International Journal of Operations & Production ManagementPerformance implications of investments in continuous quality improvementLinda C. Angel M. Jeya Chandra

Article information:To cite this document:Linda C. Angel M. Jeya Chandra, (2001),"Performance implications of investments in continuous qualityimprovement ", International Journal of Operations & Production Management, Vol. 21 Iss 1/2 pp. 108 - 125Permanent link to this document:http://dx.doi.org/10.1108/01443570110358486

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International Journal of Operations &Production Management,Vol. 21 No. 1/2, 2001, pp. 108-125.# MCB University Press, 0144-3577

Performance implications ofinvestments in continuous

quality improvementLinda C. Angell and M. Jeya Chandra

Pennsylvania State University, Pennsylvania, USA

Keywords Cost of quality, Quality, Investment, Appraisal

Abstract Quality investment decisions are complex and interrelated, with added uncertaintiesassociated with the many `̀ unknown and unknowable'' costs (such as the value of an unhappycustomer). However, existing cost of quality models are overly simplistic. In order to improvequality investment decisions, this paper thoroughly reviews the cost of quality literature, and thenproposes a multi-level model tracing the impact of prevention and appraisal program investmentson key performance results such as sales revenues, manufacturing and inventory costs, andquality failure costs. Several sub-sections of this framework are developed and described in detailwith analytical models. In particular, the variance reduction sub-model expands Taguchi's LossFunction for estimating hidden external failure costs by linking variance and process meansettings to reliability. This paper proposes analytical models to quantify the effects of qualityimprovement investments on tangible measures of firm performance.

IntroductionSince the early 1980s, US manufacturers have turned to total qualitymanagement (TQM) programs in an effort to improve their global market andfinancial performance. TQM involves a new mindset for management, wherebythe customer becomes the main focus of business, quality becomes theresponsibility of everyone in the organization, and continuous improvementbecomes the normal operating procedure (Margavio et al., 1995). Successfullyimplementing TQM requires a committed steering committee, supportive workteams, rewards and celebrations for success, and a dedicated quality costaccounting system (Burr, 1993). However, while sustained quality investmenthas become a hallmark of best-practice firms (Bottorff, 1997), determining theimpact of quality improvements on a firm's bottom line can be difficult becauseof problems measuring customer satisfaction (Margavio et al., 1993, p. 72).

Quality experts argue that a typical company can save more money byhalving poor quality costs than by doubling sales (Harrington, 1987).Specifically, manufacturing organizations spend between 25 and 40 per cent ofsales revenues on quality-related costs (Bottorff, 1997; Kiess-Moser, 1990),accounting for approximately 30 per cent of their total manufacturingexpenditures (Albright and Roth, 1992; Zemke, 1990). Juran (1951) estimatesthat, while most firms spend very little to prevent quality problems, manyspend between 10 and 50 per cent of their quality-related expenses on testingand inspection activities, which by their very nature assume the likelihood ofquality problems. In addition, he states that a whopping 50 to 90 per cent ofquality-related costs are spent to resolve problems, defects, or other `̀ failures''

The current issue and full text archive of this journal is available athttp://www.emerald-library.com/ft

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that have occurred during or after the manufacturing process. Furthermore,failure costs related to customer dissatisfaction, often described as the hiddencosts of quality because they are so difficult to measure or estimate, can total asignificant 20 per cent of the cost of sales (Margavio et al., 1993).

TQM programs, such as zero defects or six sigma, demand significantoperating expenditures and capital investment (Carr and Tyson, 1992). Inparticular, manufacturing technologies are rapidly changing, necessitatingmethods to evaluate capital investments in these new technologies, givenextensive hidden costs (Margavio et al., 1993). However, current accountingsystems `̀ are incapable of providing decision-making information (includingcost of quality information) necessary for strategic, as well as tactical,operational decisions'' (Gupta and Campbell, 1995, p. 45).

Ittner (1996) in his exploration of quality costs, has called for theoreticalwork to understand `̀ the interactions between prevention and appraisalactivities in a dynamic learning environment'', and `̀ the impact of specificactivities within the prevention and appraisal categories'' (pp. 126-7). He arguedthat a `̀ more micro-level examination of quality cost behavior may provide abetter understanding of the underlying economics of quality improvement,thereby allowing more informed decisions on the allocation of resources toquality-related activities'' (p. 127). Nandakumar et al. (1993) agree, stating that`̀ building cost models to evaluate the impact on costs of quality improvementprograms requires detailed knowledge of the impact of these programs onmanufacturing activity'' (p. 2).

In order to improve quality investment decisions, this paper proposes amulti-level model tracing the impact of investment in prevention and appraisalactivities on key performance results such as sales revenues, manufacturingand inventory costs, and quality failure costs. The next section of this papergrounds the proposed model in the cost of quality literature. Then, we overviewthe analytical models, along with several specific sub-models which apply thisframework using unique approaches to trace investments in education/training(i.e. prevention costs), and test equipment (i.e. appraisal costs). The paperconcludes with a summary of contributions and a discussion of future researchdirections.

Cost of quality literature review and model developmentThe following sub-sections review existing knowledge about the history of costof quality, drivers for and barriers to cost of quality system implementation,implementation issues, categories of quality costs, and the relationshipsbetween quality cost categories. The section ends with the development of anew model for understanding the impact of quality investments.

History of cost of qualityIn his seminal Quality Control Handbook, Juran (1951) introduces two key typesof quality: quality of design, which addresses the extent to which a product hasbeen well designed to meet customer expectations; and quality of conformance,

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which relates to the extent to which a product is produced within designspecifications to achieve customer satisfaction (Margavio et al., 1993;Tatikonda and Tatikonda, 1996; Tyson, 1990). The `̀ cost of quality'' (COQ)concept was designed specifically to address issues relating to quality ofconformance.

The first COQ system was designed by industrial engineering at GeneralElectric in the early 1950s (Albright and Roth, 1992; Bottorff, 1997; Juran, 1951).In the 1960s, the American Society for Quality Control (ASQC) formed a`̀ Quality Costs Committee'' (Bottorff, 1997), which defined quality costs as:

. . . a measure of costs specifically associated with the achievement or non-achievement ofproduct or service quality as defined by all product or service requirements established by thecompany and its contracts with customers. More specifically, quality costs are the total of thecosts incurred through (a) investing in the prevention of non-conformance to requirements; (b)appraising a product or service for conformance to requirements; and (c) failure to meetrequirements (Hagan, 1986, p. 3).

In 1963, the US Department of Defense issued a military specification requiringquality cost accounting from its vendors (Bottorff, 1997). More recently, theaccounting literature developed COQ models which address the needs ofmanufacturing management (Albright and Roth, 1992).

Drivers and barriers for COQ implementationDeming (1986) has always maintained that measuring COQ is a waste of timeand money due to numbers that are `̀ unknown and unknowable''. However,Juran (1951) and Crosby (1979) provide compelling arguments for measuring,understanding, and managing the costs of quality, and Taguchi (1993)contributes insights about the impact of hidden quality costs on businessperformance. The following firms have successfully implemented and utilizedCOQ systems that explicitly consider hidden quality costs: Xerox USMG inRochester, NY (Carr, 1992), Tennant Company (Carr and Tyson, 1992), GilroyFoods (Brinkman and Appelbaum, 1994), and Lovelace Health Systems(Waress et al., 1994). These programs served to capture top management'sattention for quality programs (Bottorff, 1997; Gray, 1995), challenge thenecessity for commonly-accepted operating expenses (Gray, 1995; Underhill,1995), measure the return on quality (ROI) investments (Gray, 1995), andjumpstart other quality improvement efforts (Bottorff, 1997). In addition, COQprograms can be used to identify, prioritize, evaluate, and select qualityinvestments (Bottorff, 1997; Gray, 1995), monitor improvements over time(Gray, 1995), and increase sales and ROI while reducing costs (Bottorff, 1997;Fine, 1986).

However, many firms run into significant roadblocks while attempting COQimplementation (Bottorff, 1997). For example, some organizations strive toquickly start-up COQ programs in the face of an inappropriate corporateculture, and without the critical support of cross-functional teams (Tatikondaand Tatikonda, 1996). Some companies lack the necessary resource allocations(e.g. time, training), finding it particularly difficult to locate individuals with

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sufficient accounting, quality management, and/or interpersonal skills tomanage COQ. Furthermore, managers will often try to `̀ budget'' COQ, ratherthan using it to continually improve. This tendency, coupled with the fact thatmost accounting systems cannot accommodate `̀ hidden'' externalnonconformance costs, typically results in a separate accounting system forCOQ (Bottorff, 1997; Carr, 1992). This can lead to other problems, since errors indata collection can distort the cost of quality and lead to inappropriatemanagement decisions (Tatikonda and Tatikonda, 1996). As a result, managersresist investments in quality failure prevention activities due to the difficulty ofestimating `̀ unknown and unknowable'' quality costs (such as the value of anunhappy customer), and downplay the importance of COQ figures because ofthe `̀ soft'' nature of quality failure estimates.

Implementing COQWhile best practice quality firms may not depend on COQ systems forcontinual improvement, companies at the beginning of their quality journeyare likely to find COQ implementation to be very beneficial (Tatikonda andTatikonda, 1996). Campenella (1990) proposes a COQ implementationstrategy which attacks quality failure costs directly, invests in appropriatefailure prevention activities to enable continuous improvement, reducesquality appraisal costs based on improvement results achieved, andcontinuously evaluates and redirects failure prevention activities topromote further improvement. Such an implementation strategy requiresmanagement commitment, organizational cooperation, systemdevelopment, reporting, and expansion resources, and a systemimprovement process (Corradi, 1994). Tyson (1990) found that theavailability of organizational resources for special accounting activities, aswell as regular personal interaction between the controller and qualitydepartment personnel, were organizational factors which also help tofacilitate the measurement of quality costs.

COQ implementation goes much more smoothly with clear communication.First, a general amnesty for initial quality cost measurements, along withassurance that these measurements will not be used to cut the workforce, willencourage honest reporting (Carr, 1992; Gray, 1995). Second, a long-term focuson improving business processes with the goal of 100 per cent customersatisfaction will ensure that COQ figures are not used for budgeting purposes,or to indicate short-term financial performance (Carr, 1992; Edmonds et al.,1989; Kiess-Moser, 1990). Third, use of readily available information utilizingdifferent measures from different organizational levels will enable COQimplementation teams to estimate hidden costs, rather than striving for exactquality related numbers (Carr, 1992; Edmonds et al., 1989; Waress et al., 1994).Finally, communication of COQ to management in terms of quality costs as apercentage of sales, or alternatively as compared to profits, will serve to sustaintheir interest in quality investment programs (Kiess-Moser, 1990).

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Types of quality costsQuality costs are typically categorized either as price of conformance or price ofnon-conformance (Albright and Roth, 1992; Crosby, 1979; Feigenbaum, 1961;Juran, 1951). The price of conformance includes both prevention and appraisalcosts, which are described variously as discretionary, voluntary (Edmonds etal., 1989), acceptable (Corradi, 1994), control-related (Feigenbaum, 1961),controllable (Harrington, 1987); hard and quantifiable (Tatikonda andTatikonda, 1996); and visible (Suver et al., 1992). Alternatively, the price ofnonconformance includes internal and external failure costs, and are thereforedescribed as non-discretionary, involuntary (Edmonds et al., 1989),unacceptable (Corradi, 1994), uncontrolled (Feigenbaum, 1961), failure costs(Morse, 1993) and oftentimes soft, qualitative (Tatikonda and Tatikonda, 1996),and hidden (Suver et al., 1992).

Prevention investments seek to eliminate the opportunity for quality defectsby supporting such activities as quality program management, training andeducation, quality promotion, process capability studies, failure mode andeffect analysis, quality function deployment, design of experiments, design formanufacturing, market research, internal and external customer surveys,quality planning, supplier certification programs, preventive maintenance, andcross-functional design teams. As mentioned earlier, prevention activities oftenreceive the least amount of investment in US manufacturing organizations,even though findings indicate that:

. . . [f]or every eight cents spent on prevention (corrective action), the corporation saved onedollar in internal failure costs (Diallo et al., 1995, p. 25).

Quality experts agree that the largest percentage of quality investment dollarsshould go toward prevention activities, since early detection of potentialproblems translates into major cost savings and ultimately greater corporateprofits (Albright and Roth, 1992). Over time, even prevention costs can bereduced to relatively low levels with the help of the learning curve effect(Brinkman and Appelbaum, 1994; Fine, 1986).

Appraisal investments become necessary whenever there exists a chance forpoor quality. These defect or problem `̀ detection'' activities include internalaudits, review of completed work, materials or inventory inspection, productinspection and test, materials/equipment consumed during inspection/test, andmeasurement equipment calibration (Gray, 1995). Ideally, appraisal effortswould enjoy the next largest portion of quality investments, after preventionactivities; however, the ultimate goal would be to drive appraisal costs closetoward zero (Brinkman and Appelbaum, 1994).

Internal failure costs are one of two `̀ price of nonconformance'', or `̀ failurecost'' categories. Internal failure costs occur when defective goods are identifiedwhile still in the factory before shipment to customers (Morse, 1993). Thiscategory includes the costs of such unwanted events as scrap, rework, retest,equipment downtime, yield losses, and final disposition. Firms typically spenda large portion of their total quality investment dollars on internal failure costs,

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and thereby often focus initial improvement efforts on these costs to improvemanufacturing efficiencies with the ultimate goal of driving these costs to zero(Brinkman and Appelbaum, 1994; Edmonds et al., 1989). However, internalfailure costs are often indirect and hidden, thus necessitating estimation forplanning and improvement purposes (Albright and Roth, 1992; Carr andTyson, 1992). For example, Schmahl et al. (1997) found factory supportpersonnel and inventory levels to be a significant source of hidden internalfailure costs. Surprisingly, factory support personnel, such as shop supervisors,manufacturing engineers, and production control, were found to spend15-18 per cent of their daily efforts addressing internal failures. Inadequateadministrative controls can also result in significant hidden internal failurecosts (Collins, 1995).

Finally, external failure costs develop when poor quality product ships tocustomers. These costs cover activities such as complaint adjustment, receiptand replacement of defective product, warranty charges, and allowances orconcessions made to customers for their trouble. Unfortunately, many externalfailure costs are unknown and unknowable, so that even with eventual perfectproduct quality, these intangible costs can linger due to the high multipliereffect of customer dissatisfaction (Albright and Roth, 1992; Carr and Tyson,1992; Deming, 1986; Diallo et al., 1995; Feigenbaum, 1961). Thus, externalfailure costs point to the need for programs involving product design and fieldservice, and are typically the initial focus for firms operating in highlycompetitive markets (Edmonds et al., 1989). External failure costs are deemedunacceptable at any level (Brinkman and Appelbaum, 1994).

Although prevention, appraisal, internal failure, and external failure costsrepresent the typical cadre of quality costs, others have occasionally beenproposed in the literature. These other costs include industry-specific qualitycosts (Heldt, 1994), costs of exceeding requirements (Collins, 1995), and lostopportunity costs (Collins, 1995). However, because these proposed costs ofquality, upon closer inspection, can typically be incorporated into hiddeninternal and/or external failure costs, they will not be considered in any furtherdetail for the purposes of this paper.

Relationships between quality cost categoriesA central debate in the cost of quality literature revolves around the extent towhich firms should strive for quality improvement. Deming's (1986)philosophy demands a continual drive toward process improvement,specifically focused on targeting the mean and reducing the variation of thedistribution of process output. This ever-present push for continuous qualityimprovement stems from his strong convictions about the importance of coststhat are unknown and unknowable, such as the cost of an unhappy customer.Because of these `̀ hidden'' costs, Deming maintained that measuring the costsof quality was an unnecessary waste of time that could be better spent tacklingimprovement activities.

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At the other end of the spectrum, Juran (1951) proposed the existence of anoptimal level of quality, based on the relationship between quality costs, andtypically defined at less than 100 per cent product conformance tospecifications. Juran's `̀ traditional'' COQ model (Albright and Roth, 1992)assumes a trade-off relationship between prevention/appraisal costs and failurecosts, so that the optimal level of quality exists where the cost curves intersectto produce a minimum total cost of quality. The general premise behind thistheory is that 100 per cent conformance costs too much (Edmonds et al., 1989).

Unfortunately, Juran's failure to account for the effects of technologicalimprovements and competitive pressures over time leads to a model whichcontradicts calls for continuous quality improvement (Carr and Tyson, 1992).While Juran's model assumes that prevention and appraisal costs becomedramatically higher as a firm approaches 100 per cent quality conformance dueto the law of diminishing returns, others have found that these costs increase ata stable rate, remain relatively fixed, or even decline slightly in amanufacturing environment with a strong learning curve, automatedinspection systems, and/or where empowered workers inspect their own work(Carr and Tyson, 1992; Diallo et al., 1995; Fine, 1986; Ittner, 1996).

Additionally, Juran's tendency to combine appraisal and prevention costs inhis traditional model has been questioned, since evidence indicates that thesecost categories maintain different behaviors and implications for cost control,and therefore should be considered separately. For example, when preventioncosts increase, defects decline causing failure costs to decrease and reducingthe need for investments in appraisal activities (Gupta and Campbell, 1995;Margavio et al., 1993). Also, unlike with prevention costs, when appraisalinvestments increase, external failures can decline while internal failurestypically rise (Gupta and Campbell, 1995).

Juran's traditional model also fails to take the indirect and intangiblebenefits of prevention activities into account, or to recognize the multipliereffects of customer ill-will as product output falls short of 100 per centconformance. For example, Nandakumar et al. (1993) argue that congestion anddisruption are not typically considered as quality costs, and hypothesize thatthis oversight underestimates and distorts quality costs leading toinappropriate quality investments. They evaluate the optimal trade-offsbetween COQ, specifically focusing on the impact of poor quality onthroughput times and the ability to meet delivery schedules, and find thatdelivery performance improves if quality improvements are geared towardproducts with large processing times, even when direct cost savings from theseactivities are low. Alternative models modify Juran's traditional prevention andappraisal curves to show that total quality costs can decrease over time toreach a minimum at the point of zero quality losses (Carr and Tyson, 1992;Ittner, 1996).

The remaining quality heavyweights, Crosby and Taguchi, providecontinuous improvement philosophies which fall somewhere in the middle ofthe Deming-Juran spectrum (Ittner, 1996). Like Juran, Crosby (1979) also

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advocates the measurement of quality costs, but argues that because of themultiplier effects of hidden internal failure costs, a firm should strive for `̀ zerodefects'' via prevention programs so that quality will ultimately be free. Hiswork is supported by Fine (1986), who shows that the learning curve forprevention programs ensures that perfect conformance can, in fact, be theoptimal quality level.

However, Crosby's limited definition of `̀ zero defects'' as 100 per cent productconformance to specifications opens the way for Taguchi's (Taguchi, 1993;Taguchi and Clausing, 1990; Taguchi and Wu, 1980) contribution, whichemphasizes the consideration of losses incurred as a result of any variationfrom the target value of a product characteristic. Taguchi's quality lossfunction provides a method for quantifying all aspects of external failure costs,including hidden costs (Albright and Roth, 1992; Kim and Liao, 1994; Margavioet al., 1995). Taguchi's model argues:

. . . if management decides not to incur the voluntary expenses of reducing the variation, itinvoluntarily will incur several times that amount in the form of warranty costs, lostcontribution because of customer ill will, and so forth (Diallo et al., 1995, p. 23).

Since Taguchi's pioneering work was introduced, other models have beenproposed for estimating the hidden costs of internal and external failure.Various recommendations include: utilizing some multiplier to predict hiddencosts based on tangible costs (Albright and Roth, 1992; Carr and Tyson, 1992;Heldt, 1994; Tatikonda and Tatikonda, 1996); market research (Albright andRoth, 1992); activity-based costing (Gupta and Campbell, 1995); root causeanalysis (Morse, 1993); value chain analysis; and measuring the opportunitycosts of failure to make quality investments instead (Margavio et al., 1993).However, none of these proposed techniques have had the significant impactthat Taguchi's quality loss function has had on improving the measurement ofcosts of quality.

Toward a new model of quality investmentsWe propose a multi-level model of quality investments which clearly addressesthe fundamental differences and relationships between discretionaryprevention and appraisal program investments and resultant internal andexternal failure costs. This model traces the impact of quality investments inprevention and appraisal programs through a variety of investment activities,improvement sources, and operating results, culminating in higher levels ofcustomer and stakeholder satisfaction (Figure 1).

In this model, level one categorizes the nature of voluntary qualityinvestments either in terms of prevention or appraisal programs. Although it isrelatively common knowledge that prevention and appraisal programinvestments in the early stages of manufacturing lead to internal and externalfailure reductions (Edmonds et al., 1989), few models have traced the path ofthis relationship. Level two begins to address this `̀ black box'' relationship bylisting some of the various investment opportunities which correspond to

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Figure 1.Quality investmentchart

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prevention and/or appraisal programs (Collins, 1995; Corradi, 1994; Edmonds etal., 1989; Gray, 1995; Suver et al., 1992).

Focusing initially on investments in prevention programs, level three thenmaps the influence of these investment activities on reducing the varianceand/or targeting the mean for product characteristics, or alternativelyimproving manufacturing throughput or product development times (Deming,1986; Nandakumar et al., 1993). Level four addresses the impact of theseprocess improvements on initial operating results such as overall productreliability as well as the proportion of rejects and, by extension, lot sizes (Guptaand Campbell, 1995; Margavio et al., 1993; Nandakumar et al., 1993).

Level five shows intermediate operating improvements, indicating thatlower rejects lead to reduced processing, rework, scrap, and ± via reduced lotsizes ± to reduced setup, finished goods inventories, work-in-process, and leadtimes. Meanwhile, product reliability improvements lead to a higher marketshares, warranties, repairs/services, liability, etc. Improvements inmanufacturing throughput and product development times lead to betteroverall lead times (Schmahl et al., 1997).

Level six then traces the impact of intermediary operating results on costs ofmanufacturing, inventories, internal failures, and external failures, as well asrevenue enhancements (Tatikonda and Tatikonda, 1996). External failure costsare directly related to customer satisfaction and revenue enhancements aredirectly related to stakeholder satisfaction, while manufacturing, inventory,internal failure, and delay/tardiness costs are related to both stakeholder andcustomer satisfaction (Kiess-Moser, 1990).

Note that prevention costs influence, and are influenced by, specificinvestments in appraisal activities (e.g. inspection, test equipment, inventoryevaluation, etc.). Investments in prevention programs, by reducing failure rates,can lead to lower appraisal costs as inspection becomes less necessary (Guptaand Campbell, 1995; Margavio et al., 1993). Investments in appraisal programscan reduce external failure costs, but sometimes at the expense of increasedinternal failures. So many resources can be diverted to addressing appraisaland internal failure requirements that prevention programs suffer (Gupta andCampbell, 1995). Alternatively, investment in appraisal programs can lead toearly detection of defects, and therefore lower internal failure costs. Lowerinternal failure costs mean improved market share, as well as reducedwarranty costs, repairs/services, and liability costs (Gupta and Campbell, 1995;Margavio et al., 1993; Nandakumar et al., 1993).

Analytical modelsAn aggregate investment model should consider all possible opportunities ofinvestment listed at level two and link them to final results listed at level sixthrough the sources of improvement, initial operating results and intermediateresults at levels three, four and five respectively. Such a model will enable theusers to predict the amounts of cost reduction and revenue enhancement andoptimally select the projects for investment. In this paper, we will present the

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framework for some potential models which cover a few sources of investment.In particular, these models study the effect of improvements in the variances ofthe quality characteristics, the deviations of their means from their targetvalues and the cycle times. A model which studies the effect of investment intest equipment is also included. These models are described in the followingsections.

Effect of variance and deviation of mean from the target valueNumerous case studies have shown that the products whose qualitycharacteristics with smaller variance and smaller deviation between thetarget value and the mean will perform longer and better. This will result ingreater customer satisfaction and increased market-share for theseproducts. Taguchi tried to capture this advantage using the loss function hedeveloped. The expected value of the loss function is the economic loss tosociety due to failures after the product is shipped and given by:

Expected loss � k��2 � ��ÿ T�2� �1�where k is a constant, �2 is the variance, � is the mean and T is the targetvalue of the quality characteristic. Taguchi's attempt to convert thevariance and the deviation of a particular product's quality characteristicfrom its target value into dollars, through the use of k, met with skepticismfrom the practitioners. This is because his definition of k is consideredsimplistic. We propose a new approach to transform variance and meansetting to financial loss. This will be accomplished by first linking varianceand process mean setting to reliability.

Traditional reliability models predict lifetime without regard to individualperformance. Typically, a sample of n items is tested and the same estimate ofreliability is used for all items in the sample. It has been shown, however, thatall of these items will not have the same time to failure. Specifically, it has beendemonstrated that individual components or products with qualitycharacteristics closer to the target value perform longer. Traditional models failto capture the important relationship between the proximity of key qualitycharacteristics to the target value and time to failure. In this research, a newfailure time distribution will be developed that addresses both the individualperformance of an item and the impact of proximity to the target of key qualitycharacteristics on reliability. To develop this failure time distribution, thefollowing concepts are used:

. individual components with different values of the same qualitycharacteristic have different failure time distributions; and

. one or more parameters of each failure time distribution should capturethe impact of key quality characteristics on reliability.

The Weibull failure-time distribution is perhaps the most widely used lifetimedistribution (Lawless, 1982). A key advantage of this distribution is that it is

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highly adaptable. That is, a variety of shapes can be obtained to fitexperimental data by adjusting the scale and shape parameters. TraditionalWeibull distribution is a function of one variable, time. The associatedreliability function commonly used is:

R�t� � exp�ÿ�t����; t > 0; �2�where

� � 1

�

� ���3�

In (2) and (3), � is the shape parameter and � is the scale parameter.Failure time distributions used in both accelerated life testing and lifetime

regression models demonstrate differences in degradation of performance orlifetime reflected in one or more parameters. In most cases, the scale parameterrather than the shape parameter was used to capture the effects of co-variates onreliability. The Weibull proportional-hazards regression model (Kalbfleisch andPrentice, 1980) provides an appropriate framework for the development of the newreliability model proposed in this paper. This is because the proportional-hazardsmodels incorporate significant factors (or variables) which affect lifetime into thefailure time distribution. This is accomplished by defining a conditionaldistribution where the time to failure, t, may be affected by X, a vector of regressorvariables. The scale parameter of the traditional Weibull is modified to capture theimpact of these variables where equation (4) is replaced by:

� � �X;B� � exp�BTX� �4�where B is a vector of regression coefficients.

This class of parameter regression models assumes that the hazard functionor failure rate is a function of the regressor variables. The modified hazard,conditional probability density and reliability functions are respectively:

'�t=X� � �t�ÿ1eXB t > 0 �5�

f�t=X� � �t�ÿ1eXB exp�ÿt�eXB� t > 0 �6�

R�t=X� � exp�ÿt�eXB� t > 0 �7�where � > 0 and is the shape parameter. This is a preliminary reliability modelwhich has been further modified to capture the effect of variances and thedeviations of the means from their respective target values.

Because of the impact of mean and process variance on reliability, it isimportant to incorporate both aspects into the scale parameter of the newreliability model. Since process capability indices attempt to assess themagnitude of the process variance as it relates to product specification, they

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can be used conveniently to develop the new hazard model. Two indices will beconsidered, the Cpk and the Cpm. Let X represent the random variable for thequality characteristic, which is assumed to be a nominal-the-best type qualitycharacteristic. Its Cpk is:

Cpk � MinUSLÿ �

3�;�ÿ LSL

3�

� ��8�

where USL and LSL are the upper and lower specification limits respectively, �is the standard deviation, and � is the process mean. The Cpm of X is defined as:

Cpm � �USLÿ LSL�6�0

�9�

where:

�0 � E

��������������������X ÿ T�2

q�10�

In (10), T is the target value of X. These two indices will have to be compared asto their suitability for use in the reliability function. The smaller-the-better andlarger-the-better type quality characteristics can be handled in a similarmanner.

In developing the reliability and probability functions, the hazard functionmust first be well defined. Specifically, the hazard function must be non-negative. Since only the scale parameter is modified, all the items manufacturedon a machine will share the same shape parameter. The shape parameterdictates the behavior of the hazard function and it must have a monotonehazard function (increasing if the shape parameter is greater than one,decreasing if less than one, and constant if equal to one). This characteristic isimportant because it allows the hazard function to represent a variety of failurerates for different types of products and components. Finally, the failure ratemust increase as the value of the quality characteristic deviates from the targetvalue.

The new reliability functions of the components can then be used to predictthe reliability of the product, for different configurations of the components.From the reliability of the product, the corresponding cumulative failure timedistribution of the product, F(u), and the failure time distribution of the product,f(u), can be derived. The seller's lifetime costs are a function of the expectednumber of replacements or repairs over a time period of product usage. In thecase of a non-repairable product, the item that fails must be continuouslyreplaced by new ones. As a result, the failures over time occur according to anordinary renewal process. For a repairable product, items that fail arecontinuously repaired. These failures also occur according to an ordinaryrenewal process because the products are repaired to `̀ as good as new''condition. This expected number of failures or `̀ renewals'' during the period[0,e], M(e), is determined by solving the renewal integration equation:

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M�e� � F�e� �Ze

0

M�eÿ u�f�u�du �11�

where F(e) is the cumulative failure distribution function of the product, f(u) isthe failure time distribution of the product and u < e is the time of the firstfailure. Once M(e) is evaluated, the expected life cycle costs of the seller can beexpressed using the models from Blischke and Murthy (1994) for non-repairable and repairable items. For non-repairable items, the expected costsfor the manufacturer over the warranty period is:

ENRCm � Cm�1�M�W�� �12�where Cm is the cost to manufacture the product and M(W) is the number ofreplacements within the warranty period. For repairable items, it is:

ERCm � Cm � Cr M�W� �13�where M(W) is the expected number of repairs in the warranty interval and Cr

is the average cost of repairing the product, including parts, labor, shippingand administrative costs.

Lead timeDue to increased global competitive pressure and compression of productlife cycles, many companies are systematically trying to shorten the totallead time of their products (Dumaine, 1991). The total lead time is the sum ofmanufacturing throughput time and product development time.Manufacturing throughput time is defined as the time manufacturing needsbetween accepting a production order and shipping it to the customer. Thebenefits of reduced manufacturing throughput time include: reduced costsassociated with tardiness (which results in customer inconvenience and lostconfidence), reduced WIP inventory and the associated carrying costs,better resource utilization, manufacturing flexibility, greater ability to offercompetitive delivery dates, and the increased probability of meeting thecommitted delivery dates. In addition, if the company is able to offer aquality product earlier than their primary competitor, and deliver ascommitted, an increase in market share may result. The relationshipbetween quality improvement and lead time reduction is somewhatintuitive. That is, when defect levels decrease, less defective items are builtin each lot, hence lot sizes decrease. Finally, the reduced lot size lessens themanufacturing throughput time of the product. This is illustrated in thefollowing relation:

CT � Max fTig � Ta �14�where CT is the manufacturing throughput time of the product, Ti is themanufacturing throughput time of component i of the product and Ta is the

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assembly time of the product. Delay and tardiness costs can then bedetermined based on the manufacturing cycle time and the committeddelivery date.

If models are developed to predict the effect of investment in theopportunities lists at level two on variances and or cycle times, then using thesuggested models in the preceding two sections, the expected cost reduction orrevenue enhancement can be predicted.

Effect of investment in test equipmentAll pieces of test equipment have inherent measurement variance, which whencombined with the measurement variance caused by the operators, contributesto measurement error. Let W and Y denote the true and measured values of thequality characteristic respectively. Let the total measurement error associatedwith the measurement system, consisting of the measuring equipment and theoperator, be V. Also, let W and V be independent. The true value W is assumedto be normally distributed with a mean � and variance �2. The measurementerror, V, is assumed to be normally distributed with a mean Bm which is themeasurement bias and variance �m

2. As the measured value of the qualitycharacteristic Y is Y = W + V, it is normally distributed with a mean � + Bm

and variance �2 + m2. Let USL and LSL be the upper specification limit and

lower specification limit respectively. If the measured value Y is within LSLand USL, the product will be accepted. Otherwise it will be rejected.

The operator decides whether to accept or reject an item by comparing themeasured value, Y, with the specification limits. As Y is not equal to the truevalue, W, he/she will reject some conforming parts (with true value within thespecification limits) and accept some nonconforming parts (with true valueoutside the specification limits). Let the probability of rejecting a conformingunit be PRG and the probability of accepting a nonconforming unit be PAB.These probabilities of wrong decisions result in costs which can be divided intotwo groups. The first group includes appraisal cost, manufacturing cost, andcost of false rejection. The second group consists of the warranty cost causedby increased external failure rates of the nonconforming products suppliedwrongly to the customers, which is the external failure cost. There is also profitdecrease due to the decline in market share, caused by low levels of customersatisfaction. Investment in better test equipment with low variance ofmeasurement error decreases the probabilities of wrong decisions and hencedecreases the resulting costs and increases profit. The link between theinvestment made in test equipment and the external failure cost is establishednext.

Let �m and 1ÿ�m denote the proportions of conforming and nonconformingcomponents respectively, among the components supplied to the customer.These proportions can be computed as follows:

�m � PAG

PAG � PAB�15�

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and

1ÿ �m � PAB

PAG � PAB: �16�

In (15) and (16), PAB is the probability of accepting nonconforming items whichcan be computed as

PAB �ZLSL

ÿ1P�LSL� < Y < USL�f�w� dw�

Z1USL

P�LSL < Y < USL� f�w� dw

�17�

and PAG is the probability of accepting good parts which is:

PAG �ZUSL

LSL

P�LSL < Y < USL� f�w� dw: �18�

In (17) and (18), f(w) is the probability density function of W. The expectednumber of repairs among the conforming items, within the warranty period d isR d

0 R1(t) dt, where R1(t) is the failure rate of a conforming item. Similarly, theexpected number of repairs among the nonconforming items within thewarranty period d is

R d

0 R2(t) dt, where R2(t) is the failure rate of anonconforming item. It is reasonable to assume that R1(t) < R2(t). Now, theexpected external failure cost is:

EFC � CR��m

Z d

0

R1�t�dt� �1ÿ �m�Z d

0

R2�t�dt�; �19�

where CR is the replacement cost per item. The probabilities in (17) and (18)depend on the variance of the measurement error, which in turn is a function ofthe investment made in the test equipment. Thus the investment made in testequipment can be linked to the external failure cost. In a similar manner, theinvestment can be linked to the costs in the first group, through the appropriateprobabilities.

Summary and future directionsIn this paper, a framework for building models to justify investments in CQIprojects was presented. Also, some basic models were given which can beexpanded to more detailed models. An aggregate model which combines all theindividual models developed is necessary for determining the optimumallocation of funds among the competing projects. As the effects of different

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investment types on any particular source of improvement may not be additive,adjustments will have to be made while estimating the total net effect on anysource of improvement. Dynamic programming (DP) algorithms can be used tosolve the resource allocation model.

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