A Waste Relationship Model and Center Point Tracking Metric for Lean Manufacturing Systems

IIE Transactions (2012) 44, 136154Copyright C IIEISSN: 0740-817X print / 1545-8830 onlineDOI: 10.1080/0740817X.2011.593609

A waste relationship model and center point tracking metricfor lean manufacturing systems

SAINATH GOPINATH and THEODOR I. FREIHEIT

University of Calgary, Mechanical & Manufacturing Engineering, 2500 University Dr. NW, Calgary, Alberta, T2N 1N4, CanadaE-mail: [email protected]

Received December 2009 and accepted May 2011

Lean manufacturing is about eliminating waste, which requires the creation of waste metrics that are tracked in order to createthe conditions for its elimination. In this article, metrics used to monitor the seven traditional non-value adding wastes types ofoverproduction, defects, transportation, waiting, inventory, motion, and processing are explored and a center point metric pair isproposed that can give systematic insight into system waste performance and trade-offs. For example, lower work-in-process levels(inventory waste)may requiremore replenishment (transportationwaste) in order tomaintain production. Awaste relationshipmodelis proposed that can be used to derive the relationship between different wastes in a Pareto-optimal waste-dependent lean system.The trade-off relationships are statistically verified using simulation experiments across different system configurations, complexities,and planning scenarios.

Keywords: Lean manufacturing, waste relationships, performance metrics, trade-offs, decision making

1. Introduction

Lean manufacturing emphasizes value creation by elimi-nating waste. Waste consists of non-value-adding activitiesthat contribute to the product cost and for which the cus-tomer is unwilling to pay. Eliminating waste can reduceproduct costs and improve quality, but it is not possibleto completely eliminate waste even in an efficient systemwhose operations are waste dependent (that is, has wasteas a part of its functionality). It is therefore necessary tounderstand the waste relationships in order to minimizesystem waste to the lowest possible level.In lean manufacturing, seven types of waste have been

defined (Womack et al., 1991).

1. Overproduction (production ahead of demand).2. Defects (any product/service that the customer is un-

willing to accept).3. Transportation (moving products when it is not actually

required to perform a processing step).4. Waiting (any resources/materials staying idle).5. Inventory (materials not being completely transformed).6. Motion (resources moving more than is required to

transform the material).7. Processing (unnecessary or processing over the mini-

mum necessary for material transformation).

Corresponding author

Womack et al. (1991), Hines and Rich (1997), Russell andTaylor (1999), Canel et al. (2000), Conner (2001), Svensson(2001), and Rawabdeh (2005) consider waste as an expen-diture of resources for any means other than the creationof value for a customer and thus a target for elimination.Historically, little attention has been given toNon-Value-

Adding (NVA) activities such as storage and transporta-tion (Rawabdeh, 2005). The result is that only minimaldifferences have been realized in the reduction of overalllead time, the improvement of quality, and the reductionof cost. For instance, Conner (2001) reported that whenlead time was examined, value-adding activities only ac-counted for 5% of the lead time. Similarly, Suzaki (1987)claimed that only 5% of an operators time adds value andthe rest adds cost to the product. Todd (2000) concludedthat waste should be eliminated to reduce lead time andallow a manufacturer to respond quickly to customer re-quirements. Samaddar andHeiko (1993, p. 19) summarizedthat

. . . the elimination of waste can be viewed as a commonissue in any production/operations system. One shouldsystematically identify and continuously work to eliminatesuch waste in order to achieve effectiveness and efficiency.

The majority of the research literature focuses on thecomplete elimination of waste in order to improve produc-tivity and quality, respond quickly to customer require-ments, and reduce manufacturing cost.

0740-817X C 2012 IIE

Waste relationship model 137

It is not possible to completely eliminate all of the sevenwaste types even in an efficient system whose operationsare waste dependent. A system that has waste as a part ofits functionality is referred to as a waste-dependent systemin this article. In these systems, complete waste eliminationis not possible. Instead, all wastes can only be reduced tothe minimum level that exhibits Pareto-optimality. Pareto-optimality (Feldman, 1980) is a term from economics thatis used to describe a set of solutions for a multiple objectiveproblem that exhibits the property that no single objectivecriterion can be improved without a trade-off making someother criterion worse (Feldman, 1980; Petrie et al., 1995).To improve upon the Pareto-optimal waste-dependent

system, work tasks within the production system mustbe redesigned to achieve functionality without the waste(waste independent), which may require significant capitalinvestment. The fullest application of lean principles leadsnaturally to transformation into Pareto-optimal waste-dependent lean systems if we consider the use of capi-tal as wasteful if the system can be improved (all wastesreduced; i.e., there is no Pareto trade-off between wastetypes) without its expenditure. Until such time that capitalis available to redesign the system, it will operate in thisPareto-optimal state. The proposed Pareto-optimal wasterelationship model is intended to aid in effective opera-tional decisions to cut costs and improve efficiency withoutthe requirement of immediate capital.The relationship between the waste types must be first

understood in order to achieve a waste-dependent efficientsystem. Wastes must therefore be measured quantitativelyin order to derive their relationships. Feld (2001) definesa manufacturing metric as a standard measure that de-scribes a performance criterion for amanufacturing processso that everyone in the organization is working towards thesame goal. An attempt has been made to identify and inte-grate a set of metrics that can quantitatively measure differ-entwaste types.However, it was found that not allmetrics inthe existing literature fulfill the requirements of this articlein that they be simple and shop floor feasible. For example,the build-to-schedule (Khadem et al., 2006) metric requirescomputer simulations and is not simple. Therefore, a set ofmetrics is proposed to provide the information necessaryto understand the waste relationships.

1.1. The center point metric

It is desirable to have a simple, feasible metric that can pro-vide, at least to some degree, a measure of all waste typesin the manufacturing system. An objective of this article isto develop a metric or set of metrics to understand the per-formance of the system in the least possible time and cost.A single metric, highly correlated to other system metrics,can reveal critical information about the whole systemsperformance. Therefore, a center point metric pair is pro-posed that can give systematic insight into the system andcan be used for decision making. Gopinath and Freiheit(2009) have proposed customer waiting waste as a supe-

rior center point metric that is highly correlated with othersystem waste types. They verified its efficacy using simplecorrelation analysis; however, this approach only providesthe direction and degree of linear relationships.In this article, the center point metric concept is more

rigorously examined using regression analysis, which pro-vides additional insight into the system sensitivity. The firstmetric of the pair is a metric that receives strong signalsfrom the system or magnifies the effect of changes or ab-normalities in the system and is termed the Detection Cen-ter point Metric (DCM). The DCM is highly correlated toother waste types and it can be used to monitor the systemperformance. The second metric of the pair sends strongsignals to the system and is termed the Pivot Center pointMetric (PCM). Small changes in the PCM are magnifiedin other system waste types, and it can be used for systemwaste optimization or system design and decision mak-ing. The best center point metric pair will be determinedthrough statistical evaluation of system waste responses.This article proposes a waste relationship model that

can be used for decision-making about trade-offs with theobjective to reduce all waste types to the minimum pos-sible level in a waste-dependent efficient system withoutjeopardizing its intended functionality. Moreover, this ar-ticle identifies, develops, and integrates a set of metrics;determines the waste relationship; and statistically verifiesthe proposed waste relationship and the center point met-ric across different production planning scenarios and dif-ferent manufacturing system complexities. The followingsections of this article elaborate further on the researchmethodology, quantification of the wastes using metrics,derivation of the waste relationships, and statistical verifi-cation of the waste relationship model and the center pointmetric using simulation experiments.

2. Methodology

A three-step methodology was followed in this research.First, the literature on lean manufacturing was reviewed todefine waste types and explore potential metrics. Second,the logical relationship between waste types was mappedusing concept mapping and a relationship model was de-veloped. Finally, the model was statistically tested usingdiscrete-event simulation to determine the trends in themagnitude and direction between the waste relationships.Note that an absolute measure of the relationship betweenthe waste types is not the intent of this analysis.The review of current research in lean manufacturing

identified a few shortcomings in existing research such asthe lack of simple, shop floorfeasible dedicated metricsto quantify waste. Next, concept mapping was selected toassimilate the relationships between waste types, which isa powerful technique for the graphical representation ofknowledge. Moreover, it is a technique that can aid in theunderstanding of relationship concepts (in this case, anidentified waste) with other concepts (other waste types).

138 Gopinath and Freiheit

Table 1.Waste definitions

Waste Definition

Defects Any product that is unacceptable to thecustomer. Handling and transformationdefects are considered

Overproduction Production ahead of demand, which iscaptured by the finished inventory

Inventory Raw materials and work-in-process notbeing processed

Motion Operators movement between workstationsProcessing Processing more than the minimum required

for material transformationTransportation Transporters movement between inventoriesWaiting Any resource staying idle during work hours

This process involves creating a global map that showsthe main topics and their relationships, and more detailedmap(s) showing specific details of a particular portion ofthe map.Simulation with ArenaR was used to test the waste re-

lationship model. Design of Experiment (DoE) techniqueswere used to run the simulation experiments, and linearregression and Analysis of Variance (ANOVA) statisticalanalysis were performed on the simulation data in orderto understand the systems sensitivity to the center pointmetric using the statistics toolbox of MATLABR .

3. Metrics

Metrics for measuring waste in a manufacturing systemsshould be easy to collect and simple to understand. To be

useful to decision-making processes in manufacturing in-dustries, metrics must be feasible for collection on a real,dynamic manufacturing shop floor. In addition, the num-ber ofmetrics should be kept to aminimum in order to keepthe data collection costs as low as possible and to minimizethe time necessary to understand what is happening in thesystem.Many manufacturing performance metrics can be iden-

tified in the research literature, but few are both feasibleand simple. A table of proposed waste metrics identifiedin the literature is summarized and reviewed in Gopinathand Freiheit (2009). Performance metrics have been de-veloped in different contexts such as lean manufacturing,total productive maintenance, and theory of constraints.Unfortunately, many of these metrics cannot be used di-rectly to measure shop floor performance because theyare too general (provide global measures), require overlycomplicated calculations (e.g., dock-to-dock as defined byKhadem et al. (2006)), or do not capture waste as definedby lean manufacturing, even though, as in machine re-liability, they are good performance indicators. In somecases, metrics are better suited for computer simulationmodels than direct shop floor measurements; e.g., build-to-schedule (Khadem et al., 2006). Additionally, some shopfloor performance metrics provide superfluous or redun-dant information andmake things look unnecessarily com-plex.Table 1 summarizes how waste types are defined in

this article, and Table 2 summarizes the proposed wastemetrics. The defects (A) waste metric should measureanything that is unacceptable for the customer. Therefore,themetric proposed byRother and Shook (1999) quantifiesthe waste by providing the percentage of unacceptable

Table 2.Waste metrics table

Waste code Waste Metric Definition

A Defects

all MC

SiP Rother and Shook (1999)

B Overproduction 1T T0 F Idt Time-persistent measure of finished inventory (Kelton et al., 2007)

C Motion TmT Percentage of time spent in motion

D Transportation FTtT Percentage of time spent in transportation

E Waiting (customer) TwT Percentage of time spent waiting

F Waiting (material WIP)

all WIP

1N

Ni=1 WQi The time spent waiting (Kelton et al., 2007)

G Waiting (machine) 1 all MCTRinT Percentage of time spent waiting

H Waiting (operator) 1 ( Tw +TmT ) 1% Operator saturationI InventoryWarehouse

T0 WHdt Time-persistent measure of raw material inventory (Kelton et al.,

2007)J InventoryWork-in-progress

all WIP

1T

T0 WIPidt Time-persistent measure of WIP inventory (Kelton et al., 2007)

K Processing Cp,Cpk Chuan et al. (2001), NIST Handbook


production. Overproduction (B) is production ahead ofdemand and it is captured by the finished inventory. Thefinished inventory should be measured based not only onthe inventory content but also the duration of time that theparts stay in the inventory. Therefore, the time-persistentmetric suggested by Kelton et al. (2007) is used, where theinventory is time-weighted based on part content duration.Similarly, work-in-process (J) and warehouse inventories(I) are quantified using time-persistent measures. Motion(C) waste occurs when an operator walks between work-stations and is measured as a percentage of time spent inmotion by the operator. Transporting material betweenprocesses, which adds no value to the product, leads totransportation (D) waste. This metric should measureboth transportation duration and frequency to provide atransportation percentage. Waiting material (F) waste isquantified by measuring the average time waiting in inven-tory (Kelton et al., 2007). Waiting resource (G, H) wasteis quantified by the time that a resource is idle, expressedas a percentage of NVA activity by the resource. Similarly,waiting customer (E) waste is quantified by the percentageof time that customers wait for product availability. Pro-cessing (K) waste occurs whenever thematerial is processedinappropriately during transformation. Process capabilityindices likeCp andCpk (Chuan et al., 2001) are appropriatemetrics to use to indicate the statistical potential of theprocess toward exceeding customer requirements.

4. The relationships between waste types

The concept map illustrated in Fig. 1 was developed to un-derstand the logical relationships between the waste types.The starting point for this map was Rawabdeh (2005), whoexamined similar waste relationships but missed a few criti-cal relationship scenarios such as transportation and inven-tory (Work-In-Process (WIP)). Building on his model, anunderstanding of the waste relationships was developed,giving the trade-offs between different waste types in anefficient waste-dependent system.The concept map shows how different waste types are

conceptually linked together in a system. Darker shadednodes are the wastes and lighter shaded nodes are con-necting concepts. An example of the interpretation of theconnections is that as a transportation resource replen-ishes inventory, larger batch sizes will lead to higher mate-rial storage resulting in high inventory waste and lowerreplenishment frequencies (lower transportation waste).Therefore, an inverse relationship can be derived betweentransportation (D) and inventory waste (J).From the concept map, a trade-off model of relation-

ships was developed and is summarized in Fig. 2. Theserelationships can be used for multi-level decision makingby selecting the appropriatemetrics fromTable 2 and deter-mining the relative impact between the waste types result-ing from waste reduction program. Processing waste (K) is

not considered in this model as it is specific to particularmanufacturing processes. Rawabdeh (2005) also has simi-lar views on processing waste. Whether a waste type has adirect or inverse relationship with another waste type canbe obtained by multiplying the signs on the path betweenthem. For example, the relationship between overproduc-tion (B) and WIP (J) is obtained by multiplying the 1 +1 +1 +1 = 1, showing that it has an inverserelationship.

5. Testing the relationship model using simulation

The waste relationship model is tested using discrete-eventsimulation in three similar serial manufacturing systemmodels of increasing complexity and different productionplanning time horizons. The results of the simulation runswere also used to identify and screen center point metriccandidates. Each complexity model was run at three lev-els of demand rate where no resource was deliberately setas a bottleneck. Rather, the resources become system bot-tlenecks automatically by the randomness induced by thesimulation. The demand rate was varied by 10% with re-spect to the system throughput time. The system constantsare summarized in Table 3. The system responses are over-production (finished inventory (B)), inventory (WIP (J),warehouse (I)), waiting (material (F), machine (G), cus-tomer (E), and operator (H)), motion (C), transportation(D), and defects (A).

Table 3. Simulation model constants

Variables Values

Batch size B1 30 UnitsBatch size B2 4 UnitsLead time LT 90 MinDistance D1 1900 FtVelocity V1 265 Ft/minScrap S1 0.4 %Scrap S2 0.2 %Scrap S3 0.0 %Scrap S4 0.0 %Scrap S5 0.1 %Scrap S6 0.0 %Cycle time CT1 4 MinCycle time CT2 4.3 MinCycle time CT3 4 MinCycle time CT4 3.9 MinCycle time CT5 4.2 MinReorder point ROP1 30 UnitsReorder point ROP2 15 UnitsAvailability A1 90 %Availability A2 95 %Availability A3 97.5 %Availability A4 90 %Availability A5 95 %

Fig.1.A

conceptmap

oflogicalw

asterelationships.(Color

figureavailableonline.)

140


Fig. 2. The waste relationship model.

The intermediate complexity model, illustrated in Fig. 3,has one raw goods warehouse (WH), a rawmaterials trans-porter (TR), five serial work stations (WS) with five inter-spersed WIP buffers (W), a finished goods inventory (FI),two machine operators (O), and a customer (CU). The raw

Fig. 3. Schematic of intermediate complexity manufacturing system model.

goods supplier replenishes the warehouse inventory withlarge batch sizes. Production control is a pull system withthe transporter and other system resources triggered bythe finished goods inventory level. The transporter movessmall batches from the warehouse to theWIP buffer. Then,


the workstations pick the parts from their respective WIPbuffers and process them. Operator 1 loads, unloads, andtransfers parts between workstations 1, 2, and 3 and oper-ator 2 controls workstations 4 and 5. Finally, the customerconsumes from the finished goods inventory.The simple model has the same features as the above-

described model except for the number of resources. It hastwo machines and one operator to load, unload, and trans-fer between them. In contrast, the complex model has eightmachines and three operators. The increase in the resourcescomplicates the material flow and increases the overall sys-tem complexity. All models are considered to be efficientbecause the resources were saturated to the maximum pos-sible level, line balanced, made highly reliable, use pullsignals to control the excess inventory build-up, and thesystem was operated close to the takt time. At the sametime, stochasticity was introduced into the system to repli-cate the real, dynamic environment, such as resource failurepatterns following an exponential distribution, demand fol-lowing a Poisson distribution, and process times followinga triangular distribution. While these models are appropri-ate to explore the relationship between the waste types, thissimulation model is limited to efficient waste-dependentlean systems.Each complexity simulation run was performed across

three different production planning time horizons, namely,Long-Term Steady State (LTSS), Short-Term (ST), andProduction Ramp-up (PR). The LTSS (truncated replica-tion steady state) was run for 249 600 min of productiontime (representing a year) for 30 replications using Arena.System performance statistics were collected after a 4800-min warm-up to avoid the initialization biases. The ST sim-ulation was run for 4800 min after a 4800-min warm-up for30 replications, whereas the PR simulation used terminat-ing replications and was run for a total time of 4800 minwithout clearing the initial statistics. The waste responsesfrom the simulation model were normalized in order toaddress slope magnitude variation because waste responsemagnitudes can vary significantly.A test for Pareto optimality was conducted on the sim-

ple model to ensure that the selected system parametersshowedappropriate trade-off relationships. Thewaste typeswere minimized by integrating the Arena simulation soft-ware with the optimization toolbox of MATLAB. Ten sys-tem parameters, consisting of the independent variablesoperator transfer time, machine cycle times, finished inven-tory re-order point, supplier lead time, operator cycle time,warehouse re-order point, internal batch size, warehouseorder batch size, and transporter scrap rate, were numer-ically optimized using the MATLAB fmincon function tominimize the objective function of the weighted sum ofthe simulation response waste metrics. The variation of thesimulation model was controlled by using random num-ber seeds, steady-state truncated replication simulationstrategy, and averaging the waste function value from fivereplications. The system parameters for the waste relation-

ship verification models were chosen to be in between thePareto-optimal bounds obtained from this optimization.

5.1. Preliminary data visualization

The raw simulation waste measures from the various com-plexity and demand LTSS runs were aggregated and thenplotted pair-wise in a matrix scatterplot to visualize the re-lationships between the wastes; see Fig. 4. Note that thereis considerable dispersion in the data and in many casesmultiple distinct lines can be seen. In general, wastes withhighly consistent data spread, defined as a tendency to becoherent yet have a distributed data frequency (short barsin the histogram), have higher sensitivity to other wastetypes. For example, consider waiting customer and waitingmaterial wastes. The histogram for waiting customer waste(E) is more consistently distributed (more toward a uni-form distribution) than waiting material (F), which resultsin a slope tending to the extremes of either zero or largewhen predicting one waste from the other. Motion (C),transportation (D), waiting machine (G), waiting operator(H), and warehouse (I) wastes have similar histograms towaiting customer (E) waste and tend to show coherent dis-tributions and are expected to have higher sensitivity levelsto the other wastes. Overproduction (B) waste is incoher-ent and has a concentrated interval frequency that resultsin lower system sensitivity. Defects (A) and WIP (J) wasteshow random scatter, which is also expected to show lowersystem sensitivity. The diverging multi-streams that lead tothe incoherence in these plots is due to noise factors such asdemand and complexity, which can be filtered out to givebetter insight into the system.The raw waste data were filtered of the obscuring effects

of the known noise factors, namely, demand and complex-ity, by regressing each waste against another waste type butblocking for the noise, which is possible in a controlled ex-periment. Blocking is a statistical technique used to removethe obscuring effect of factors and their sources of variabil-ity (Montgomery, 2008). Equation (1) is the pair-wise wasterelationship model used in the regression analysis:

Wi = 0 + 11C1 + 12C2 + 2D + jWj + ,i, j = , . . . , 10, i = j. (1)

The system complexity has two regression coefficients forblocking. Demand, a continuous variable, was scaled inthe regression equation and took the values 0, 0.5, and 1.0.Unlike demand, complexity is a categorical variable and aDoE-based coding convention was adapted for complexityblocking, where (C1, C2) are respectively (1, 0), (0, 1), and(1,1) for low, intermediate and high complexity (Mont-gomery, 2008). This regression allows the response wastefrom every simulation sample k to be adjusted to accountfor the effect of complexity and demand, giving a noisefiltering equation:

Wik = Wik 0 11C1 12C2 2D. (2)


Fig. 4. Pair-wise waste comparisonpreliminary data visualization.

In other words, the effect of the predicted variation ofthe complexity and demand resulting from the regressionmodel is removed from the simulation waste response data,and the resultant pair-wise relationships can be examinedwith minimal influence of noise; see Fig. 5. As can be seen,the data are much more coherent and the histograms aremore symmetric. Consider again the example of waitingcustomer (E) and waiting material (F), the diverging multi-streams of waiting customer waste have for the most partdisappeared, and the data are generally more coherent forboth waiting customer and waiting material wastes. Thefiltered data make response predictionmuch clearer; for ex-ample, when customerwaitingwaste is predicted bywaitingmaterial waste, the slope is generallymore distinct, and viceversa. Complexity and demand parameters were includedin all subsequent regression analyses of the data.

5.2. The influence of complexity and demand on waste

An ANOVA test was conducted on the complexity anddemand noise factors to determine their contribution to

the waste variation. Table 4 summarizes the effect of noisefactors for the LTSS simulation waste measures. It showsthat defects (A), motion (C), waiting machine (G), waitingoperator (H), and WIP (J) waste variation is influenced bycomplexity. This follows because these factors are scaleddirectly by the amount of processing required and this in-creases with system complexity. Example patterns in themagnitude of the complexity coefficients are illustrated inFig. 6(a). Low complexity tends to decrease the overpro-duction (B) waste response, whereas intermediate complex-ity is more neutral, and high complexity tends to increase

Table 4. Contribution of noise (in %) to waste variation

Waste (see Table 2 for code)

Response A B C D E F G H I J

Complexity 54 17 65 19 21 13 64 73 14 47Demand 4 64 3 8 0 0 3 2 10 9Other 43 19 32 73 79 87 33 25 76 44


Fig. 5. Noise-filtered pair-wise waste comparisonpreliminary data visualization.

overproduction (B) response waste. The WIP (J) and mo-tion (C) response waste exhibits an opposite behavior, withlow complexity increasingWIP andmotion waste responseand high complexity decreasing them. The waste responseshows a trade-off between internal (WIP) (J) and finishedgoods inventory (B) when going from low to high complex-ity. The pattern of motion (C) response waste follows di-rectly from the simulationmodels,where for low complexitythere is one operator for two stations, for intermediate thereare two operators for five stations complexity, and for highcomplexity there are three operators for eight stations.Table 4 also shows that, as expected, overproduction

(B) is most influenced by demand because finished inven-tory, its metric, acts as a cushion for demand fluctu-ation. Likewise, other inventory waste measures such aswarehouse (I) and WIP (J) are also influenced by demand.The demand coefficients, Fig. 6(b), are much higher thanthe complexity coefficients, indicating a strong couplingof demand to inventory waste. The demand coefficientsfor the response wastes of both overproduction (B) andWIP (J) were both large and had mixed signs depend-ing on the predictor waste. When defects (A), motion (C),

and transportation (D) were predictor wastes, demand in-creased over-production (B) and WIP (J) response waste.This is because these predictor wastes are tightly coupledwith higher production volumes. The demand coefficientsfor the other response wastes were of similar magnitude foreach predictor waste.

5.3. Pair-wise linear regression of waste relationships

A pair-wise linear regression analysis was performed whereeach waste response from the simulation experiments wasused to predict every other waste response to understandtheir relationship. The regression analysis provides a slopewhose direction determines whether the relationship is di-rect or inverse, and a magnitude which determines thestrength of the relationship. The regression also providesan adjusted R2, which, as a measure of the models fit, pro-vides an estimate of how effective a givenwaste is in predict-ing changes in another waste. Equation (1) is the pair-wisewaste relationship model used for this regression analysis.Tables 5 and 6 summarize the slope and adjusted R2 val-

ues derived for the time horizon of the LTSS. As can be


Fig. 6. Effect of system complexity and demand on waste relationship (LTSS).


Table 5. LTSS predictor waste regression coefficients (slope)

Predictor waste

Response waste A B C D E F G H I J

Defects (A) 1 0.69 0.86 0.90 0.83 1.08 0.91 0.86 0.86 0.81Overproduction (B) 0.58 1 0.55 0.57 0.57 0.79 0.58 0.54 0.56 0.71Motion (C) 1.08 0.82 1 1.05 0.97 1.21 1.06 1.00 1.00 0.95Transportation (D) 1.02 0.78 0.95 1 0.92 1.13 1.01 0.95 0.95 0.90Waiting customer (E) 1.10 0.90 1.02 1.08 1 1.26 1.09 1.02 1.03 0.99Waiting material (F) 0.53 0.47 0.48 0.50 0.47 1 0.50 0.47 0.50 0.58Waiting machine (G) 1.00 0.77 0.94 0.99 0.91 1.12 1 0.94 0.94 0.89Waiting operator (H) 1.08 0.82 1.00 1.06 0.97 1.20 1.07 1 1.01 0.95Warehouse inventory (I) 0.95 0.74 0.88 0.93 0.86 1.11 0.94 0.88 1 0.90WIP inventory (J) 0.75 0.79 0.71 0.75 0.70 1.10 0.76 0.71 0.76 1

seen, the magnitude of the slopes and the fit of the rela-tionships between the wastes are not symmetric, whereasthe directions are perfectly symmetric between the wastes.Consider waiting customer (E) and waiting material (F)wastes. While their direction relationship is direct, posi-tive, and symmetric, their magnitude relationship is non-symmetric because the two wastes change in a dissimilarrate with respect to each other; i.e., one or more of thewastes are non-linear. In this case, waiting customer wastechanges at a rate 1.26 times that of the waiting materialchange, whereas the waiting material waste only changesby 0.47 times. In other words, waiting material waste is lesssensitive to change than waiting customer waste is.The slope magnitudes and directions were found to be

uniformly consistent across the RU, ST, and LTSS produc-tion planning time horizons. Figure 7 shows an example ofthe variation in predictor waste coefficients and adjustedR2 for customer waiting (E) and WIP (J) response wastes.As can be seen, the variation in slopes between the timeframes is generally small, less than 1020%, with only afew predictor wastes such as defects (A) and material wait-ing (F) having larger variation. These two predictor wastesare relatively rare events in the simulation model, as can beseen by their poorer model fit at shorter time frames.

5.4. Center point metric analysis

Three broad criteria were established to test for the centerpoint metrics. The first is the ability of the metric topredict the system waste performance, as measured bythe Pearson r correlation coefficient. The second is theoverall sensitivity of the metric to other waste metrics, asmeasured by its regression coefficient slope, ignoring itsdirection. A third customized measure, referred to as apredictive slope, is the product of the adjusted R2 and theslope and represents the sensitivity of the metric weightedby its ability to predict the waste relationship.A four-step methodology was adopted to determine the

center point metric pair. First, a correlation analysis wasconducted in order to identify the dependence relationshipbetween the wastes (Gopinath and Freiheit, 2009). Then, astatistical comparison was conducted between the correla-tion coefficients of all the system wastes to identify the topfour center point metric candidates that have correlationssignificantly larger than the others. Second, each candidatewaste was compared using a two sample, one-tailed t-testfor statistical difference to determine the number of wastesthat have statistically highermeanwaste sensitivity and pre-dictive slope in order to identify the metrics that send orreceive significantly higher signals. Third, the magnitude of

Table 6. LTSS waste relationship model fit (adjusted R2)

Predictor waste

Response waste A B C D E F G H I J

Defects (A) 0.48 0.94 0.93 0.92 0.63 0.92 0.93 0.84 0.66Over production (B) 0.85 0.86 0.86 0.88 0.84 0.86 0.86 0.85 0.89Motion (C) 0.93 0.51 1.00 0.99 0.63 1.00 1.00 0.90 0.71Transportation (D) 0.94 0.58 1.00 0.99 0.67 1.00 1.00 0.92 0.76Waiting customer (E) 0.93 0.61 0.99 0.99 0.67 0.99 0.99 0.90 0.76Waiting material (F) 0.62 0.44 0.62 0.61 0.64 0.61 0.62 0.61 0.68Waiting machine (G) 0.94 0.59 1.00 1.00 0.99 0.68 1.00 0.92 0.76Waiting operator (H) 0.93 0.54 1.00 1.00 0.99 0.65 1.00 0.91 0.73Warehouse inventory (I) 0.86 0.54 0.91 0.91 0.91 0.65 0.91 0.91 0.76WIP inventory (J) 0.73 0.70 0.78 0.78 0.79 0.76 0.78 0.78 0.79


Fig. 7. Effect of time frame on waste relationship.


the difference between thewaste slopeswas compared in or-der to identify thewastes that send and receive the strongestsignals to and from the system. Finally, the magnitude ofthe predictive sensitivity difference was also compared.Pearson product-moment correlation coefficients, r ,

were determined and compared for all waste pairs in or-der to obtain the center point metric candidates. A Pearsoncoefficient ranges from +1 to 0 to 1, indicating relation-ships that are perfectly linear and direct to unrelated toperfectly linear and inverse, respectively. Correlation co-efficients are not directly comparable because they ignorethe inherent variance of the sample, so they must be trans-formed into a normally distributed variable using a Fisherz-transformation (Shen and Lu, 2006):

r = 12loge

1+ r1 r . (3)

The statistical comparison methodology suggested byWuensch et al. (2002) was used to compare the correla-tion coefficients as well as the slope and predictive slopemagnitudes of different wastes. The transformed correla-tion coefficients, r , can now be directly compared using astatistical z-test:

z = ri r j

(1/(ni 3))+ (1/(n j 3)) . (4)

Table 7 summarizes the number of times a predictorwaste had a significantly higher correlation coefficient toa response waste than the other predictor wastes. The zstatistic is used as the t in a one-tailed t-test conducted ata 95% confidence level for the LTSS production planningscenario. The top five candidates with the highest count ofcorrelations that are statistically significantly higher thanother wastes are motion (C), transportation (D), waitingcustomer (E), waiting machine (G), and waiting operator(H), which were significantly higher approximately 57% ofthe time. The number ofwaste types that tested significantlyhigherwas found to be similar for all three production plan-ning scenario time frames.

Table 7. Correlation analysisdetection center point metric(LTSS)

Predictors

Responses A B C D E F G H I J Sum

Defects (A) 0 7 0 0 0 1 0 0 0 2 10Overproduction (B) 1 0 0 0 0 0 0 0 0 0 1Motion (C) 8 7 0 1 5 6 2 0 4 6 39Transportation (D) 8 7 2 0 4 6 1 1 4 6 39Waiting customer (E) 8 8 2 2 0 8 2 2 2 6 40Waiting material (F) 3 7 2 1 0 0 1 2 2 3 21Waiting machine (G) 8 7 2 0 4 6 0 1 4 6 38Waiting operator (H) 8 7 3 0 5 6 1 0 5 6 43Warehouse inventory (I) 8 7 0 0 1 6 0 0 0 6 29WIP inventory (J) 3 8 1 1 1 2 1 1 1 0 19

The slopes and predictive slopes of the wastes were nextcompared to identify center point metric candidates thathad the strongest response to and from the system andwere most predictive of the system (Wuensch et al., 2002).The t-statistic was calculated by first determining the stan-dard error of each predictor waste slope (regression coeffi-cient) from the mean standard error (MSE) of the regres-sion model:

s j =

MSEjn

. (5)

Then, determining the standard error of the differencebetween two predictor slopes:

si j =s2i + s2 j , (6)

and then the two sample t-test formula at a 95% confidencelevel was used to determine whether a predictor waste slopewas significantly greater than another candidates slope:

t = i jsi j

. (7)

For both the slope andpredictive slope, theDCMcandidatewastes ranked as having the highest number of significantbetter differences are (i) waiting customer (E) (100% and97% of the slope and predictive slope, respectively, werehigher in their paired comparison); (ii) waiting operator(H) (86% and 76%); (iii) motion (C) (76% and 69%); and(iv) transportation (D) (60% and 58%). The PCM candi-date wastes ranked as having the highest number of signifi-cant differences are (i) waiting material (F) (100% and 42%for slope and predictive slope, respectively); (ii) defects (A)(74% and 56%); (iii) waiting machine (G) (65% and 81%);and (iv) transportation (D) (56% and 72%). As can be seen,weighting the slope for its model fit reduces the attractive-ness of some candidate wastes. In fact, motion performedbetter than material waiting with a count of significantlybetter predictive slope differences of 43%.Taking into account the correlation, slope, and predictive

slope significant difference counts for the LTSS planningperiod, the top threeDCMcandidates arewaiting customer(E), waiting operator (H), and motion (C), whereas the topthree PCM candidates are waiting machine (G), defects(A), and transportation (D). While waiting material (F)was a promising PCM candidate because of its high slopes,as can be seen by inspecting Table 5, its model fit is poorand was eliminated from the finalists.The difference in the magnitude of the slope and predic-

tive slope for the DCMwas then calculated using Equation(8), where R2i is set to one for the slope difference and setto the adjusted R2 for the predictive slope difference. Inthis equation, jk is the coefficient for predictive waste j forcandidate response k, whereas ji is the coefficient for thesame predictive waste j for all other response wastes i . Thisdifference represents how much stronger a candidate waste


Fig. 8. DCM candidate slope and predictive slope comparison (LTSS).


Table 8. Contribution (in %) of factors with an inverse relationship to DCM slope variation

Predictor waste j

A B C D E F G H I J

Demand 11.2 5.7 5.0 4.8 12.7 9.4 10.2 10.5 4.7 33.0Complexity 14.1 9.1 1.6 1.4 10.3 33.3 11.0 11.7 61.4 42.9Response wasteA 0.0 0.1 0.0 0.0 0.1 0.0B 0.6 0.0 0.4 0.4 0.0 0.0C 0.0 0.0 0.0 0.0 0.0 0.0D 0.0 0.0 0.0 0.0 0.0 0.0E 3.4 4.3 3.9 3.9 F 0.7 1.3 1.5 1.5 G 6.4 8.0 7.7 7.7 H 12.8 16.1 15.6 15.6 I 5.8 6.0 5.6 5.6 J 0.0 0.0 0.0 0.0

Other 45.6 49.6 59.4 59.4 76.4 57.1 78.4 77.4 33.9 24.1

receives a signal from the predictive waste. Figure 8 illus-trates this difference for the three finalist candidate wastesand indicates that for both slope and predictive slope, cus-tomer waiting (E) receives the strongest signal from thepredictive wastes.

DCM =R2k jk R2i ji , i, k = j. (8)

Similar to the DCM, the predictor waste j that sends thestrongest signal to response wastes can be calculated forthe PCM, Equation (9)

PCM =R2k ik R2j ij , j, k = i, (9)

where in this equation, ik is the coefficient for candidate kpredictive waste for response waste i and ij is the coeffi-cient for all other predictive waste j for the same response

waste i . Figure 9 illustrates this difference for the three final-ist PCM candidates. While defects (A) sends the strongestsignal to the response wastes, second only to material wait-ing (F), when weighing for the regression model fit, waitingmachine (G) waste is a more favorable PCM.This analysis indicates that the best DCM is customer

waiting (E) and the best PCM is waiting machine (G). TheST and RU planning scenarios generally yield the sameconclusion as the LTSS. The PCMpredictive slope analysisconducted for the ST planning scenario found transporta-tion (D) to be the best PCM, although it was only a littlebetter than waiting machine (G) in terms of sending strongsignals to the system. However, this result may be due tounknown outliers or noise in themodel. Therefore, it is sug-gested that transportation waste should not be discountedas a PCM for short-term planning.

Table 9. Contribution (in %) of factors with a direct relationship to DCM slope variation

Predictor waste j

A B C D E F G H I J

Demand 13.9 15.2 12.6Complexity 13.6 11.7 6.9 28.8 16.7Response wasteA 1.0 B 1.7 C 7.1 3.7 D 20.5 10.9 E 3.3 3.6F G 5.0 1.8H 8.3 3.5I 0.0 17.3 0.0 0.0 12.6J 21.8 29.2 21.2 21.2 10.4

Other 43.3 57.5 100.0 100.0 78.3 29.9 78.9 78.9 60.8 49.2


Fig. 9. PCM candidate slope and predictive slope comparison (LTSS).


6. Discussion

This article assumes that the only noise factors in a sys-tem are demand and complexity. However, real, dynamicmanufacturing systems have many potential noise factors.The sources of variance outlined in Table 4 support thatonly demand and complexity are noise factors in this arti-cles simulation models. Wastes such as defects (A), motion(C), waiting machine (G), waiting operator (H), and WIP(J) are significantly affected by complexity because it is as-sumed that increased system complexity can be modeled asincreases in the number of machines, interspersed buffers,scrap accumulation locations, and operators. However, thisassumption may not hold in all cases. For instance, systemcomplexity may increase as a result of complex materialflow, resource movement, or batch size.Moreover, all wastetypes in this article are equally weighted, which may not re-veal accumulation of the most critical costs in the systemthat could be understood if the wastes were weighted by us-ing financial metrics. The PCM, which is only identified inthis article, has the potential for effective system waste costminimization and prevention when used with the financialmetrics.The objective of this article was to find the waste types

that are most coupled to other wastes in the system. Thewaste types are not only sensitive to system noise such ascomplexity and demand but are also sensitive to variationin other wastes. Two tests for robustness of the DCM wereconducted. First, the contribution of noise to waste re-sponse variation was evaluated and, second, ANOVA testswere conducted on the predictive waste slopes. Equation(10) is the regression model used to calculate the responsevariable, j , for the ANOVA factors of noise (complexityand demand) and the other predictor wastes. The responsewaste Wi was kept constant for the ANOVA tests. The re-sponses were separated out for the direct relationships (pos-itive slopes) and the inverse relationships (negative slopes)to prevent the misleading conclusion that results from ag-gregating all of the waste slopes.

Wi = 0 + jWj + . (10)

Table 4 shows the effect of noise factors on waste re-sponses. It can be observed that most of the variation inthe DCM (waiting customer (E)) is due to factors otherthan noise. This is desirable because the DCM should beas independent as possible from sources of noise. Second,Tables 8 and 9 show the percentage contribution of differ-ent system factors and noise to the waste slope variations.Robust wastes, i.e., those that have lower sensitivity to vari-ations in the system, have a high percentage in the otherfield, as higher unexplained variation indicates that waste isinsensitive to other factors andmost of its slope variation isdue to inherent random variation. By this measure, waitingcustomer waste is a robust metric, performing as well orbetter as any other waste.

A sense of how important a given variance factor is tothe overall strength of a signal can be derived by examiningthe contribution to variation, F (%), as weighted by a ratioof the range of variation to its average value, Equation(11):

F = max( j )min( j )E( j )

F. (11)

For all sources of variance, this weighted variation aroundthe waiting customer DCM is only 15.6%, the lowest ofthe predictive wastes. Furthermore, Table 8 indicates that12.7% of the DCM slope variation is due to the noise fac-tor demand, but this contribution to the slope magnitudeis small when applying Equation (11), where its weightedcontribution is only 2.0%.

7. Conclusions and recommendations

The relationship between the waste types in waste-dependent Pareto-optimal lean manufacturing systems hasbeen examined in this article. Metrics that are simple andfeasible to measure on the shop floor have been proposed.A trade-off relationship between the waste types in efficientwaste-dependent systems was demonstrated using discrete-event simulation and examined across different system con-figurations, complexities, and planning scenarios. A centerpoint metric pair has been identified by examining the pair-wise slopes between the wastes. Customer waiting time (E)has been identified as a DCM, which is an important per-formance measure for responsive production systems andcan be used for system monitoring and abnormality diag-nosis. Waiting machine time (G) has been identified as aPCM, which can be readily obtained from the commonshop floor performance measure machine saturation andcan be used for system optimization, waste prevention, anddecision making. In addition, the center point metric pairhas been tested for robustness.The DCM is expected to reflect and magnify system

changes. Most systems are designed to have waiting cus-tomer waste, which is a measure of the inverse of the sys-tems service level, to be as low as possible because lowservice levels are viewed to be detrimental to the business.However, this may not always be true in waste-dependentPareto-optimal lean systems, as it depends on the nature,location of waste cost accumulation, and efficiency priorityof a particular system. Therefore, it is suggested that cus-tomer waiting waste be used tomonitor the system changesand machine waiting waste be used to aid in making effi-cient system changes.In future work, the above assumptions and limitations

should to be addressed. It is suggested that financial wastemetrics be developed and their relationships verified in or-der to determine the critical waste cost contributors of thesystem. Moreover, it is suggested that the potential of the


PCM be further explored by combining it with the finan-cial metrics for product waste cost minimization. Finally,the waste relationships should be verified in a real, dynamicmanufacturing environment.

Acknowledgement

The authors thank the support of the Canadian Auto21Network Centres of Excellence and the University ofCalgary.

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Appendix

Notation

WS WorkstationPI Inventory from previous stationTR Transportation resourceWIP Work-in-process inventoryI InspectionFI Finished inventoryS ShipWH Warehouse inventoryO OperatorCU CustomerMC MachineUtil UtilizationSat SaturationSU SupplierF Transportation frequencyn Number of machines, buffers, or workersMCi i th Machining center or workstationP Total units producedSi Scrap from the i th machining centerT Total horizon timeTm Time spent in motionTRi i th Machine operation timeTt Transportation timeTw Idle or waiting timei, j Wastesni/n j Number of samples with respect to the waste i/jSi/j Standard error with respect to the waste i/jb Slope with respect to the waster i Transformed correlation coefficientMSEi/j Mean squared error0 Regression constant jWj Slope of the predictor waste Predictor wasteWi Response waste in the simple linear regression Error term in the regression equation1 Regression coefficient of complexity2 Regression coefficient of demand

Biographies

Sainath Gopinath received an M.Sc. degree in Mechanical Engineeringfrom the University of Calgary, Canada, in 2010; an M.S. degree inIndustrial Management from the Royal Institute of Technology, Sweden,


in 2008; and a B.Eng. degree in Production Engineering from AnnaUniversity, India, in 2005.Hehas been aManufacturingEngineer atLeanManufacturing Engineer atMagna International since 2010.His researchinterests includemanufacturing systems, competitivemanufacturing, andstatistical engineering.

Theodor Freiheit is an Associate Professor in the Department ofMechanical and Manufacturing Engineering at the University of

Calgary. His expertise is in both product and manufacturing sys-tem design and testing. He has a Ph.D. (2003) in Mechanical En-gineering an MBA (1995) from the University of Michigan, andan MSE (1988) in Design Optimization from Purdue University.At the University of Calgary, he runs the senior capstone designcourse. He has an active research program in the psychology of de-sign innovation, design and analysis of manufacturing systems, andmicro-engineering.

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A Waste Relationship Model and Center Point Tracking Metric for Lean Manufacturing Systems

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