Volume 16 Number 2
April 2019
Article Contents
Chang-Jun Li, Zong-Shi Xie, Xin-Ran Peng and Bo Li. Performance Evaluation and Improvement of Chipset Assembly & Test Production Line Based on Variability. International Journal of Automation and Computing, vol. 16, no. 2, pp. 186-198, 2019. doi: 10.1007/s11633-018-1129-8
Cite as: Chang-Jun Li, Zong-Shi Xie, Xin-Ran Peng and Bo Li. Performance Evaluation and Improvement of Chipset Assembly & Test Production Line Based on Variability. International Journal of Automation and Computing, vol. 16, no. 2, pp. 186-198, 2019. doi: 10.1007/s11633-018-1129-8

Performance Evaluation and Improvement of Chipset Assembly & Test Production Line Based on Variability

Author Biography:
  • Chang-Jun Li received the B. Sc. degree in administration management from Xichang College, and in computer science and technology from University of Electronic Science and Technology of China, China in 2012, respectively. He is currently a Ph. D. degree candidate in guidance, navigation and control (GNC) at University of Electronic Science and Technology of China, China. His research interests include production planning and control, fault prediction and diagnosis and maintenance, system integration and automation, computer simulation. E-mail: yeslcj@163.com ORCID iD: 0000-0002-1082-2732

    Zong-Shi Xie received the B. Sc. degree in mechanical engineering from University of Electronic Science and Technology of China, China in 2016. Currently, he is a master student in systems engineering at School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, China. His research interests include mechanical manufacturing and automation, production planning and control. E-mail: hlvyuxfe@gmail.com

    Xin-Ran Peng received the B. Sc. degree in industrial engineering from Guizhou University, China in 2010, and the M. Sc. degree in pattern recognition and intelligent system at School of Aeronautics and Astronautics, University of Electronic Science and Technology of China (UESTC), China in 2013. She currently works for Bank of China Guizhou branch and engages in project management.Her research interests include mechanical manufacturing and automation, production planning and control, computer simulation. E-mail: playingxr@163.com

    Bo Li received the B. Sc. degree in mechanical engineering from the Nanchang Institute of Aeronautic Technology, China in 1997, the M. Sc. degree in mechanical engineering from Guizhou University of Technology, China in 2000, and the Ph. D. degree in mechanical engineering from Zhejiang University, China in 2003. He is now a professor and doctoral supervisor in University of Electronic Science and Technology of China (UESTC), China. He has published about 30 refereed SCI/EI/ISTP journal and conference papers. He is the director of the Intel-UESTC joint lab for advance semiconductor manufacturing and industrial engineering. His research interests include production planning and control, fault prediction and diagnosis and maintenance, system integration and automation. E-mail: libo@uestc.edu.cn (Corresponding author)ORCID iD: 0000-0002-7095-4841

  • Received: 2017-06-14
  • Accepted: 2018-03-20
  • Published Online: 2018-06-13
  • " Factory physics principles” provided a method to evaluate the performance of a simple production line, whose fundamental parameters are known or given. However, it is difficult to obtain the exact and reasonable parameters in actual manufacturing environment, especially for the complex chipset assembly & test production line (CATPL). Besides, research in this field tends to focus on evaluation and improvement of CATPL without considering performance interval and status with variability level. A developed internal benchmark method is proposed, which established three-parameter method based on the Little′s law. It integrates the variability factors, such as processing time, random failure time, and random repair time, to meet performance evaluation and improvement. A case study in a chipset assembly and test factory for the performance of CATPL is implemented. The results demonstrate the potential of the proposed method to meet performance evaluation and emphasise its relevance for practical applications.
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Performance Evaluation and Improvement of Chipset Assembly & Test Production Line Based on Variability

Abstract: " Factory physics principles” provided a method to evaluate the performance of a simple production line, whose fundamental parameters are known or given. However, it is difficult to obtain the exact and reasonable parameters in actual manufacturing environment, especially for the complex chipset assembly & test production line (CATPL). Besides, research in this field tends to focus on evaluation and improvement of CATPL without considering performance interval and status with variability level. A developed internal benchmark method is proposed, which established three-parameter method based on the Little′s law. It integrates the variability factors, such as processing time, random failure time, and random repair time, to meet performance evaluation and improvement. A case study in a chipset assembly and test factory for the performance of CATPL is implemented. The results demonstrate the potential of the proposed method to meet performance evaluation and emphasise its relevance for practical applications.

Chang-Jun Li, Zong-Shi Xie, Xin-Ran Peng and Bo Li. Performance Evaluation and Improvement of Chipset Assembly & Test Production Line Based on Variability. International Journal of Automation and Computing, vol. 16, no. 2, pp. 186-198, 2019. doi: 10.1007/s11633-018-1129-8
Citation: Chang-Jun Li, Zong-Shi Xie, Xin-Ran Peng and Bo Li. Performance Evaluation and Improvement of Chipset Assembly & Test Production Line Based on Variability. International Journal of Automation and Computing, vol. 16, no. 2, pp. 186-198, 2019. doi: 10.1007/s11633-018-1129-8
    • Performance evaluation and improvement of the semiconductor manufacturing system based on current factory resources has become more and more important for the manufacturing factory, especially for a chipset assembly & test production line (CATPL) which needs much money investment for the manufacturing system. Variability, which exists in all manufacturing systems and can have enormous impact on production performance[1], plays an important role in design and improvement of manufacturing systems. Thus, variability should be taken into account[2, 3].

      Some approaches have been proposed to evaluate the performance. Akhavan-Tabatabaei et al.[4] proposed a Markov chain framework to approximate the cycle time (CT) in semiconductor manufacturing line. Then, Kang et al.[5] developed an embedded Markov chain model to study the multi-product manufacturing systems with non-exponential processing time. Jarrahi and Abdul-Kader[6] proposed an approximation method to evaluate the performance of a multi-product unreliable production line. Recently, Grema and Cao[7] proposed a dynamic data-driven approach for control variable selection to optimize feedback strategy for increment performance. Loganathan et al.[8] suggested a methodology for availability evaluation using semi-Markov model considering variable failure or repair rates distribution. Although the parameters successfully show the different performance of a production line to some extent, it is difficult to evaluate the integrated performance of the production line across-the-board. Besides, quite few of them focused the impact of variability level on the performance of the whole production line.

      The complicated characteristics in CATPL include: random setup time, re-entrant flows, scheduled and unscheduled machine downtimes, product-machine qualification, levels of automation, and the fact that some processing steps require auxiliary resources[9]. Due to the complexity of practical production systems, it is inconvenient to take all the details into account. Hence, much recent work have mainly focused on performance evaluation and improvement considered variability[1014]. Those evaluations can tell the performance of production line and have been used in practical literature. However, like approximation models[1518], they do not readily provide the same qualitative insights which may be possible via performance interval results. In addition, these approximation models have not explicitly incorporated issues, such as coefficient of variation, namely variability level.

      Recently, some studies have been conducted about using the three-parameter method of production line. Research in the field of performance evaluation and improvement tends to focus on issues, such as cycle time[1922], throughput (TH)[2326], work in process (WIP)[27, 28], and their combinations[11, 15, 29]. These approaches primarily focus on determined parameters (i.e., processing time, failure time, and arrival time) while widely disregarding variability other than quantized variability[30, 31]. This finding is attributable to the neglect of variability level in academic research, as well as in practice, despite its increasing significance. There has been an increasing interest in variability factors and variability level in the last years, for instance focusing on variability[1, 2, 22, 32] or scheduling[3335]. However, to the best knowledge of the authors, there is no evaluation method focusing on the variability level with internal benchmark that combines with Little′s law and is applicable for CATPL.

      Little′s law points out the intrinsic relationship between these parameters, has been widely used[3638]. Li and Xiong[39] proposed a quantitative evaluation criterion based on the Little′s law. Kalir and Bouhnik[40] made an effective change of parameter values of the governing WIP management policy to reduce the CT of a semiconductor factory based on P-K formula. Li et al.[41] extended the principles of factory physics and developed a methodology called O_L graph about semiconductor assembly which integrates overall equipment effectiveness, cycle time, TH, WIP level, etc. But most of them are still extremely difficult to adapt the algorithms to different production lines because they are usually designed for domain-specific problems[42]. Dong et al.[43] constructed a multi-model, multiple-assembly-line, mixed-lines assembling for improving the utilization of assembly lines and the order fulfillment rate. Although many methods, as reviewed above, for performance evaluation and improvement have been successfully employed, the performance state still does not seem to be clear yet. Besides, they do not point out the best state line or the performance interval.

      Moreover, CATPL produces different jobs, and mixed jobs are processed at the same time and same workstation, the next moment they will be transported to different workstations. To distinguish the type and quantity of jobs and calculate the parameters by a production line is not simple. Therefore, the model methods from “factory physics principles” cannot directly be employed to deal with the actual data and evaluate the performance of the production line effectively. Besides, while performance prediction has been used to improve the practical CATPL[4446], no closed form expressions considering variability have been obtained.

      To address the issues above, an evaluation and improvement approach that combines internal benchmark evaluation model of the production line with variability level is proposed. This paper aims to calculate performance interval results and find the improvement direction of performance. To this end, a variability quantification and three-parameter method based on Little′s law is adopted.

      This paper is organized as follows. Section 2 introduces the evaluation and improvement of CATPL, which shows parameters calculation method for logical production lines, internal benchmark evaluation and performance improvement based on variability level. Section 3 presents a case study to demonstrate its strength and limitations. The method is compared with the results obtained by different parameters that include each workstation and whole production line. Finally, conclusions and future research directions are discussed in Section 4.

    • As shown in Fig. 1, the performance evaluation method of CATPL based on Little′s law includes the CATPL analysis, product-mixed problem solution, parameters calculation method for 4 kinds of logical production line, (i.e., the single, series, parallel and series, and parallel workstation), parameters collection of each workstation and the whole production line, the internal benchmark evaluation of production line performance, and the improvement concern with variability. The performance evaluation and improvement in Fig. 1 may be repeated until the production plan ultimately reached. Assume CATPL has no influence on manual operators, and validating evaluation results. There are infinite buffers at each workstation and the service discipline is first come first served (FCFS).

      Figure 1.  Model of the performance evaluation

      The schematic diagram presented in Fig. 1 below illustrates the performance evaluation model to be studied. $T_0$ is the raw processing time of the production line, it is the sum of the long-term average processing times of each workstation in the production line. Alternatively, $T_0$ can be defined by the raw processing time as the average time it takes a single job to traverse the empty production line. $r_b$ is the bottleneck rate (parts per unit time or jobs per unit time) of the production line. $W_0$, namely, critical WIP, is the work in process level for which a production line with given values of $r_b$ and $T_0$, but having no variability achieves maximum TH (i.e., $r_b$) with minimum CT (i.e., $T_0$), it is defined by $W_0=r_bT_0$. $TH_{\rm min}$ is the minimum process rate of the workstation in the series production line.

    • Regarding special process mode of CATPL, the parameters, such as actual TH, CT and WIP, are difficult to obtain in the stochastic environment, because the same production line may have different TH with different jobs. In actual manufacturing environment, the operators always evaluate the WIP and TH by single job, not for all jobs. One type of jobs is considered in proposed method, which also decreases the complex level of the evaluation problem and can meet the actual demand well.

      In this paper, the internal benchmarks of three-parameter method of the production line performance status based on Little′s law is illustrated as Fig. 2.

      Figure 2.  Internal benchmark of production line

      The dot indicates the performance status of the actual production line. According to the internal benchmark in Fig. 2, more knowledge can be obtained as below:

      1) If the performance state of the actual production line is between best-case and actual worst-case, it is figured as “good”, and if the performance state of the actual production line is between worst-case and practical worst-case performance status, it is figured as “bad”. The improvement opportunities could be got by comparing the figure of CT-WIP and TH-WIP.

      2) As seen in Fig. 2 (a), increasing work in process level will inevitably increase the CT. Therefore, the work in process level cannot be increased without limit.

      3) Fig. 2 (a) shows the line, which is through the dot (157.33, 40.30) and parallel to the best-case, it means the trends with WIP, CT and TH when the variability and utilization are not changed. The proof shows below:

      When the variability is constant and WIP $>{W_0}$, the CT-WIP relation is a straight line parallel with the best-case line in rectangular coordinate system. As the effect of variability is to make the jobs wait before the workstations and form a queue, the average queue length is a constant. Assume a single machine workstation, its process rate is $r_e$, average queue length is $WIP_q$, extra work in process is $WIP_e$ (variable), so actual $WIP = {WIP_q} + $${WIP_e}$, as Fig. 3 shows.

      Figure 3.  Actual WIP

      When ${WIP_q} \!+\! {WIP_e}>{W_0}$, $CT \!\!=\!\!\displaystyle\frac{1}{r_e}\!\!+\!\!\displaystyle\frac{(WIP_q \!+\!WIP_e)}{r_e}\!=$$\displaystyle\frac{1}{r_e}+\displaystyle\frac{WIP_q +WIP_e}{r_e}$. $\displaystyle\frac{1}{r_e}+ \displaystyle\frac{WIP_q}{r_e}$ is a constant, and $WIP_e$ is a variable. Therefore, the function represents linear equation whose slope is $\displaystyle\frac{1}{r_e}$, intercept is $\displaystyle\frac{1}{r_e}+$$\displaystyle\frac{WIP_q}{r_e } $, and the function of the best case line is $CT = \displaystyle\frac{w}{r_e}$. According to the mathematical knowledge, two lines with the same slope and different intercept are parallel.

      When the variability level changed, the line which is parallel to the best-case will be also changed. In order to improve the performance of the production line, how should engineers adjust or control? As we know, the fastest decline is the vertical direction in the optimization theory. Thus, the best improvement to change the variability is in the vertical direction. How to contrast the performance of the production line? The answer is distance. Assume that there are two actual dots at the same area in the evaluation figure, the one which is shorter from the best-case has better performance.

      Because in actual production, the TH mostly exceeds the critical dot $W_0$. Assume the best case is more than the coordinates of any two dots ($w_1$, $ct_1$) and ($w_2$, $ct_2$) of $W_0$ on the internal benchmark. The formula of parallel line (PL) is

      $y = kx + b.$

      (1)

      By the basic theory that the slopes between two parallel lines are equal, the slope of PL can be calculated as

      $k = \frac{{c{t_1} - c{t_2}}}{{{w_1} - {w_2}}}.$

      (2)

      By substituting (2) into (1), it obtains

      $b = CT - \frac{{c{t_1} - c{t_2}}}{{{w_1} - {w_2}}} \times WIP.$

      (3)

      Therefore, PL can be written:

      $y = \frac{{c{t_1} - c{t_2}}}{{{w_1} - {w_2}}}x + CT - \frac{{c{t_1} - c{t_2}}}{{{w_1} - {w_2}}} \times WIP.$

      (4)

      Thus, value of TH can be calculated by the Little′s law, and the PL line of the WIP-TH figure of the production line can be drawn.

      According to the performance of prediction model and the parameters in the internal benchmark, it can be seen that with the change of the ideal parameters, the location of the benchmark varies with the job type and the parameters. The goal of the enterprise is to make the production state good. As seen in Fig. 2 (a), it can be seen that each actual performance dot is at a distance from the improvement state, which arises from variability. According to the optimization theory, the rate of vertical descent is the fastest, namely, the improvement direction of the current performance point is the best in vertical direction. In the two different benchmark scenarios, the relative merits of actual performance can be judged by comparing the actual performance with the shortest distance of the best theoretical state. The work in process level is higher than the critical work in process level, based on the performance evaluation method. Get the distance $d$ between actual performance dots $J\left( {wip, ct} \right)$ and best case line $C{T_{best}} = \displaystyle\frac{w}{r_b}$. The distance formula from dot $\left( {{x_0}, {y_0}} \right)$ to the line $Ax + By + C = 0$ is

      $d = \frac{{\left| {A{x_0} + B{y_0} + C} \right|}}{{\sqrt {{A^2} + {B^2}} }}.$

      (5)

      Thus, the distance $d$ from actual performance to the best case line can be written as

      $d = \frac{{\left| {\frac{1}{{{r_b}}} \times wip - ct} \right|}}{{\sqrt {{{\left( {\frac{1}{{{r_b}}}} \right)}^2} + 1} }}.$

      (6)

      By using this formula, the performance can be compared from the quantitative evaluation.

    • The performance improvement of basic parameters (such as TH, $T_0$, tool quantity) or variability are considered.

      1) TH. Increasing TH is a way to improve the performance of the production line. Factory may consider to make the TH reach its maximum value of the bottleneck rate $r_b$, and the performance could be the best-case. But due to the negative impact caused by the variability, the TH only could be closer to $r_b$. If the TH is slightly changed, the massive work in process should be supplied as the TH and WIP are with exponential growth. But in actual process, it is impossible to be achieved. Consider to adjust lot size that would be a good method to increase the TH. The relationship between lot size and CT is shown in Fig. 4.

      Figure 4.  CT varies with lot size

      As seen in Fig. 4, the lot size has a severe impact on CT. When the lot size is increased from 1 to 150, the CT declines from 2 600 to 500 rapidly. However, as the lot size continues to increase, the CT tends to increase slowly. As a result, the appropriate lot size can help to improve the CT.

      2) $T_0$. If the variability remains unchanged, the CT will be changed obviously with the lot size. Increasing lot size could decrease the processing time and increase the TH of a workstation at the same time when the total quantity has not been changed.

      3) Tool quantity. Increasing tool quantity could reduce the processing time when producing the same quantity jobs. But the factories may have limitations for it. Firstly, tool quantity should not exceed the total tool quantity. Secondly, tool quantity should be setup to keep the bottleneck invariant.

      Since the performance prediction model of the production line can reflect the relationship between variability level and performance, and the improved internal benchmark quantitative evaluation methods can correctly evaluate the performance status and the results of the comparison. By combining the predictive model and the quantitative evaluation method, an analysis method of “What if” can be employed to pre-optimization or optimize the parameters of the production line. Choose the improvement direction by the evaluated and compared results once more. The steps of the method are shown in Fig. 5 and described as follows:

      Figure 5.  Improvement steps of performance

      Step 1. Use the prediction model to predict production performance.

      Step 2. Evaluate the performance by using internal benchmark methods, analyse the status of production line, and determine the improvement direction. By analysing the parameters and figure of internal benchmark, the improved space of performance can be judged.

      Step 3. Find the optimized direction and put forward the improvement scheme by combining with the actual situation. Use performance prediction model to predict the adjustment scheme repetitively.

      Step 4. Apply internal benchmark to evaluate and re-evaluate the results of the improvement scheme.

      Step 5. The improvement scheme of performance is finally determined by evaluation-judgment-adjustment and re-prediction & re-evaluation repeatedly.

      4) Variability. The variability mostly comes from natural, pre-emptive outages, non-pre-emptive outages, and operators, while reducing variability plays a key factor in decreasing system queue time[32]. To improve the performance by variability control may be the hardest work. However, the variability level in an appropriate way could help engineers evaluate or improve the performance. To analyze variability levels, variability must be quantized. The coefficient of variation (CV) $c$ can be written as[1]

      $c = \frac{\sigma }{t}$

      (7)

      where $\sigma $ and $t$ indicate the standard deviation of the time and mean time, respectively.

      Consider the pre-emptive variability, such as machine random failure. The availability of a machine can be written as

      $A = \frac{{{m_f}}}{{{m_f} + {m_r}}}$

      (8)

      where $m_f$ and $m_r$ indicate the mean time to failure (MTTF) and mean time to repair (MTTR), respectively.

      Thus, the mean effective processing time $t_e$ can be calculated as

      ${t_e} = \frac{{{t_0}}}{A} = \frac{{{m_f} + {m_r}}}{{{m_f}}}{t_0}$

      (9)

      where $t_0$ indicates the average natural processing time, i.e., average raw processing time of the workstation.

      In CATPL, the situation of setup and re-work are existing, which belong to non-pre-emptive variability, so the mean effective processing time $t_e$ can be rewritten as

      ${t_e} = {t_0} + \frac{{{t_s}}}{{{N_s}}}$

      (10)

      where $t_s$ is the setup time, and $N_s$ is the average number of jobs produced between two setup times.

      The variance and mean effective processing time can be calculated as[1]

      $\left\{ {\begin{aligned} & {\sigma _e^2 = \frac{{\sigma _0^2}}{{{A^2}}} + \frac{{\left( {m_r^2 + \sigma _r^2} \right)\left( {1 - A} \right){t_0}}}{{A{m_r}}}}\\ & {c_e^2 = \frac{{\sigma _e^2}}{{t_e^2}} = \sigma _0^2 + \left( {1 + c_r^2} \right)A\left( {1 - A} \right)\frac{{{m_r}}}{{{t_0}}}} \end{aligned}} \right.$

      (11)

      where $\sigma _0^2$ and $\sigma _e^2$ are the variance of natural and effective processing time, respectively. $c_r^2$ is coefficient of variation for mean repair time interval, $m_r$ is mean time to repair, $\sigma _r^2$ is the variance of repair time.

      Increasing the availability of machines could decrease the processing time efficiency, and shorten the down time and queue time. Decreasing squared coefficient of variation could shorten the expected waiting time spent in queue of production line. Decreasing the down time variance specially the scheduler down time will balance the average down time and shorten the fluctuation. Therefore, the CT also could be improved.

      Factories could use the relationship between CT/WIP/TH and variability combining with the performance evaluation model to establish CT-model to get a reference dot which shows the good performance state. Position of the dot in CT-model gives a performance improvement direction. Also, the model could show the variation tendency of performance clearly when one or more parameters have been changed.

    • The raw data of the production line should be filtered and processed to obtain the initial parameters of the model, namely basic parameter (such as $T_0$, $r_b$, $T_{pro}$, $T_{time}$, TH) and variability parameter ($m_f$, $m_r$, $T_s$, $N_s$, $T_z$, $m$, $k$, $u$). Parameters of the production line and workstation could be divided into two types: theoretical and actual parameters.

      The theoretical parameters are equal to the actual parameters, if the variability is not considered. However, in the actual production process, only some approximate parameters are obtained, but not actual parameters are obtained. The variability among the workstations in a link has a weak impact on performance. Therefore, a link is taken as the research unit in this paper. It can centrally get the parameters of $T_0$, TH and $W_0$.

      There are four types of logical production lines, such as single, series, parallel and series-parallel lines. The parameter calculations are shown in Table 1.

      Raw process timeT0
      rb = TH${\displaystyle\frac{1}{T_0}}$
      Raw process timeT01+ T02+···+ T0n
      rbTHmin
      Raw process timeT0
      rb${\displaystyle\frac{m}{T_0}}$
      Raw process timeT01+ T02+···+ T0n
      rb${\displaystyle\frac{1}{T_{\rm 0max}}}$

      Table 1.  $T_0$ and $r_b$ of 4 kinds of logical production lines

      A common production line in semiconductor manufacturing factory consists of one or more workstations in series, and a workstation is consisted of one or more links in parallel. The link in a workstation consists of one or more machines in series and parallel. Those computation methods depicted in Table 1 are theoretical formula of the evaluation parameters hereinbefore. But in practical production process, quite a few parameters are extremely complex to obtain. The complete prediction model is developed and illustrated in Fig. 6

      Figure 6.  Performance prediction model of CATPL

      $PLTH$ indicates the TH of the production line. $m$ is the number of parallel machines in a workstation. $k$ is the batch size. $u$ is the utilization of the workstation. $N_s$ is the number of jobs processed in the time interval of switch the mould. $T_{pro}$ and $T_{time}$ are the actual processing time and total processing time of the workstation, respectively. $T_s$ is the average time to switch the mould. $T_z$ is the time a job batch transfers from the last workstation. $T_e$ is the average effective processing time of a batch of jobs. ${c_a}\left( i \right)$ and ${c_d}\left( i \right)$ are the jobs arrival and departure coefficient of variation at workstation $i$, respectively. $n$ is the total number of workstations in production line. $l$ is the number of overlapping workstations.

      The model reasonably reflects the relationship between the variability and the production performance. If the parameter values of the model are used in the way of forward rolling for several weeks, the production performance can be predicted relatively stable. Then, the parameters of the production line are adjusted and optimized. Finally, in order to solve the lagging problem that the optimal solution can only get the results afterwards, the relations of the model parameters are optimized with the results adjusted in advance.

    • $T_0$ collection. $T_0$ will be got except for the time of machine failure, downtime, blocked state and products waiting. A stopwatch is employed to measure the time from a unit entering a workstation to leave the workstation in relatively stable status and there is no faulty workstation (that means the time without failure and down).

      Measuring the $T_0$ is frequently inconvenient by general method, and it should be checked at regular intervals. However, measuring the effective practical processing quantity per unit time is viable in practice. Equation (12) could be used to obtain the $T_0$ of the workstation.

      ${T_0} = Lotsize \times \frac{s}{k}$

      (12)

      where $k$ is the effective practical processing quantity per unit time, $Lotsize$ is the quantity of job transport unit, and $s$ is the job process quantity per unit time.

      Some large workstations are impracticable to collect the $T_0$, but its TH and WIP are easy to obtain. According to the Little′s law, $T_0$ could be got by the TH and WIP.

      As the factory has monitored the all workstations in the process of production, the $T_0$ could be got by the monitored control system. But in actual production, in order to decrease the jobs transit times, the factory uses several units of jobs as a large monolithic process unit. $T_{0other}$ is the processing time of other jobs processed in the production line, which can be computed by

      ${T_{0other}} = {T_0} +\frac{n - 1}{T{H_{\rm max}}}$

      (13)

      where $n$ is the quantity of lots in a large monolithic process unit. $TH_{\rm max}$ is the raw process rate of the workstation.

      TH collection. TH could not be got easily in general ways, which can be calculated by $T_0$ and WIP. For other workstations, the stopwatch can be used to measure the time after the previous job left while the workstations in steady process status. In order to obtain TH in another job process unit, it is given by

      $TH =\frac{{r_b} \times {p_p}}{n'}$

      (14)

      where $n'$ is the batch size of a type of jobs processed at the workstation. ${p_p}$ is the percentage of the batch size passed by the workstation.

    • TH collection. The TH of the same production line in every week might be different. Thus, the requirement of the parallel workstation is different. The logical production line is different, though the physical production line is not changed. The parameters of the logical production line should be collected every week.

      For workstations which are in series or parallel operated in the same process, the procedure could be seen as a “black box”. This production line can be seen as composed of many “black boxes” like this. Similarly, a logical production line consisted of one or more workstations in series or parallel can obtain the parameters by the similar way. The $T_0$ and TH obtained by the proposed method is similar to Table 1. For sample workstation, (15) is used to compute the TH.

      $TH = \frac{k}{Lotsize}.$

      (15)

      $W_0$ and WIP collection. The $W_0$ of the logical production line will be obtained by WIP summation, and the WIP is actual work in process, which is controlled by the factory in practice.

    • Take the job B processed in the production line A in a semiconductor manufacturing factory as an example, whose process route mainly includes 19 workstations, of which include 4 diffluent workstations. The workstation 10 is a bottleneck. In this paper, the actual data of the production line is obtained through two ways. One is through the stopwatch in the steady state of production line, and the other is through the monitoring system records or manual records of historical data.

    • Performance evaluation of the production line based on the Little′s law could improve the evaluation model. Focus on a single job and use the method described above to get the data of each parameter. The primary data calculated and adjusted are shown as Table 2.

      WorkstationCVTH (Batch/hour)${A}$${u}$${\sigma _r^2}$$\sigma _s^2$${t_s}$${m_r}$
      10.005.960.950.850.360.319.131.13
      20.606.040.980.830.040.204.524.61
      30.707.120.980.840.220.047.360.41
      40.705.890.960.761.751.644.151.54
      50.748.390.990.870.130.153.550.77
      60.778.390.990.870.130.153.550.77
      70.786.210.930.760.460.3614.061.51
      80.828.390.990.870.130.153.550.77
      90.253.040.960.876.5210.770.031.36
      103.024.780.980.910.450.364.190.36
      111.031.870.990.800.000.007.780.02
      121.129.240.990.862.3911.306.490.32
      131.326.840.980.780.000.510.020.00
      140.360.630.980.880.000.440.030.00
      150.845.560.990.671.731.5613.690.70
      160.957.180.990.710.001.210.130.00
      170.955.60.990.880.000.450.090.00
      180.785.80.990.880.000.330.020.00
      190.693.480.980.880.000.110.210.00

      Table 2.  Performance and parameters of each workstation

      Comparing with the TH of each workstation, the bottleneck workstation of the production line is found, namely workstation 10 as described above. Therefore, the workstation 10 is taken as a key analysis object.

      To better analyze the parameters of workstation 10, Table 3 lists the first 16 workstations in production line. Based on TH in Table 3, by contrasting the TH of every workstation, the minimum TH is chosen as the actual TH (TH') of production line. In the actual situation, some sample workstations have little influence on whole production line. It needs not consider the sample TH of workstation in comparing. As the $r_b$ of whole production line is similar to the TH, take TH = 5.84 as bottleneck rate. Then, $W_0=r_b \times T_0$ = 5.84 $ \times $ 20.94 = 122.29 (units). Thus, the other parameters could be obtained: $W_0$ = 122.29 (units), TH = 5.84 (units per unit time), $T_0$ = 20.94 (unit time).

      WorkstationTH (single station)Amount of workstationsTH′ (actual)Sample percentage
      11.366.148.37
      24.641.818.40
      32.054.238.66
      40.6610.416.83
      51.5910.9417.40
      61.556.8010.53
      71.4810.1515.03
      80.837.15.9
      90.641.010.6510%
      100.2821.095.84
      110.288.372.3430%
      121.998.3216.55
      130.678.996.04
      140.9610.8110.37
      150.164.060.65
      160.105.490.55

      Table 3.  TH of each workstation

    • Since quite a few factors commonly use the sample percentage of jobs, based on the data of each workstation, the $T_0$ of whole production line can be calculated as

      ${T_0} = {T_{01}} + {T_{02}} + \cdots + {T_{0n}} + \sum\limits_1^m {{T_{0i}}} \times {a_i}\% $

      (16)

      where ${a_i}$ is the sample percentage of the i-th sample workstation. Thus, the $T_0$ of whole production line results is 20.94 (unit time).

      Comparing the total actual TH of every workstation, by using (17):

      ${r'_b} = {\rm min}\left( {TH'} \right) = {\rm min}\left( {b \times TH} \right)$

      (17)

      where ${r'_b}$ indicates the actual bottleneck rate of the whole production line. $TH'$ indicates the total actual throughput of a workstation. $TH$ and $b$ indicate the throughput of the single link and the number of links in a workstation, respectively.

    • Based on the three-parameter method and the formulas in Table 1, the internal benchmark evaluation model could be developed by actual production line. It reflects that the dot represents the practical production performance is in the area between best-case and practice worst-case, though the dot is in good area. It is closer to practical worst case than best case, that means the performance is good but not good enough. According to the two figures of internal benchmark, the work in process level is good. However, the CT is twice $T_0$, and the TH is just 70% of the $r_b$. Engineers can develop TH when the variability had no change. They could also control the variability level and let the actual producing performance closer to the best-case along the vertical direction. As described above, the workstation 10 is a bottleneck workstation of the production line. Therefore, workstation 10 is focused and the squared coefficient of variation ($c_a^2$, $c_e^2$) is decreased to shorten the CT. By using the relationship between variability and CT, the reduced results of $c_a^2$ and $c_e^2$ are shown in Table 4.

      Workstation 10${c_e^2}$${c_a^2}$CT
      Original0.8375.240.3
      Changed0.55.239.85
      Changed0.8374.839.64
      Changed0.54.839.52

      Table 4.  Reduced parameters of $c_a^2$ and $c_e^2$

      Obviously, when either one of the $c_a^2$ and $c_e^2$ or both of them are decreased, the CT is decreased simultaneously. Especially, when $c_e^2$ equals to 0.5 and $c_a^2$ equals to 4.8, the corresponding CT is from 40.3 to 39.52 with the saving of 1.9%. It is an intuitive direction to improve the performance by variability level control.

      The improved performance evaluation method is mainly used for the performance analysis and the selection of the improvement scheme. Performance evaluation results of the production line B which has processed job A in the week $J$ are shown in Fig. 7.

      Figure 7.  Performance evaluation results

      As seen in Fig. 7(a), the actual case dot (198.09, 41.65) is closer to the best case than the actual worst case. This indicates that the CT is in a better status. Comparing with Fig. 7(b), the maximum TH and the minimum CT appear when $W_0$ equals to 116.7. It is noticed that when the TH increases to $r_b$(5.93), the maximal TH will be obtained. That is to say, the CT and TH have the potential space to improve. However, due to the unavoidable variability existence, both of them are practically impossible to reach the best case. It just provides an improved direction and a possible improvement range of performance.

      With the analysis of the performance status for prediction model, the performance of production line can be improved through the change of variability parameters. By contacting the engineers of the enterprise, two major improvement directions can be identified. Firstly, increase the number of functional sub lines $m$ at the bottleneck workstation. Secondly, adjust the planned downtime of the workstation 9 and workstation 12 to reduce the variability fluctuation parameter $\sigma _s^2$. The evaluation results of two methods are illustrated in Fig. 8.

      Figure 8.  Performance evaluation results with two methods

      As can be seen in Fig. 8 (a), since the number $m$ of sub production line of A job in the bottleneck workstation is increased, the utilization ratio of the workstation is changed, which leads to the increase of the bottleneck rate and the decrease of the CT. Similar to Fig. 7 (a), when $t_0$ equals to 19.68, both of their CT increased with the WIP. But the slope of the parallel line in Fig. 8 (a) decreased because of the increasing of the $m$. Besides, the $W_0$ in Fig. 7 (a) and Fig. 8 (a) are 116.7 and 132.64, respectively. In other words, the latter can keep a higher work in process level under the condition of the same $T_0$. After reducing the fluctuation $\sigma _s^2$ of the planned downtimes, the CT is also shortened, although the processing rate is not changed, see Fig. 8 (c). The TH of Fig. 8 (b) is higher than Fig. 8 (d), but the distance from the $W_0$, the performance in Fig. 8(d) is better. By using the formula of the distance from dot to the line, the distance of the line is increased by $d_1$, and the distance of fluctuation planned downtimes $\sigma _s^2$ is reduced by $d_2$. The results are that $d_1$ = 8.89 $>$$d_2$ = 7.95. It can be seen that in the week $J$, the method of balanced planning downtimes is better than directly increasing the bottleneck rate of the workstation. Therefore, it is better to improve the performance by reducing the fluctuation of planned downtime.

    • This paper proposes a method based on the variability theory in factory physics using internal benchmark to address the problems of performance evaluation and improvement in semiconductor manufacturing factory. The performance evaluation method is expanded based on Little′s law. According to a single job, the method of obtaining the fundamental parameters is introduced, which includes parameters calculation for 4 kinds of logical production lines, parameters collection of each workstation and whole production line. Then, the internal benchmark is used to evaluate and improve the performance. A case study in a chipset assembly and test factory shows that the method can evaluate the performance of CATPL quantitatively and effectively. It is a visual way to help manufacturing factories know the performance state of their production line under current production condition. Furthermore, by evaluating the performance of the production line, the managers and operators could establish a performance estimation model, which could be used to guide improving the performance of production line significantly.

      Some limitations of this study should be noted, although our method performs well in the examined cases. Firstly, in real production lines, the practical situation could be much more complicated, the values of $T_0$, $c_a^2$ and $c_e^2$ can be affected by practical issues, such as random interruption and preventive maintenance. Secondly, the proposed method can only evaluate the performance improvement scheme from the qualitative and partial quantitative description. More details of the variability parameter process model still need to be perfected. Furthermore, there can be multi-product processed in CATPL simultaneously, which may have different performance but share the same resources. Those situations have not yet been considered in our method and will be continually improved in future research.

    • The authors are thankful to the anonymous reviewers for their constructive and helpful comments that have led to this much improved manuscript. This work was supported by National Natural Science Foundation of China (No. 71671026) and Sichuan Science and Technology Program (Nos. 2018GZ0306 and 2017GZ0034).

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