پیشنهاد برای تابع از دست دادن کیفیت اقتصادی

Quality loss functions have found widespread application in production engineering and today are an indispensable part of quality management. However, they share an obstacle with most other quality concepts concerning their limited communicability to top management. In the allocation of financial resources, a company's executive board is commonly interested in the profit implications of competing projects, but existing concepts fail to capture the profit impact of changing quality levels, thus putting quality initiatives at a disadvantage compared with more “classical” investment opportunities. To address this problem, in this paper, we propose a new type of function we call “economic quality loss function.” The suggested function is composed of measures for the single profit parameters and indicates how sensitive a company's profit function is to defect levels. By providing a simple comprehensive measure, it helps the practitioner evaluating quality initiatives and communicating their desirability to top management.

Despite the often-changing tides and fashions of managerial concepts, the topic of quality improvement has endured and re-surfaced to prominence several times, lately in the concept of Six Sigma. This permanence might be most easily explained by quality's paramount importance for business success (Russell and Taylor, 1995; Bisgaard and Freiesleben, 2000). Whereas the discussion of quality has in the past been largely dominated by a focus on practical methods or managerial concepts, Six Sigma incorporates a strong numerical and analytical focus (Hoerl, 1998; Hahn et al., 1999; Harry and Schroeder, 2000). This in effect represents a partial return to early contributors such as Shewhart (1931) and Tippett (1936), who perceived quality improvement as equivalent to a scientific endeavor based on hard data and analytical reasoning. Six Sigma projects have been found to be important profit drivers in a variety of industries (Caulcutt, 2001), highlighting the economic dimension of quality improvement. From a microeconomic perspective, a profound discussion of production quality started about 20 years ago with the work of Porteus (1986). Previous “economic” concepts of quality, such as the widely cited cost of quality (COQ) models, have not only attracted substantial criticism (Plunkett and Dale, 1988), but also present an incomplete perspective on quality's economic effects (Freiesleben, 2004). Porteus's model captured the relationship between quality and production economics by examining the effect of defect rates on optimal lot sizes and one-shot preventive investments. This model was later refined by Fine and Porteus (1989) to include the effect of small but continuous preventive investments. The research into the economic effects of quality has since been greatly advanced and firmly established in the production economics and operation research literatures. However, most of these contributions concern specific aspects of production and do not create a single comprehensive economic model of quality. In the same year of Porteus's original contribution, Taguchi (1986) highlighted the economic consequences of deviating from production target values by conceptualizing the “quality loss function” (QLF). Taguchi was the first to apply the loss function concept, which by then found widespread appreciation in economics, statistics and decision theory, to the quality management field. Due to his seminal work and subsequent extensions (Taguchi et al., 1989; Taguchi and Clausing, 1990), loss functions today are an indispensable part of quality engineering. Although profoundly influential in process design and production management, QLFs share an obstacle with most other quality improvement concepts concerning their limited communicability to top management. In the allocation of resources a company's executive board is commonly interested in the profit implications of competing projects, and quality initiatives often have a disadvantage when compared with “classical” investment opportunities such as new product development or marketing campaigns. This disadvantage might be connected to a lack of understanding of quality's economic effects and its rare perception as an investment but also to relatively scarce and inconclusive quantitative data on its profit effects (Wruck and Jensen, 1994; Powell, 1995; Terziovski and Samson, 2001; Dale et al, 2001). Most importantly, the existing COQ and QLF models cannot provide management with a measure of how the quality of a certain production unit affects the company's profitability. In this paper, we want to propose a new type of function we call “economic quality loss function” (EQLF) to capture the profit impact of changing quality levels. Our aim is to find a simple and communicable yet comprehensive model of quality profitability, which is adjustable to different production scenarios such as differences in the market reaction to poor quality or the absolute quality distance to competitors. Therefore, the suggested EQLF is composed of measures for the four profit parameters price, variable costs, sales volume and fixed costs and provides an indication of how sensitive a company's profit function is to defect levels. It adopts the loss perspective of QLFs and uses deviations from quality perfection to demonstrate the underlying economic logic of quality improvement. By providing a simple comprehensive measure, it helps quality practitioners in communicating the desirability of quality initiatives to top management. The remainder of this paper is organized as follows. In Section 2, we review the main types of QLFs and specifically describe Taguchi's contribution. In Section 3, we evaluate QLFs and identify their limitations as a communication tool. In Section 4, we develop a model for the proposed EQLF. Properties of a uniform EQLF are described in Section 5. Section 6 provides an example from a production facility to illustrate the functional capability of the model. Discussion and concluding remarks are presented in Section 7.

The EQLF is an estimator for quality's profit effects and can be used for different problems and settings. All included parameters are observable for a producer and hence there is little room for misinterpretations or misevaluations, given the parameter settings are based on sound analysis. Its main value as an estimator is its suitability as a communication tool to top management, producing a single graph depicting the measure top management is most interested in: profit reduction or profit increase in dependency of the quality level. By calculating the delta in profits between old and new defect rate, as done in the DC drive example, the profit implications of discrete quality improvements can be shown. The model's focus on hard numbers for enhancing decision processes makes it similar to Six Sigma techniques. Nonetheless, it incorporates much of Taguchi's holistic thinking by including all measurable costs into the function and showing the profit effect of deviating from quality perfection. In fact, the resemblance between the QLF and the EQLF is graphically visible. However, the EQLF is clearer and more comprehensive in its composition, thereby addressing our third criticism of the QLF. The second and fourth criticisms, the balancing of the losses and gains and the potentially biased losses, are evaded by the EQLF since it is purely a producer's profit function. The customer's losses are not directly included, but they are indirectly accounted for by the customer's reaction to quality differences. This is, as pointed out, firmly based on the assumption of a competitive market where customers have switching options. In a globalized world with abundant offerings in every imaginable product category, it seems more realistic to assume that the customer will seldom incur losses, and if, then only once. His reaction will most likely be a switch of producers should he get disappointed, thereby limiting the extent of Taguchi's proposed customer loss. The loss will be dominantly on the side of the producer, which is why a producer-centered EQLF seems adequate. The first criticism concerning the estimation of the cost coefficients is only partially resolved by the EQLF. One could argue that both functions are only rough estimators of quality's economic implications, and that the parameters of the EQLF, especially in its uniformity version, are also only approximations. Although this is true, the EQLF offers a higher degree of preciseness since it consists of clear cost and revenue measures that jointly establish the profit metric. Finally, it overcomes the fifth criticism by offering a comprehensive and communicable model of quality profitability, which can be used to assess the economic impact of quality in a production unit, and hence gives management a broader picture than a multi-dimensional and rather technical QLF. There are certain limitations of this approach that have to be mentioned. The presented EQLF is a static estimator and neglects the time dimension and connected economic effects, especially regarding discount factors. Sales effects, for instance, might in reality be delayed. Both EQLF and QLF are static models with the purpose of enhancing decision making regarding a given improvement aspect with low uncertainty. This might however be sufficient when no disruptive changes to the production process or market situation are to be expected. By limiting itself to the measurable effects of quality, the EQLF omits parts of Taguchi's original concept, such as the “loss to society.” Such a loss could be included, however, we do not think this enhances the significance or applicability of the EQLF. As has been pointed out, this type of loss is hard to quantify and has its main merits as a philosophical point. An inclusion might even be counterproductive for its purpose as a communication tool since it blurs preciseness of the function. An EQLF can furthermore not be taken as a substitute for a thorough problem investigation and calculation since it is built on simplifying assumptions to retain its communicability. However, as an estimator, it can provide a company with an initial assessment of the expected economic effects of a quality improvement project. Similar to project calculations commonly used for marketing initiatives or new product developments, the expected profit enhancement must be contrasted with the costs of a quality improvement project, thus giving the company an assessment whether the project will likely pay off. Quality is an optimality problem concerning the right investment amount, the latter being measured by its depreciation rates since the improvement normally benefits the company for multiple periods. First estimating quality's economic effects provides companies with a clearer picture of the range of potentially profitable investments, thereby overcoming initial reservations or misperceptions about quality initiatives. A cost dimension we neglected in constructing the EQLF is the costs of maintaining a high-quality level. Although we assumed the producer inspects his output, this is not congruent with quality maintenance since inspection has no effect on the internal but only on the external quality level. Due to entropy and wear, quality problems incessantly evolve and trigger improvement investments if no maintenance system is in place. Effective quality maintenance is best done by automated process monitoring and fine-tuning of the process. Automated monitoring systems, observe whether quality-relevant process parameters stay within their assigned control limits, thus indicating the emergence of a new problem by the occurrence of abnormal data (Box and Luceno, 1997). Such a system comprises variable costs for running sensor networks and the depreciation rates for the network investment. Its cost impact can therefore be regarded as small and readily justified when we contrast it by the profit loss incurred from letting quality degrade. Hence, its inclusion into the model would slightly reduce the maximum absolute profit, but would not alter the shapes of the curves. The EQLF unambiguously shows that deviations from quality perfection cause losses, and that these losses can be substantial even for medium complex products (i.e., small values for n) at low defect rates. It provides an economic rationale for Six Sigma projects, i.e. striving for a defect rate smaller than 3.4 parts per million in every production stage, since greater defect rates directly lead to the depicted loss of profitability. As numerous examples from industry show, poor quality can indeed threaten a company's competitive standing, if not its survival. By the same token, it shows that there exists an economic incentive for companies to remain or become high-quality producers. A thorough problem investigation and a correct estimation of the improvement's economic benefits and costs are indispensable ingredients for reaching a substantiated decision. Using the EQLF approach to estimate the loss incurred by poor quality and thereby demonstrating the potential benefits of quality improvement to top management might be a good way to start.