Coordinating and Evaluating of Multiple Key Performance Indicators for Manufacturing Equipment:Case Study of Distillation Column☆

LiZhu,Hongye Su*,Shan Lu,YueWang,Quan ling Zhang

State Key Laboratory of Industrial Control Technology,Institute of Cyber-Sy stems and Control,Zhejiang University,Hangzhou 310027,China

Coordinating and Evaluating of Multiple Key Performance Indicators for Manufacturing Equipment:Case Study of Distillation Column☆

LiZhu,Hongye Su*,Shan Lu,YueWang,Quan ling Zhang

State Key Laboratory of Industrial Control Technology,Institute of Cyber-Sy stems and Control,Zhejiang University,Hangzhou 310027,China

A R T I C L E I N F O

Article history:

Received 1May 2013

Received in revised form 24 January 2014 Accepted 3March 2014

Available on line 20 June 2014

Key performance indicator

Coordination

Manufacturing equipment

Evaluation

Manufacturing equipment takes the task of operation and directly effects on the manufacturing process.One single Key Performance Indicator(KPI)is mainly employed to evaluate equipment inmost studies,neither integrating the KPIs into a completed evaluation system nor considering the impact and conflict among KPIs.In this paper,a KPI evaluation architecture is presented to define and analyze KPIs,and then a common structure for KPI to obtain the KPI set of manufacturing equipment is introduced.An available multi-KPI coor dination model is proposed to discern and balance the relationship among multi-KPI.Finally,a case study is introduced to illustrate the applicability of the coor dination model by using multi-objective optimization strategy and an efficient solution is obtained.

?2014 Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

1.Introduction

Manufacturing equipment plays a principal role in the manufacturing process and directly influences the yields and profits of manufacturing companies.There are manufacturing equipment design,operation and maintaining all the way through the entire manufacturing process.To ensure the stability and efficiency of production process,it is necessary to evaluate the performance of manufacturing equipments.

Many investigations have been reported in the literatures about equipment evaluations.Ljung berg[1]introduced overall equipment effectiveness in the formulation and execution of a total productivity maintenance strategy to measure the performance of equipment as a metric.Yacoub and MacGregor[2]presented a data analysis method to assess the equipment performance in manufacturing processes.Chen et al.[3]proposed a performance indicator of process manufacturing time,which can be transform ed to production capacity and to evaluate equipment performance.Geng et al.[4]developed a fuzzy analytic hierarchy process method to get energy efficiency ind ices to assess energy utilization states of different equipments.Shen et al.[5]made a determination on the benchmark of manufacturing equipment and took production ratio as an instance.Younes et al.[6]presented the application of parameters design to improve both the product quality and equipment performance in a hot sheet rolling plant.Irshad et al.[7]provided total quality model and applied productivity and quality indicators to evaluate performance.Garza-Reyes et al.[8]investigated the relationship between overall equipment effectiveness and process capability for measuring the performance.

However,most studies pay attention to use a single performance indicator to measure the manufacturing equipment without integrating the key performance indicators in to a completed evaluation system. And qualitative analysis methods of equipment performance are in the majority,which lacks systematicness,generality and accuracy.In addition,there are conflicts and inconsistence in the relationship of multi-KPI,thus it is helpful and essential to find out the trade off compromises to balance the multi-KPI,which is useful to narrow down the choices in decision-making in the manufacturing process[9].

Considering these aspects for evaluating the performance of manufacturing equipment,evaluation architecture of key performance indicators for manufacturing executive system is introduced to define and analyze KPIs in this study.Based on the common structure of KPIs proposed by the international standard ISO 22400[10],a set of KPIs to measure manufacturing equipment performance is established and described.To discern and coordinate the relationships among the multi-KPI in this KPI set,a multi-KPI coordination model is proposed, which takes in to account coordinating objectives selected,mass balance,energy balance,quality and safety constraints,etc.The trade off among the multi-KPIis explored by collaboration model,which is not limited to evaluate the special manufacturing equipment,but also accounts for the evaluation of different levels in manufacturing process.To demonstrate the effectiveness of the presented model,themethanol-water packed distillation column is taken as a real case study. The trade off compromise between production rate and unit energy consumption is obtained by using multi-objective optimization strategy.

2.KPI Evaluation Set of Manufacturing Equipment

Key performance indicators(KPIs)are defined as quantifiable and strategic measurements that reflect the critical success factors in the manufacturing process.KPIs are very important for understanding, benchmarking and improving the performance of manufacturing executive system from both the manufacturing process perspective of eliminating waste and the corporate perspective of achieving strategic goals[10].Zhu,etal.[11]proposed KPI evaluation architecture and divided KPI analysis in to two parts including KPI definition and KPI utility, as shown in Fig.1.The International Organization for Standardization (ISO)22400 Automation systems and integration—key performance indicators for manufacturing operations manage men t[10]established a set of general evaluation system to express the objectives and critical factors,and proposed a common structure for standardizing KPI definition.The performance of manufacturing equipment directly influences production security,quality and efficiency,so it is necessary to evaluate manufacturing equipment from many aspects.There are different key performance indicators from different evaluation aspects,such as production ratio,unit energy consumption,quality ratio,equipment load rate,and overall equipment effectiveness,which form the KPI evaluation set of manufacturing equipment.According to KPI evaluation architecture and KPI common structure,Tables 1 and 2 give the definition and description of production ratio,and unit energy consumption.

Production rate indicator is defined as output-input ratio and higher ratio means the efficiency is better.However,it is complicated to compute the production rate because of the interaction among the quantity of different products in the multi-input and multi-output process.For the manufacturing equipment,the ratio of target product and produced quantity is used to evaluate the operating state and production efficiency.

Unit energy consumption indicator is used to evaluate energy consumed by equipment for energy savings,environmental protection and cost reduction.Though energy can be considered as a form of raw material,it helps to evaluate the consumption of energy using distinct indicators.

The relationship between the good quantity and the produced quantity is denoted as quality ratio.The higher the quality ratio,the more products meet the quality requirement.The information about the ratio of produced quantity in relation to the maximum equipment production capacity is provided by equipment load rate indicator,which reflects production efficiency,technical performance,equipment production state and equipment utilization by researching the usage of equipment.The value of equipment load rate impacts the production cost and profit.The optimal results of manufacturing process in the nondisturbance condition assess production loss and improve product quality represented by over all equipment effectiveness,which could be applied to evaluate either single production equipment or production unit which consists of multiple production equipments.These indicators could be defined and described on the basis of KPI common structure, and form the KPI set for manufacturing equipment with other indicators.

3.Multi-KPI Coordination Model of Manufacturing Equipment

According to the KPI evaluation architecture and common structure, one single KPI reflects the effectiveness of the certain concern point in the equipment operation state.However,due to managing the manufacturing equipment more effectively and efficiently,it is necessary to analyze and coordinate the relationships among multi-KPI in the KPI evaluation set,as shown in Fig.2.

The relationships of KPIs are complicated and they interact and impact each other in the KPI set,which affects decision making.For instance,production rate may have a direct effect on the overall equipment effectiveness of the manufacturing equipment[8].Raising production rate while simultaneously reducing unit energy consumption is often conflicted and inconsistent.Therefore,finding out the trade off compromises to keep the multi-KPI balance is crucial.According to the multi-objective optimization methodology,the multi-KPI coordination model of manufacturing equipment contains two parts:coordinate objectives and constraint condition.

3.1.Coordinate objectives

Minimizing or maximizing the focused KPIs is the coordinate objectives.The optimal overall objective is obtained by balancing the relationship among KPIs.

Fig.1.Evaluation architecture of key performance indicators.

Table 1Production ratio indicator

whereχ1,χ2…,χmand y1,y2,…ynare variables for calculating each KPI, such as production yield for calculating production rate indicator,and fault time for computing mean operating time between failure indicator.

3.2.Constraint condition

To discern the relation among KPIs,it is required to analyze the effect of variables on KPIs in the constraint condition,which can be considered from the aspects of mass balance,energy balance,quality and safety constraints,etc.Mass balance is closely related to equipment performance and production process.In broad term s,the input material is equal to the output material for the certain equipment.Meanwhile, energy transfer takes p lace in the production process,which includes complicated physical and chemical changes.Hence,it is necessary to keep balance between produced and consumed energy.The quality and safety require men ts would be taken in to consideration in the process to ensure economical and social benefits for equipment.

where z1,z2,…,zkare variables for the special equipment.For instance, material quantity,purity,energy medium quantity,temperature, pressure,etc.

Table 2Unit energy consumption indicator

4.Multi-KPI Coordinate Model Application for Distillation Column

Distillation process is widely applied in the production of metallurgy and chemical enterprise and it is a unit operation with high energy consumption.It is of great practical significance for gaining anticipative economical and social benefits by keeping the balance between production yield and energy consumption.For the typical distillation equipment, production rate and unit energy consumption are the key performance indicators for evaluating the production process of distillation column. In the case of methanol-water packed distillation column,coordinating the relation between production rate and unit energy consumption is a typical way to evaluate the equipment on the condition of quality standard.

4.1.Distillation process description

In the distillation process,the input materials are separated to satisfy the desired purity through repeated vaporization and condensation by pre-heater,distillation column,condenser,re-boiler,re flux drum,etc. [12].For themethanol-water packed distillation column,the raw material flows in to distillation column after being p reheated by pre-heater. The rising steam is condensed in to liquid by overhead condenser and divided in to product and re flux.The production methanol is kept in the storage after cooling.During this process,the steam and water are taken as heating and cooling energy medium to meet the energy demand by energy transfer,respectively.Fig.3 shows the distillation process.

F is the quantity of input material which contains methanol and water,B is the production quantity of column bottom,and D is the quantity of high purity methanol product.χF,χB,χDare the purity of input material,production of column and methanol production,respectively.L means the re flux quantity and V stands for the steam quantity in the column.

Thevalues and hard limits of themethanol-water packed distillation column[13,14]are given in Tables 3 and 4.

4.2.Formulation of the KPI coordination model for distillation column

4.2.1.Coordinate objectives

Two key performance indicators of production rate and unit energy consumption are considered to evaluate the distillation column in this case study.Themethanol-water packed distillation column is used for producing the methanol which satisfies the quantity requirement, while in this distillation process,the energy is consumed,such as the heating for re-boiler and the cooling for condenser.In order to raise the production rate,the unit energy consumption is increased.Thus,it is necessary to regulate these KPIs to achieve the balance.

The production rate indicator of distillation is described as

where D and B are the production of column top and bottom, respectively.

The unit energy consumption indicator is expressed as

where Wsteamis the heating steam quantity used in the re-boiler and Wwateris the cooling water quantity consumed in the condenser.

Given the profit of the production and the cost of energy consumption,there are two in dependent objective functions of the coordinated model in this paper,namely,maximizing the production rate andminimizing the unit energy consumption at the same time,which is form ulated m athem atically as follows,

Fig.2.Relationship among multi-KPI in the KPIset.

Fig.3.Methanol-water packed distillation column.

4.2.2.Mass balance constraints

When the distillation column reaches the steady state,the input material and the outputmaterial achieve the balance.Thus,them ass balance constraint of the entire column is

Them ass balance constraint of the product methanol is considered as

The rising steam is congealed totally by the overhead condenser and divided into top column product and re flux.Hence,mass balance of the overhead re flux d rum is

4.2.3.Energy balance constraints

There are conversion phenomenon between vapor and liquid in the distillation.Because of the change of re flux ratio R=l/d,energy balance constrain t of gas and liquid is

The energy balance constraint of the whole reactor-distillation is expressed as follows in the steady state,

Table 3Nominal values for the variables of the reaction-distillation column

Table 4Hard lim its on the flow rates of the reactor-distillation column

4.2.4.Quality constraints

The product methanol quality is the focus of the distillation process. According to the quality requirement,the quality constraints are

4.2.5.Safety constraints

In order to ensure safety in production,it is necessary to keep the equipment meet capacity requirem en ts,

4.3.Solution strategy and result discussion

In order to raise the production rate and reduce the unit energy consumption,the variables that affect the relationship between the two KPIs are analyzed using mechanism method,including methanol production quantity from column top(D),byproduct production quantity from column bottom(B),steam quantity in the column(V),re flux ratio(R),methanol production pu rity(χD),byproduct purity(χB), heating steam quantity(Wsteam)and cooling water quantity(Wwater). According to the characteristics of the coordinate model and the requirement of methanol production quantity,methanol production quantity from column top(D)and methanol production purity(χD) are considered as the main decision variables for optimization in this study.

Due to the relationship between production rate and energy consumption,the appropriate set point value of one variable for maximizing the production rate may not be suitable for minimizing the unit energy consumption.Hence,the applicable trade-off solutions for both two KPI objectives should be considered.

It is appropriate to solve the multi-KPI coordinate problem by using multi-objective optimization strategy,which aims at searching for one or more satisfying solutions in Pareto optimal set.Multi-objective optimization strategy contains two main algorithm s:one is converting the multi-objective problems to a single objective problem using some methods,and another is selecting the satisfying solutions using some trade-off criterion in the Pareto optimal set.To get the Pareto optimal set,mathematical programming approach and genetic algorithm(GA) are applicable[15,16].Following the vector evaluated genetic algorithm (VEGA)first proposed by S chaffer in 1985[17],many multi-objective evolutionary algorithms are studied,such as multiple objectives with particle swarm optimization algorithm(MOPSO)[18],the nondominate sorting genetic algorithm(NSGA)and the non-dominatesorting genetic algorithm II(NSGA-II)[19].In this study,εrestriction method is employed to acquire and evaluate the Pareto solution set due to containing strong nonlinear constraints[20].

Table 5Distillation process parameters of Pareto optimal solution

Fig.4.Pareto carve obtained by ε restriction method for the coordinated model.

For this study,the production rate is considered to the critical object because it directly influences the enterprise's income,while unit energy consumption is taken as one of constraints,less than ε.The range of energy consumption is[UECmin,UECmax],where UECminand UECmaxare the minimum and maximum unit energy consumption respectively. In this paper,the minimum and maximum unit energy consumption is the solution of optimization model under the present constraints.The solution byε restriction method is given in Table 5.

An efficient Pareto curve is generated by the optimal solutions of optimization problem.The conflict between the effects of the decision variables on the two KPI coordinated objective functions results in the optimum being a Pareto optimal set rather than a unique solution.The characteristic of the Pareto set for this studied case is that the two objects could not achieve the satisfied results.When one point in the Pareto optimal set is moved to another,one objective function is improved but the other becomes worse.Therefore,there is no dominated solution within the Pareto optimal set.The additional in formation like KPI priority is required to choose the p referred solution from the whole Pareto optimal set for operation[21-23].The obtained Pareto carve is shown in Fig.4.

Fig.4 describes the relationship between the two KPIs,production rate and unit energy consumption,which provides a better perspective for operator to make an effective decision.The dotted points in Fig.4 give the maximum and minimum production rate with the change of unit energy consumption within the present constraints.It is shown that the rising of the production rate causes the increasing of unit energy consumption correspondingly.However,the change of gradient is not as enormous as it is in the beginning.Due to the equipment capacity bound and quality requirement,production rate remains the same with the growing of unit energy consumption.

Each dotted point on the Pareto carve is an optimal solution under the present constraints,which is related with a set of decision variables. And according to the present constraints and requirements,three key points from the corresponding objective values of the solutions are listed in detail in Table 6,respectively.

From this table,it is observed that there is a trade off set between maximizing production rate and minimizing unit energy consumption. Under the quality requirements,the energy consumption raises simultaneously with the growing of production yields,while the methanol production purity decreases.There are different emphasis points and analysis view s for these three cases.Case A produces high purity product preferred by the market and low unit energy consumption cost, but low production rate leads to less total benefit.On the contrast, Case C produces more low purity product with abundant heating steam and cooling water,and also receives little total benefit.Case B falls in between Case A and Case C,and though production rate does not reach the maximum and unit energy consumption is high,more benefit is achieved.Considering the actual constraints and require men ts,decision-makers balance the relation between the two KPIs and select one operating point to get the maximum benefit.

5.Conclusions

Manufacturing equipment plays an important role in the manufactuing process.It is useful and helpful to evaluate manufacturing equipment for improving its capability.The paper addresses the challenge of key performance indicator evaluation.Th rough describing and analyzing each KPI,the KPI evaluation set for manufacturing equipmentbased on KPIs evaluation architecture and common structure is obtained. To discern the relationship among KPIs,an available coordination model is presented and a case study about methanol-water packed distillation column is used to demonstrate the effectiveness.With coordinating the relation between production ratio and unit energy consumption based on multi-objective optimization strategy,an efficient solution set denoted as Pareto set is gained.The relation between these KPIs is explored and used for choosing the appropriate solution from the Pareto set. Furthermore,the coordination model and strategy are not only limited to evaluate the special manufacturing equipment,but also accounts for the evaluation of different levels in manufacturing process.

Table 6Comparison between coordinated objectives and decision variables from three selected cases

Nomenclature

B production quantity of column bottom,kg·h?1

b the molar mass of production from the column bottom, kmol·h?1

Cpfmeththe specific heat of methanol,kJ·kg?1·°C?1

Cpfwatthe specific heat of water,kJ·kg?1·°C?1

D the quantity of high purity methanol product,kg·h?1

d the molar mass of high purity methanol product,kmol·h?1

E energy consumed in the manufacturing process

Ef plate efficiency

F the quantity of input material,t·a?1

f the molar mass of input material,km ol·h?1

ΔHmethanolevaporation latent heat of methanol,k J·kg?1

ΔHsteamevaporation latent heat of steam,k J·kg?1

ΔHwaterevaporation latent heat of water,kJ·kg?1

L the re flux quantity,kg·h?1

l the molar mass of re flux,kg·h?1

M material used in the manufacturing process

Mbaverage relative molecular mass of the production from the column bottom,g·m ol?1

Mdaverage relative molecular mass of the high purity methanol product,g·m ol?1

Mfaverage relative molecular mass of input material,g·m ol?1

m ax maximum

m in minimum

n number of stages

PR production rate

Q quality requirement

QBheat load of reboiler,k J·h?1

QCheat load of condenser,kJ·h?1

QC1heat load of chiller,kJ·h?1

QDheat load of column top,kJ·h?1

QFheat load of p reheater,kJ·h?1

Qsheat load of steam,k J·h?1

R re flux ratio,%

S safety requirement

t temperature,°C

UEC unit energy consumption

V the steam quantity in the column,kg·h?1

v the molar mass of the steam in the column,km ol·h?1

Wsteamthe heating steam quantity used in the re-boiler,kg·h?1

Wwaterthe cooling water quantity consumed in the condenser,kg·h?1

χBthe purity of production in the column bottom,%

χbthe mole fraction of production in the column bottom,%

χDthe purity of methanol production,%

χdthe mole fraction of methanol production,%

χFthe purity of input material,%

χfthe mole fraction of input material,%

χidata and variables for calculating each KPI

yidata and variables for calculating each KPI

zivariables or data for the special equipment

αrelative volatility

ηheat loss ratio in the column bottom,%

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☆Supported by the National Natural Science Foundation of China(61134007, 61320106009).

*Corresponding author.

E-mailaddress:hysu@iipc.zju.edu.cn(H.Su).