An Integrated Supplier-Buyer Lots Sampling Plan With Quality Traceability Based on Process Loss Restricted Consideration

Supplier-buyer relationships have been the focus of considerable supply chain management and marketing research for decades. To validate the process capability of a supplier, practitioners usually operate the acceptance sampling plan (ASP). The most basic ASP is a single sampling plan (SSP) due to its straightforward lot-disposition mechanism. However, since the lot-disposition mechanism of SSP cannot accommodate the historical lot-quality levels information, it requires a large sample size for inspection to validate the submitted lot’s process capability. To obtain these benefits from historical information, multiple-lot dependent state (MDS) sampling plans have been proposed. The MDS plans have manufacturing traceability of historical lot-quality levels information to sentence the submitted lot. However, the MDS plan’s manufacturing traceability has a drawback that cost-efficiency decreases as more historical lot-quality levels information are considered, which contradicts its initial development goal. To overturn this contradictory situation, we proposed the adaptive MDS (AMDS) plans based on the process loss restricted consideration with combinatorial mathematical treatment that can correct the MDS plans manufacturing traceability of historical lot-quality levels information that help practitioners to adopt more historical information into lot-disposition freely without bearing the reduction of cost-efficiency. Meanwhile, their performances are superior to existing MDS plans in terms of cost-effectiveness and discriminatory power. Moreover, we further developed a web-based app for our proposed plans to improve the convenience of applying them in practice. By operating the web-based app, practitioners can quickly obtain the optimal plan criteria without bearing the burdens of table-checking or mathematical model solving. These improvements can genuinely help buyers distinguish reliable suppliers efficiently and build up a strong partnership with them. Finally, the applicability of the proposed plan is demonstrated in a real-world case study.


I. INTRODUCTION
Supplier-buyer relationships have been the considerable focus of supply chain management and marketing research for decades [1], [2]. Yu and Pysarchik [3] suggested the long-term supplier-buyer relationship to be the most critical construct to establish optimal business relationships. Constructing a long-term supplier-buyer partnership is a progressive process that requires accumulating trust for each The associate editor coordinating the review of this manuscript and approving it for publication was Chi-Tsun Cheng .
other. In this process, suppliers should demonstrate their process capability for a long time to earn buyers' trust. To validate the process capability of suppliers, practitioners usually inspect the submitted lot from the suppliers [4]. An acceptance sampling plan (ASP), a compromise between 100% inspection and no inspection, is a practical and widely used tool for lot disposition [5]- [7]. A well-designed ASP can not only protect both supplier-buyer under a riskcontrollable condition but also improve the cost-efficiency of lot-disposition [8]. VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ A single sampling plan (SSP) is the most basic ASP because of its straightforward lot-disposition mechanism [9], [10]. Nevertheless, since the lot-disposition mechanism of SSP only considering the current lot's information that cannot accommodate the historical lot-quality levels information, it requires a large sample size for inspection to validate the submitted lot's process capability [11], [12]. With the rapid development of manufacturing technology, the supplier has widely adopted continuous-flow production processes [13], [14]. Continuous receipts and acceptance inspections produce substantial useful information. This information feedback corrects the inspection rules, mechanisms, and action plans to maximize supplier-buyer resource benefits. In this scenario, the ASPs should have manufacturing traceability to accommodate such valuable information [15], [16]. However, the basic SSP cannot help practitioners to gain such valuable information. To overcome this, several lot-dependent ASPs such as chain sampling plan [17], lot-fixed dependent states sampling plan [18], and multiple-lot dependent states (MDS) sampling plan [19]- [22] have been developed.
Generally, the ASPs can be classified into attributes-type and variables-type. One of the differences between them is the attributes-type ASPs demand a larger sample size for inspection than variables-type ASPs when acceptable quality levels are very small., Nowadays, as many buyers begin to stress suppliers improve their production process, variables-type ASPs have become more attractive [23]. The variables-type MDS sampling plan is firstly introduced by Balamurali and Jun [24]. Subsequently, Aslam et al. [25] further proposed the variables-type MDS plan based on process loss restricted consideration.
The MDS plans have manufacturing traceability of historical lot-quality levels information to sentence the submitted lot. However, when more historical lot-quality levels information is considered by practitioners, we discover the MDS plans' required sample size for inspection presents an upward trend, and the lot-accepted criterion shows a downward trend. This outcome indicates the MDS plans' cost-efficiency and discrimination power will decrease as more historical lot-quality levels of information are considered, which contradicts the initial goal of the development of MDS plans. Especially, this contradiction may become serious for the long-term supplier-buyer relationship since it has numerous traceable deliveries and lot-disposition operations. Consequently, in practice, the manufacturing traceability of MDS plans has been limited.
To tackle this contradictory situation, we proposed an adaptive MDS (AMDS) plan based on the bilateral quality-characteristic capability index with the process loss restricted. The proposed AMDS plan has three significant contributions. Firstly, the combinatorial mathematical treatment of this paper for the proposed AMDS plans activates their manufacturing traceability of historical lot-quality levels information, which is of necessity in the implementation of the manufacturing execution system. Secondly, its performance is superior to existing MDS plans in terms of cost-effectiveness and discriminatory power. Thirdly, the AMDS plan can integrant the traditional SSP and MDS plan for building up a long-term supplier-buyer relationship. We tabulated the progressive development of the lot-dependent ASPs in Table 1 and marked our contribution as follows.
So far, most studies of ASPs usually provided tables for practitioners to execute their introduced sampling plans. However, the tables cannot accommodate all the regulations in practice, which is a disadvantage and inconvenience for practitioners. Thus, to improve the convenience of applying our proposed plans in practice, we develop a web-based app. By operating the user interface of our proposed web-based app, practitioners can quickly obtain the optimal plan criteria without bearing table-checking or mathematical-model solving burdens.
The notations and abbreviations used throughout this paper is listed in Table 2, as follows.

II. PROCESS-LOSS-RESTRICTED-BASED INDEX AND ACCEPTANCE SAMPLING PLAN A. PROCESS-LOSS-RESTRICTED-BASED INDEX
Process capability indices (PCIs) are functional tools that measure the producer's manufacturing capability within the customer's required tolerance scope. In practice, C p and C pk are widely used PCIs, which are defined as follows, respectively, where USL is the upper specification limit and LSL is the lower specification limit; µ and σ are the mean and standard deviation of quality characteristics, respectively; d = (USL − LSL)/2 and M = (USL + LSL)/2 are the half-length and the midpoint of the specification tolerances, respectively. However, these two PCIs cannot differentiate among the product that falls inside the specification limits. To measure the situation that the quality characteristic deviated from the target value, the process loss index, C pm , is proposed by Chan et al. [26], which is defined as follows.
where T is the process target. From Eq.
(2), we can find the C pm index is designed based on the quality loss function, the farther the quality characteristic deviated, the quality loss becomes greater, the C pm value becomes smaller [27].
Unfortunately, the C pm index involves a reciprocal transformation of the process mean and variance [28]. Moreover, the C pm index cannot provide an uncontaminated separation between the information concerning the process precision, and process accuracy, where process precision relates to product variation and process accuracy relates to the degree of process targeting [28]. To tackle these drawbacks, Johnson [29] proposed another process loss index L e , which is defined as follows.
For application convenience, we tabulate some commonly used L e values and their corresponding status in Table 3.
In practice, the process parameters µ and σ are unknown, so we consider the following natural estimatorL e to estimate the L e index.

B. ACCEPTANCE SAMPLING PLAN WITH PROCESS LOSS RESTRICTED CONSIDERATION
Generally, the ASP with process loss restricted consideration is created on a pair of loss-and-risk levels, (L APLL , 1 − α) and (L RPLL , β), to regulate supplier-buyer purchase contracts, where L APLL and L RPLL are the accepted process loss level (APLL) and rejected process loss level (RPLL) of the L e index, respectively; α and β denote the risks borne by the supplier and the buyer, respectively. To be more precise, a well-designed ASP should satisfy two conditions: (i) the probability of accepting a lot at the L APLL should exceed 100 (1 − α)%, and (ii) the probability of accepting a lot at the L RPLL should lower than 100 β%. Both designated points of interest on the operating characteristic (OC) curve, (L APLL , 1 − α) and (L RPLL , β), can be expressed by

III. DISCUSSION OF THE L e -BASED MDS PLANS WITH MANUFACTURING TRACEABILITY AND ITS DRAWBACKS
The L e -MDS plan was developed by Aslam et al. [25]. In the L e -MDS plan, every quality level of the submitted lot is recorded because of its manufacturing traceability. Let l (i) , for i = 1, 2, . . . , c, be a sequential lots submission from the supplier. Each l (i) is randomly sampled n items to compute its quality level, i.e.,L e(i) . EachL e(i) has three possible results asL where c a and c r are the lot-accepted criterion and the lot-rejected criterion, respectively. The L e -MDS plans' lot-disposition of the current lot with these three results are tabulated in Table 4. Given the specified L e value and lot-traceability parameter m, the acceptance probability of the current lot is a function of (n, c a , c r ), denoted as π c ( n, c a , c r | L e , m), which can be expressed mathematically as π c ( n, c a , c r | L e , m) where P L e(c) ≤ c a |L e is the outright acceptance probability of the current lot and P L e(c) > c r |L e is the outright rejectable probability of the current lot. By referring to Eq. (5), these two probabilities can be expressed as follows.
According to Eq. (6), a nonlinear constrained model can be constructed to determine the plan criteria with the target of minimizing the required sample size.
where n is the smallest integer greater than or equal to n.
The L e -MDS plan indicates better performance than the ordinary L e -based single sampling plan (abbr. L e -SSP) in terms of the cost-efficiency and the shape of OC curves because of its manufacturing traceability. In the study of the L e -MDS plan, only m = 1, 2 and 3 conditions have been considered and discussed [25]. However, when more preceding lots' process records, i.e., m, are considered into the current lot-disposition, more inspection costs are demanded, and the process loss requirement is declined. This phenomenon can be observed more clearly in Figure 1.

IV. DEVELOPMENT OF THE L e -AMDS PLANS WITH MODIFIED-MANUFACTURING TRACEABILITY
To tackle the drawback of L e -MDS plans, we develop the L e -AMDS plans with modified-manufacturing traceability, which has a two-parameter mechanism (m, j). The L e -AMDS plans allow at most j lots' process loss records to situate within the marginal admissible process loss level [c a , c r ] to be incorporated. To receive the benefits of L e -AMDS plans without enduring too many of the related management burdens, we suggest j being limited in the range of j ∈ {0, 1, . . . , m/2 }, where m/2 is the largest integer less than or equal to m/2.  Step 1: Specify the L e -AMDS plan's regulation, i.e., (L APLL , L RPLL , α, β, m, j).
Step 2: Randomly draw n samples from the current lot with normality check and compute itsL e(c) value.
Step 3: Sentence the current lot with the following rules.

B. ACCEPTANCE PROBABILITY AND OPTIMIZATION MODEL
Evidently, the sentencing of the current lot is made in Step 3 and Step 4, respectively. In Step 3, by referring to Eq. (7), the acceptance probability of the current lot is Nevertheless, the acceptance probability of the current lot in Step 4, denoted as π 2 c ( n, c a , c r | L e , m, j), is somewhat complicated. To be more precise, a system backtracking m lots is from current lot l (c) to lot l (c−m) . Let S = {c − 1, c − 2, . . . , c − m} be a set of m backtracking lots' numbers containing m elements. A j−combination of the set S is a subset of j distinct elements from S, denoted as S j . Since S has m elements, the number of j−combinations is equal to the binomial coefficient C (m, j). Let subset S h j be named as the h − thj−combination, for h = 1, 2, . . . , C(m, j). The j elements of S h j is denoted as S h j = s h j (1), s h j (2), . . . , s h j (j) . Hence, the other subset S − S h j has m − j elements that can be expressed as ) . Therefore, the acceptance probability of the current lot in step 4 is In summary, the overall acceptance probability of the current lot can be formulated as π c ( n, c a , c r | L e , m, j) = π 1 c ( n, c a , c r | L e ) + π 2 c ( n, c a , c r | L e , m, j) Subsequently, according to Eq. (12), we can construct the nonlinear constrained optimization based on economic consideration, i.e., minimizes the required sample size, to further determine the plan criteria.  From Figure 3, we can find the combinations ξ APLL = 0.0 and ξ RPLL = 0.0 have the largest required sample size n. The investigations for different regulations (L APLL , L RPLL , α, β, m, j) were also conducted but are not reported here because they all show the same results. Consequently, the nonlinear constrained optimization of Eq. (13) can be rewritten as minimize (n,c a , c r |L APLL ,L RPLL ,ξ APLL ,ξ RPLL ,α, β,m,j ) n Subject to π c ( n, c a , c r | L APLL , To further validate this secure viewpoint, we computed the true producer's risk α * , and the true consumer's risk β * with varying estimated values ξ * ∈ [−1, 1] for our proposed L e -AMDS plans (see Figure 4 Figure 4 indicate both true risks α * , and β * all lie below the tolerable risks α = 0.01 and β = 0.05 specified in the purchasing contract; therefore, our proposed methodologies and their results can truly safeguard both the supplier and the buyer without sacrificing their mutual interests in verification and validation of the quality of the products.

D. ESTABLISHMENT OF A WEB-BASED APP FOR COMPUTATION OF PLAN CRITERIA
For the convenience of the practitioner to utilize our L e -AMDS plans, we program Eq. (14) in the form of R function [31] to obtain the optimal plan criteria, where the optimization package ''nloptr'' in R software [32] is used with a direct search algorithm [33]. Moreover, by using Shiny package [34], we further created a web-based app for the online computation of the L e -AMDS plans' optimal criteria. It can be connected through the hyperlink: https://qualityand-reliability-lab.shinyapps.io/le-amds_calculator/.

V. THE DISCUSSION OF THE PLAN CRITERIA (n, c a , c r ) WITH ADAPTIVE MECHANISMS m, j
Subsequently, we tabulated the plan criteria (n, c a , c r ) of the L e -AMDS plans and illustrated an example in the first sub-section. Next, in the second sub-section, we further investigated the adaptive mechanism (m, j) in more detail to demonstrate the superiority of our proposed plan.
A. THE PLAN CRITERIA (n, c a , c r ) OF THE L e -AMDS PLAN In this sub-section, we tabulate the plan criteria (n, c a , c r ) under commonly used regulations (process loss levels and risks) and some specified adaptive mechanisms in Table 5.
For example, if the regulations (L APLL , L RPLL , α, β) are set to (0.06, 0.11, 0.05, 0.10), and the adaptive mechanism is (m, j) = (6, 2), we can obtain the plan criteria (n, c a , c r ) = (23, 0.0702, 0.1483) by checking Table 5. Under this situation, we will straightly accept the current lot if the 23 inspected product items loss measurements withL e(c) ∈ [0, 0.0702] and straightly reject the lot ifL e(c) ∈ [0.1272,∞); otherwise, the preceding lots' process loss information should be considered into current lot disposition. The current lot will be accepted if the preceding six lots on the condition of no more than two lots with the process loss atL e(i) ∈ (0.0702,0.1483) and the other lots are straightly accepted underL e(c) ∈ [0, 0.0702]. Otherwise, the current lot would be rejected.

B. THE INTERACTION BETWEEN m AND j MECHANISMS OF THE L e -AMDS PLAN
By checking Table 5, we can find the (m, j) mechanism is a significant factor affecting the plan criteria under the same regulation. To investigate the (m, j) mechanism in more detail, we plot the required sample size n and lot-accepted criterion c a under (L APLL , L RPLL , α, β) = (0.04, 0.06, 0.05, 0.05) for m ∈ {1, 2, . . . , 14} and j ∈ {1, 2, . . . , 7} in Figure 5.
From Figure 5, we point out three noted phenomena of our proposed L e -AMDS plans. First, if j fixed, the required n increases and the c a also increases as m increases. Second, if m fixed, the required n decreases and the c a also decreases as j increases. Third, the required n decreases and the c a also decreases as m increases with j = m/2 .
These phenomena indicate the (m, j) mechanism of the proposed plan can not only reduce the required n but also make process loss compliance stricter. In other words, the (m, j) mechanism can help the proposed plan include more historical lot-quality levels information into current lot disposition without suffering the reduction of cost-effectiveness like L e -MDS plans. VOLUME 9, 2021 TABLE 5. The plan criteria of the L e -AMDS plan with m = 6, j ∈ 1, 2, 3 .

C. ADAPTIVE APPLICATIONS OF THE PROPOSED PLAN
Our proposed L e -AMDS plan with (m, j) mechanism is a flexible and integrated ASP, which can be useful for a different type of purchasing contract. First, as theoretical expected, when k a = k r or m → ∞ with j = 0, then the L e -AMDS plans will shrink to the L e -SSP, which established by Yen and Chang [30], is suitable for those purchases that are made on a nonrecurring or limited basis with few lots or no intention of developing an ongoing relationship with the supplier. Second, the proposed plan with m ∈ Z + , j = 0 will become the L e -MDS plan, developed by Aslam et al. [25], which is appropriate for those purchases that are routinely made over relatively limited lots (limited period). Thirdly, the proposed plan with m ∈ Z + ∩ m = 1, j ∈ {1, 2, . . . , m/2 − 1}) is useful for those purchases that are made continuingly for relatively large specified lots. Finally, as the proposed plan with (m ∈ Z + ∩ m = 1, j = m/2 ) becomes a long-term ASP, it is beneficial for those purchases that are made continuingly for a long period. We summarize the abovementioned points in Table 6 to indicate the applicability of L e -SSP, L e -MDS plans, and L e -AMDS plans. It can be discovered from Table 6 that the proposed L e -AMDS plans are adaptive for the whole purchasing type, especially for the longer-term partnership. These outcomes indicate the proposed L e -AMDS plans are favorable for constructing a long-term supplier-buyer relationship.

VI. PERFORMANCE COMPARISONS
Generally speaking, the performance of ASPs can be compared from two aspects, (i) cost-effectiveness and (ii) discriminatory power. First, the cost-effectiveness is related based on the required n for inspection, i.e., the less the required n, the higher cost-effectiveness. Second, the discriminatory power of ASPs can be discussed in the OC curve and the average run length (ARL). The OC curve plots the probabilities of accepting a lot versus the process loss level. The greater is the inflection-point slope of the OC curve, the higher the discriminatory power.
The ARL is used to represent the expected number of inspections required to make a lot-rejection decision, which is designed based on the plan's acceptance probability by using the mean of the geometric distribution of the run length, that is ARL = [1 − π (L e , m, j|n, c a , c r )] −1 . Under the specified rejected process loss level, the smaller the ARL value, the higher the discriminatory power because the faster the lot-rejection decision can be made. On the contrary, under the specified accepted process loss level, the higher the ARL value, the higher the discriminatory power because the harder is it to make the wrong decision [35].

A. COMPARISON OF COST-EFFECTIVENESS
In this sub-section, we tabulate the required n in four ASPs, which are the basic L e -SSP, the most efficient L e -MDS plan (i.e., m = 1), and two kinds of L e -AMDS plan (i.e., (m, j) = (7, 3), (8,4)), for various regulations (L APLL , L RPLL , α, β) in Table 7. Additionally, we also compute the reduction rate of required n of L e -MDS plan and L e -AMDS plans when comparing with the basic L e -SSP.
From Table 7, we can find the L e -MDS plan with m = 1 only reduces the required n from 32% to 38%, but the L e -AMDS plan with (m, j) = (7, 3) reduces the required n from 45% to 66% and the L e -AMDS plan with (m, j) = (8, 4) reduces the required n from 50% to 70%. Consequently, the proposed plans are more cost-efficient than the existing L e -MDS plan and L e -SSP. It is worthy to note from Figure 6 that the proposed L e -AMDS plans can operate the less required n to obtain the better shape of OC curves (i.e., more approach to ideal). In other words, the proposed L e -AMDS plans have superior discrimination with higher cost-efficiency than L e -SSP and L e -MDS plans.
Figures 7(a) and 7(b) display the ARL curves of proposed L e -AMDS plans have a more significant upward trend than the L e -SSP and L e -MDS plan under the evident acceptance area. This outcome reveals the proposed plans are more difficult to reject a good lot than the other ASPs, i.e., more difficult to make a wrong decision. Thence, the results of both OC curves and ARL curves indicate the proposed plans have superior discriminatory power, thereby sentencing the submitted lot more efficiently and accurately.

VII. CASE STUDY
An organic light-emitting diode (OLED) are widely used to create digital displays in devices such as television screens and smartphone. OLED is a multi-layer structure, which is shown in Figure 8. The emissive layer will emit light when electricity is applied so that OLED can work without a backlight. Hence, it can display deep black levels that achieve a high contrast ratio, especially in low ambient light conditions, and can be thinner and lighter than a traditional liquid crystal display.
To obtain high working efficiency, balanced charge injection and transfer are required. Therefore, the thickness of the electron transport layer is a critical quality characteristic of OLED since it can be used to balance charge. We investigated a specific OLED, which thickness of the electron transport layer with the process target T = 40nm, upper and lower specification limits of USL = 45nm, LSL = 35nm. Suppose    In this case, suppose the supplier and buyer make a longterm purchase agreement; we recommend conducting the L e -AMDS plan with (m, j) = (16,8) to take more capability records into lot-disposition. The plan criteria can be determined (n, c a , c r ) = (33, 0.0419, 0.0985) by operating the interactive web-based app https://quality-and-reliabilitylab.shinyapps.io/le-amds_calculator/, which we mentioned in Section 4. Then, the practitioner should draw 33 OLED products from the current submitted lot randomly and measure their thickness. Firstly, we conduct a normality check for these measurements. Subsequently, we compute theL e(c) value and sentence the submitted lot. The submitted lot will be accepted outright if theL e(c) showsL e(c) ∈ [0, 0.0419] and rejected outright ifL e(c) ∈ [0.0985, ∞). IfL e(c) ∈ (0.0419, 0.0985), the preceding 16 lots' capability records should be considered. Meanwhile, the current lot will be accepted if preceding 16 lots on the condition of no more than eight lots with the process loss atL e(c) ∈ (0.0419, 0.0985)  and other lots were accepted underL e(c) ∈ [0, 0.0419] directly; otherwise, the current lot will be rejected. Table 8 lists the measurements of the 33 samples. By utilizing the Anderson-Darling normality test, these 33 samples were approximately normally distributed with p-value = 0.4873 > 0.05. The theoretical quantiles against empirical ones (Q-Q plot) are also displayed in Figure 9. According to Eq. (4), theL e(c) can be computed asL e(c) = 0.0337. Hence, in this case, the current lot should be accepted outright sincê L e(c) ∈ [0, 0.0419].

VIII. CONCLUSION
The existing MDS plan has manufacturing traceability that can include historical lot-quality levels information into the current lot disposition. However, the MDS plan's manufacturing traceability has a drawback that cost-efficiency decreases as more historical lot-quality levels information are considered, which contradicts its initial development goal. Meanwhile, this drawback is unbeneficial for the long-term supplier-buyer relationship because it not only limits the cost-efficiency of lot-disposition but also impliedly forces practitioners to abandon valuable historical lot-quality levels information.
To overturn this contradictory situation, we proposed the AMDS plans based on the process loss restricted consideration with combinatorial mathematical treatment that can correct the MDS plans manufacturing traceability of historical lot-quality levels information, which is necessary for implementing the manufacturing execution system. In other words, the AMDS plan has reasonable manufacturing traceability that can help practitioners freely include historical lot-quality levels information into lot-disposition without enduring the problem of cost-efficiency decrease. Additionally, since more valuable historical lot-quality levels information can be considered, the proposed AMDS plans have shown superior performance than both traditional SSP and MDS plans in terms of the comparisons of the cost-efficiency and discriminatory power.
On the other hand, the adaptive mechanism of the proposed plan can integrate both the MDS plan and SSP by adjusting the operational parameters (m, j), which have broad applicability for different purchasing (stages) in the supplier-buyer partnership. Additionally, we further developed a web-based app for practitioners or any potential operator to execute our proposed AMDS plan easily and quickly without bearing any burden of table-checking or mathematical model solving. These improvements can genuinely help buyers distinguish reliable suppliers efficiently in the long run and build up a strong partnership with them.
MING-HUNG SHU received the M.S. degree in electrical engineering and the Ph.D. degree in industrial, manufacturing, and system engineering from the University of Texas at Arlington, USA, in 1993 and 1996, respectively. He is currently a Professor of industrial engineering and management with the National Kaohsiung University of Science and Technology and an Affiliate Professor with the Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Taiwan. His research interests include quality and reliability engineering, decision-making analysis, and applied soft computing. He has been awarded as an Outstanding Young Researcher and the Best Yearly Research Project from the Ministry of Science and Technology.
TO-CHENG WANG received the bachelor's degree in aeronautical and mechanical engineering from the Republic of China Air Force Academy (ROCAFA), Kaohsiung, Taiwan, and the M.S. and Ph.D. degrees in industrial engineering and management from the National Kaohsiung University of Science and Technology, Kaohsiung. He is currently an Assistant Professor with the Department of Aviation Management, ROCAFA. His research interests include quality and reliability engineering and operations research.
BI-MIN HSU received the Ph.D. degree in industrial, manufacturing, and system engineering from the University of Texas at Arlington, USA, in 2002. She is currently a Professor of industrial engineering and management with Cheng Shiu University, Taiwan. She has long-time joint research with Kaohsiung Chang Gung Memorial Hospital. Her research interests include machine learning, quality and reliability engineering, and applied bioinformatics. VOLUME 9, 2021