs). A fab that is assigned prodprod-ucts that are easier to produce will generally exhibit superior perfor-mance. In other words, a greater number of wafer outputs with fewer layers are always preferred since it means fewer steps in manufacturing.
The combinations of resource-output pairs in both stages are identical to the most commonly used productivity indi-ces. Ratio (layer/headcount) is the layer labor productivity measure, and (layer/equipment) is the layer equipment pro-ductivity. Index (layer/space) corresponds to the effective-ness of space usage, and (time/layer) is the layer cycle time. With respect to wafer, combining wafer output and the four resources gives the same meaning as the four indices. For
example, wafer output per headcount is the commonly used wafer labor productivity.
Although number of wafer outputs is commonly used as output in productivity indices, the two-stage model shows that this output may skew the performance of fab operations. Only Stage 1, productivity, stands for real operations per-formance. Poor performance using wafer outputs consists of activities determined and contributed by other functions (e.g., R&D in manufacturing recipes) and central produc-tion planning (e.g., in product allocaproduc-tion). Good operaproduc-tions (productivity) may yield less wafers due to poor manufac-turability. In fact, the “real” responsibility of fab operations is to process various layers based on certain manufacturing recipes using the resources at hand. That is, the operations consume resources to provide services—the layer process-ing—so that the final product—the wafer—is produced via completing the required processes. The two-stage model pro-vides a more accurate picture of this process, and thus the performance evaluation can be conducted with fewer argu-ments, a more effective diagnosis, and proper identification of departmental responsibilities.
For practical implementation, detailed definitions of resources and outputs for monthly performance reviews are listed as follows:
• Layers (L): total number of effective masking layers pro-duced monthly. It is collected as (total layers propro-duced) × (average layer yield rate).
• Wafer outs (W): total number of effective wafers pro-duced monthly. It is collected as (total number of wafers produced)× (average wafer yield rate).
• Headcount (HC): total direct and indirect labor employed monthly. It also includes management and assistant staff. • Equipments (MC): total installed capacity of steppers and scanners (exposure tools) used monthly. Since lithog-raphy equipment is generally the bottleneck among all machine types, it serves as the best proxy for the fab’s equipment capacity. The literature uses total number of steppers and scanners, e.g.,Leachman et al.(2007). Num-ber of tools, however, ignores the difference in production capability of the machines. For example, new tools may have higher throughput than old machines, and/or a more expensive machine may have better throughput as well. The difference on resulting throughput can yield a sig-nificant impact on production performance. Hence, the weighted sum of installed tool capacity is a better proxy. • Space (S): total floor space used and available for man-ufacturing. It reflects the infrastructure investment that becomes the limit of production capacity.
• Time (T ): total time needed to produce the total num-ber of layers. It is computed as (total numnum-ber of layers) × (average cycle time per layer). It should be noticed that total layers, including effective layers and defects,
are considered. Time is a resource and defects result in resource waste; thus defects should be taken into account. Service level is not considered in the proposed model. Good operations use fewer resources including time to pro-vide more outputs and thus contribute to good delivery satis-faction levels. However, a fab operating efficiently will have a poor service level if it is allocated more outputs than it can produce.
Measuring operational performance
As noted earlier, there are up to four measures for any aspect in the proposed model. However, trade-offs exist among performance indices and they can lead to inconsistent conclu-sions. DEA, a mathematical programming approach intro-duced byCharnes et al.(1978), computes a single relative performance score while considering various resources and outputs simultaneously without assuming weights or func-tional form. Because of this attractive characteristic, DEA has been adopted for measuring performance in semicon-ductor manufacturing (e.g.,Leachman et al. 2007). An intro-ductory discussion on DEA can be found inChen and Hong (2008), and Cooper et al.(2000) provide a comprehensive introduction.
Following the proposed two-stage fabrication process model, the output-oriented CCR DEA model (Charnes et al. 1978) is employed to measure the performance on productiv-ity, manufacturability and wafer-based performance as fol-lows: max φt k,λj φt k s.t. j∈St xi jλj ≤ xi k ∀i ∈ It, j∈St yr jλj ≥ φktyr k ∀r ∈ Ot, λj ≥ 0 ∀ j ∈ St (1)
where t∈ {p, m, w} represents models for productivity (p) and manufacturability(m) and wafer-based performance (w), respectively. Sets It and Ot are the resource set and out-put set associated with t, namely, It = {HC, MC, S, T } for t ∈ {p, w}, Op = {L}, Im = {L} and Ot = {W} for t∈ {m, w}. Set Ststands for the collected records for model t . Moreover, xi j and yr j are the amounts of resource i and
output r associated with record j , respectively, given the cor-responding model for record set St. Subscripts k represent a particular record under evaluation, and k ∈ St. It should be noted that (1) is output-oriented, i.e., to maximize out-puts using given resources, because in reality there is less
flexibility in reducing resources. The result also hints at the maximum outputs, the production capacity.
Equation (1) evaluates record k∈ Stby comparing against all records in St. Let φtk∗ t ∈ {p, m, w} be the optimal values in (1) corresponding to three different models. They are the record k’s performance scores for different aspects. For model t, valueφkt∗indicates that the record k can gener-ateφkt∗times for current output level while using the same level of resources, because a best practice comprised by the records in St can be identified and used as the comparison reference. The comprised best practice derives from three simple assumptions: engineering interpolation, free disposal and constant returns to scale (CRS). Free disposal means that if a resource-output bundle is feasible, it is also feasible to use more resources or to produce fewer outputs. CRS assumes that any observed output-resource ratio will hold constant for different sizes of outputs and resources. (CRS is com-monly used.) For example, assume that(x, y) = (2, 6), i.e., y/x = 3, then x should be 4 when y = 12. Moreover, the reciprocal of the score, ekt = φ1t∗
k t ∈ {p, m, w}, normalizes
the performance score to be within 0 and 1. A best practice has a value of 1; thus ekt can be interpreted as the efficiency of record k, i.e., the ratio of record k’s performance to the best practice performance. Clearly,φkt∗ ≥ 1(etk ≤ 1) t ∈ {p, m, w}. φp∗
k = 1 suggests that record k is CCR-efficient in
productivity. Larger value ofφkp∗, smaller ekp, reveals poorer (less efficient) performance in productivity, i.e., it has a more significant edge losing to the best practices. The record k is said to be CCR-efficient in manufacturabilityifφkm∗= 1, i.e., has products that are the easiest to produce. A higherφkm∗ (or smaller emk) shows less manufacturability, i.e., more diffi-cult to produce (because the reference, the easiest to produce, goes through the same number of layer processes to comprise more wafer outputs). Similarly,φkw∗= ewk = 1 indicates that record k is CCR-efficient in wafer-based performance; the interpretation is identical to productivity (t = p), but with wafer as the output.
The dual of Model (1), which will give the same optimal value of Model (1), is (Charnes et al. 1978):
min ui,vr i∈It uixi k s.t. r∈Ot vryr j ≥ i∈It uixi k ∀ j ∈ St, r∈Ot vryr k= 1, (2) ui ≥ 0 ∀i ∈ It, vr ≥ 0 ∀r ∈ Ot.
Model (2) is equivalent to the following problem: min uivr i∈Ituixi k r∈Otvryr k
s.t. i∈Ituixi k r∈Otvryr j ≥ 1 ∀ j ∈ S t, ui ≥ 0 ∀i ∈ It, vr ≥ 0 ∀r ∈ Ot. (3)
Without loss of generality, taking productivity model(t = p) as an example, Model (3) can be rewritten as:
min uH CxH C,k+ uMCxMC,k+ uSxS,k+ uTxT,k vLyL,k s.t.uH CxH C, j+ uMCxMC, j+ uSxS, j+ uTxT, j vLyL, j ≥ 1 ∀ j ∈ Sp, uH C ≥ 0, uMC ≥ 0, uS≥ 0, uT ≥ 0, vL ≥ 0. (4) LetuH C vL = wH C, uMC vL = wMC, uS vL = wS, and uT vL = wT,
Model (4) is rewritten as: minwH C xH C,k yL,k + w MC xMC,k yL,k + w S xS,k yL,k + w T xT,k yL,k s.t.wH C xH C, j yL, j + w MC xMC, j yL, j + w S xS, j yL, j + w T xT, j yL, j ≥ 1 ∀ j ∈ Sp, wH C≥ 0, wMC ≥ 0, wS≥ 0, wT ≥ 0. (5)
Model (5) evaluates record k and has a straightforward inter-pretation. Indeed, xH C, j
yL, j is the number of headcount needed
per layer associated with the commonly used labor produc-tivity in the semiconductor industry. The index used here is the reciprocal of the formal academic labor productivity measure, which is another form used in practice to represent productivity from the resource consumption viewpoint. Ana-logically, xMC, j
yL, j associates with the equipment productivity, and xS, j
yL, j associates with the return rate on space.
xT, j
yL, j is the layer cycle time. Therefore, an overall index is provided and used for all records by weighting productivity values on four aspects in the objective function and constraints. Without assigning subjective predetermined weights of four individ-ual indices, weights are selected in favor (to minimize the weighted index) of record k, while normalizing all records’ score being no< 1 using the same weights.
The manufacturability model is more straightforward since there is only one resource and one output. The con-ventional single productivity ratio approach can be easily adopted. Model (1) will give the same results as using wafer per layer—“how many layers needed to become a complete wafer?”—for the comparison metric.
Model (1) is a useful tool to measure the overall perfor-mance based on resources and outputs. Applying (1) to the proposed two-stage model gives three overall performance scores for three different purposes. It should be noted that the conclusion consistency referring to the performance of a particularly aspect (or responsibility), e.g., productivity or manufacturability. The commonly adopted wafer-based
performance is biased and should be decomposed into ductivity and manufacturability. Manufacturability and pro-ductivity performance have different managerial meanings and are the responsibility of different functions within a firm. For fab operations performance, productivity is the proper aspect to be considered, and this is explained by the two-stage model addressed in section “fabrication production process”. Further, there are some concerns and limitations when implementing DEA. For examples, DEA is a weighting scheme in response to the need of consistency. Its evalua-tion results vary upon different resource-output sets, which should be carefully defined such as our two-stage model. Another important pitfall is that the records should be suffi-ciently larger than number of resources and outputs to have reasonable results. There are some useful references when applying DEA. For example,Golany and Roll(1989) suggest a standard procedure to apply DEA, andDyson et al.(2001) provide a comprehensive review on the pitfalls of DEA.
Case study
This section presents the performance analysis results for a real-world firm in Taiwan. The original goal of the study is to find a way to properly review fab operations by com-paring various fabs within the same firm, i.e., the intra-firm comparison. The four 8-inch fabs operating under similar environments are studied (reviewed together) via peer com-parison. One hundred fifty-six records collected in a 19-month period in 2000s represent the monthly resources consumed and outputs produced. To maintain confidentiality, all records are transformed and then pooled to compute three different performance scores (wafer-based performance, pro-ductivity and manufacturability) based on Model (1). The efficiency scores etk t ∈ {p, m, w} are presented because the values are between 0 and 1 and easier to read.
To estimate the validity of the proposed approach, we conducted a case study in real setting to demonstrate how to use the proposed performance evaluation model; show how wafer-based performance is biased. We also discuss the ways in which the bias affects the decisions. In addition, sec-tions “scale vs. productivity” and “resource slacks” present byproducts of the tool we proposed, which include the scale issue and possible ways to monitor the resources slacks. Performance analysis
Figure2is the box plot for the wafer-based efficiency scores for the four fabs. The y-axis represents the efficiency scores obtained by (1), that is, the reciprocal of optimal value of Model (1), where value 1 is the best and the smaller values indicate poorer performance. The x-axis associates with the fabs. Figure2 shows the fabs’ very different performance
D C B A 1.0 0.9 0.8 0.7 0.6 fab efficiency scores
Fig. 2 Wafer-based efficiency
ranges. Fabs B and D perform slightly better with average scores around 0.93, while fab C is the most inefficient with an average score around 0.77. The difference suggests that fab C does not transform resources to wafer outputs effi-ciently; there is roughly a 20% performance gap compared to fabs B and D.
Figures3 and 4 are the box plots regarding productiv-ity and manufacturabilproductiv-ity, respectively. Figures2and3have the same interpretation. Manufacturability efficiency score 1 indicates that it is the easiest to produce, while a smaller score suggests a more complex product (Fig.4). Efficiencies related to productivity have fewer differences among the fabs, particularly for fab C (Fig.3). Although fab C is still the worst on average, the gap of the mean is significantly reduced to <10% compared to fabs B and D. Fabs A and D have aver-age manufacturability efficiency scores around 0.94, and fab B is slightly worse than A and D (Fig.4). Fab C has the poorest manufacturability; half of its records have efficiency scores from 0.81 to 0.83. The comparison suggests that fab C produces products with special or complicated processes (Fig.4). In fact, fab C mainly produces memory products that typically require more layers than logic products, i.e., memory fabs have poorer manufacturability than logic fabs. Comparing Figs.2,3and4shows that fab C has poor wafer-based performance and manufacturability, but with a much smaller gap in productivity than the other fabs, again because it produces more complex products.
Figure5 shows the efficiency scores for fab A over time. The x-axis represents the time stamp in month and the y-axis the efficiency scores. Squares are scores for produc-tivity, triangles are for manufacturability, and circles are for wafer-based performance. There are no significant trends, either improvement or decline, on productivity and wafer-based performance overall, but there is a decline in manu-facturability (Fig.5). Figures6,7 and8represent efficiency across 39 months for fabs B, C and D. The interpretations are identical to Fig.5. All four figures show relatively stable
D C B A 1.0 0.9 0.8 0.7 0.6 fab efficiency scores
Fig. 3 Productivity efficiency
D C B A 1.00 0.95 0.90 0.85 0.80 fab efficiency scores
Fig. 4 Manufacturability efficiency
manufacturability. Manufacturability for fabs B and D is slightly worse, while fab C trends in a positive direction (as noted, it has worse manufacturability than the other fabs). Figure7shows significant gaps between wafer-based perfor-mance and productivity compared to Figs.5, 6 and 8. The differences are due to fab C’s poor manufacturability.
In addition, a comparison of the three different efficiency scores finds that wafer-based performance and productivity have almost identical patterns, yet with different magnitudes. One the other hand, manufacturability is relatively indepen-dent on the growth or decline pattern change. Periods 10–15 in Fig.5 provide a significant example, where wafer-based and productivity performance drop tremendously in period 11 from about 0.85 to below 0.65 while manufacturability remains stable in score. Although manufacturability has rel-atively stable trend over time, larger gap between wafer based performance and productivity arises when average manufac-turability efficiency is low (e.g., Fab C in Fig.7). Therefore, we can conclude that wafer-based performance is mainly contributed by productivity and manufacturability plays a role of multiplier.
Table1 presents the results of simple linear regression analyses for three models in which the independent variable
0 5 10 15 20 25 30 35 40 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 time efficiency score productivity manufacturability wafer-based
Fig. 5 Changes of efficiency scores (Fab A)
0 5 10 15 20 25 30 35 40 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 time efficincy score productivity manufacturability wafer-based
Fig. 6 Changes of efficiency scores (Fab B)
0 5 10 15 20 25 30 35 40 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 time efficiency score productivity manufacturability wafer-based
Fig. 7 Changes of efficiency scores (Fab C)
0 5 10 15 20 25 30 35 40 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 time efficiency score productivity manufacturability wafer-based
Fig. 8 Changes of efficiency scores (Fab D)
is time and the dependent variables are efficiency scores. Instead of slope coefficient, we present the annual growth rate, namely, 12× (slope coefficient). For wafer-based per-formance, fab C has the best growth rate (3.7%); fab B’s growth rate is 2%. Wafer-based growth rates associated with fabs A and D are not statistically significant. Fab A has the best growth rate (3%) in the productivity model, followed by fab B (2.9%), and fabs C and D (below 2%). For manu-facturability, fabs A, B and D have negative annual rates, suggesting that the products are becoming more complex to produce over time. However, fab C’s positive manufactura-bility growth rate (1.1%) shows that the products assigned to it are becoming easier to produce.
These observations demonstrate both the biases of wafer-based performance and how manufacturability affects wafer-based performance. Thus, a detailed decomposition of wafer-based performance is recommended, and it is prefera-ble to use layer as the output to evaluate fab operations.
We note that fab C is the worst in wafer-based perfor-mance with significant loss (Fig.1), mainly due to product allocation so that fab C also has the poorest manufacturability (Fig.2). Interviews with company personnel reveal that prod-uct complexity is always a key challenge in reviewing perfor-mance using traditional wafer-based indices. Consequently, the production planning department has made modifications in product allocation. We observe that the manufacturabil-ity for fab C is improving (Fig.7); fab C is the only one with improvements in manufacturability (1.1% in Table1). The adjustment made for fab C results that fab C has the best annual wafer-based performance growth rate (3.7%), which has significant edge to others, but the worst annual growth rate for productivity (1.5%). Therefore, we surmise that there may be an over-adjustment. Using conventional methods, manufacturability is a masking effect for argument and so that the real problem is possibly ignored. Moreover,
Table 1 Simple linear regression over time
Fab Productivity Manufacturability Wafer-based
Rate (%)a p Value Rate (%)a p Value Rate (%)a p Value
A 3.0 0.01 −1.6 0 1.3 0.232
B 2.9 0 −2.0 0 2.0 0.003
C 1.5 0.032 1.1 0 3.7 0
D 1.9 0.024 −1.4 0 1.1 0.152
a12× Slope coefficient
manufacturability may have significant multiplier effect to wafer-based performance, namely wafer-based performance is sensitive to change in manufacturability. This effect should be taken into account when make resource allocation deci-sions.
Scale vs. productivity
The following two sub-sections investigate relative produc-tivity performance(t = p) comparisons among different fabs under the well-studied DEA framework. This section analyzes the relationship between productivity and scale in the data set.
Another popular DEA model proposed byBanker et al. (1984) is: max θp k,λj θp k s.t. j∈Sp xi jλj ≤ xi k ∀i ∈ Ip, j∈Sp yr jλj ≥ θkpyr k ∀r ∈ Op, j∈Sp λj = 1, λj ≥ 0 ∀ j ∈ Sp. (6)
Model (6) has additional convexity constraint,j∈Spλj =
1, compared to (1). The difference of optimal values for a par-ticular record k between (1) and (2),φ
p∗
k
θp∗
k
, measures the scale effect, named scale efficiency (Banker et al. 1984). Clearly,
φp∗ k θp∗ k ≤ 1; φp∗ k θp∗
k = 1 indicates that record k is at the proper
pro-duction scale, the most productive scale size (MPSS).φ
p∗
k
θp∗
k <
1 reveals that k is scale inefficient, namely k is too large or too small (Banker et al. 1984). Smaller φ
p∗
k
θp∗
k
shows more differ-ences from the correct size. Moreover, the optimal solution of (1) related to k, σk=
j∈Spλ∗j, provides information on
k regarding the relative scale position to the corresponding MPSS.σk = 2 suggests that the size of k is twice that of
MPSS, and scaling down in production scale may increase
D C B A 1.000 0.975 0.950 0.925 0.900 0.875 0.850 fab scale efficiency
Fig. 9 Scale efficiency
D C B A 2.00 1.75 1.50 1.25 1.00 0.75 0.50 fab relative scale
Fig. 10 Relative scale
the performance in productivity. Similarly, σk = 0.8 says
that the size of k is only 80% of the correct size.
Figures9and10are box plots for scale efficiency and the relative scale to the MPSS. Figure9shows that all records of fabs A and C are scale inefficient, unlike in MPSS. Fab B is only half the size with respect to MPSS, while fabs A and C can be twice as large as the MPSS (Fig.10). In order to balance the fab utilization, resources can be transferred from a fab operating at decreasing return to scale to a fab operating at increasing return to scale.
Resource slacks
It is important to monitor the resource slacks to provide feed-back on resource allocation. Model (7) further investigates the resource slacks, i.e., the exceeded amount of resources needed to provide the maximum outputs:
max λj,si i∈Ip si s.t. j∈Sp xi jλj+ si = xi k ∀i ∈ Ip, j∈Sp yr jλj ≥ θkp∗yr k ∀r ∈ Op, j∈Sp λj = 1, λj ≥ 0 ∀ j ∈ Sp; (7)
whereθkp∗is the optimal solution from (6). Optimal solution si∗ indicates exceeded unnecessary amount for resource i , namely record k can produce the maximum outputsθkp∗yr k
r ∈ Opwithout this amount of resource. We note that (7) is not unit invariant; different optimal solutions will be obtained with scaling on different resources. However, we can gain useful insights about resource allocation and management by observing the trends from the results.
Figure11shows the changes of resource slacks over time for fab A. y-axis is the percentage of slack for a particular resource of the record under evaluation, s∗i
xi k. Squares
repre-sent slack percentages for headcount; triangles, circles and crosses represent slack percentages for equipments, space and time. We find that equipment slacks are significant among four resources. Fab A gets more headcount slacks as time moves. Most of time, space and time slacks are <5%. In par-ticular only three of the 39 time periods show time slacks, suggesting that time is the bottleneck resource for fab A in most situations.
Figures12,13 and 14 have the same interpretation as Fig.11, but represent slacks for fabs B, C and D, respec-tively. Fab B has the least slacks among the four fabs; there are no slacks on space and time (Fig.12). However, head-count and equipment slacks start to exist with vibrations as time passes. This is a negative sign for fab B’s headcount and equipment allocation and usage. Fab C is the worst in terms of slacks among the four fabs, but Fig.13 also shows sig-nificant improvements for fab C. There are improvements in resource slacks for fab D (Fig.14); the space slacks decrease over time from >15 to 0% in the last four periods.
Comparing Figs.11,12,13 and14 shows no slacks for time. This observation may suggest that time is typically the bottleneck resource and is intensively controlled and moni-tored, although we cannot identify the causes and/or effects. We also note that two fabs improving their exceeded resource
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 slacks (%) headcount equipments space time time
Fig. 11 Change of resource slacks (Fab A)
0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 time slacks (%) headcount equipments space time
Fig. 12 Change of resource slacks (Fab B)
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 time slacks (%) headcount equipments space time
0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 12 14 16 18 time slcks (%) headcount equipments space time
Fig. 14 Change of resource slacks (Fab D)
level while the other two show declining performance may signal an important message for future improvement.
This case study demonstrates how a proper (and/or inap-propriate) performance analysis influences the decisions, e.g., resource allocation and management. The results sug-gest that, first, productivity indices using wafer as output are biased. The wafer-based performance should be decomposed as productivity and manufacturability. Wafer-based metrics may mislead the adjustments in response to the critics. The ultimate evaluation metrics for individual fabs should be carefully defined. Second, the scale effect “bigger is better” does not always exist. Third, exceeded resource usage must be controlled. Typically more than 10% slacks are for phys-ical resources such as headcount and equipments; however, time is the largest binding constraint.
Conclusion
Performance evaluation and analysis are important for maintaining competitive edges and survival in the globally competitive semiconductor industry. This paper is motivated by a real case in Taiwan to evaluate operations performance by comparing various fabs within the same firm. The intra-firm competitive performance comparison has always been controversial. We present a two-stage fabrication process model to provide a reasoning platform to discuss, organize, and explain performance metrics. The model suggests that conventional wafer-based metrics are biased for operations performance since it includes the manufacturability aspect that is not the responsibility for fab operations. The case study provides evidence to support our suggestion for evalu-ating fab operations. The empirical results show that wafer-based performance is mainly contributed by productivity
while manufacturability plays a role of multiplier that results in masking effects that may cause misinterpretation of the real problem. The results also suggest that exceeded resource usage must be properly controlled, especially since there are typically more than 10% slacks for physical resources such as headcount and equipments. Surprisingly, “bigger is better” is not true in our case, which suggests further investigation of scale decisions. The proposed model with DEA provides an overall performance measure through relative comparisons. In addition, we present its strong linkages to various, widely used productivity ratios, and offer a mechanism to promote its adoption in practice.
Acknowledgments This research is partially supported by National
Science Council, Taiwan (2221-E-007-111-MY3 and NSC97-2221-E-009-113), Taiwan Semiconductor Manufacturing Company (96A0279J8), and the Faulty Empowerment Award of National Tsing Hua University (97N2521E1) from Ministry of Education, Taiwan. The authors appreciate the invaluable comments from anonymous review-ers and the Guest Editors Professor Mitsuo Gen and Professor Hark Hwang.
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