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Dec 1993

Quality improvement technology using the Taguchi method. (CPA in Industry)

by Fink, Ross L.

    Abstract- The Taguchi method enables accountants to measure the unobservable external failure costs of customer dissatisfaction. Thus, the Taguchi approximation provides an opportunity for the assessment of quality-improvement projects in a more rigorous fashion because the previously unquantifiable customer dissatisfaction aspect can be accounted for. After the external failure cost of customer dissatisfaction has been measured, it can now be weighed in with internal failure, prevention and appraisal costs, thereby, completing the quality-cost equation of the company. Because every aspect of quality-cost management has been covered, managers can now confidently make the necessary changes for their quality improvement efforts. An example of how the Taguchi method can be applied is provided.

For this reason, the effect of quality improvements on a company's bottom line is difficult to measure and assess. Although accountants have made great strides in identifying and measuring the costs of making and monitoring quality improvements, they have been less successful in identifying the benefits associated with such improvements. This is largely because the major benefit, increased customer satisfaction, is not easily identifiable or measurable.

In the long term, this benefit may translate into increased sales revenue. In today's competitive environment, however, a more short-term concern may be to preserve eroding sales. This suggests a more appropriate measure of the benefit of quality improvement is the opportunity cost (i.e., customer dissatisfaction or lost sales) of not making such improvements. Although measuring this opportunity cost is still difficult, a technique for estimating the opportunity cost was developed in 1984 by Japanese engineer Genichi Taguchi.

Types of Quality Costs

Concerns about quality improvement can be broken down into two components: quality of design and quality of conformance. Quality of design relates to the functioning and physical characteristics of the product to satisfy customer expectations. Quality of design is largely viewed as the responsibility of inventors, engineers, architects, and draftsmen. Once these groups have achieved quality of design, the product moves into the manufacturing process.

Quality of conformance becomes important in the manufacturing process where design specifications are translated into manufacturing specifications and into a final product. Quality of conformance relates to how closely this final product achieves its design specifications and, ultimately, customer satisfaction. It is in this assessment of quality of conformance that managers and accountants have focused their efforts. Hence, the costs associated with this quality of conformance are what accountants refer to as quality costs.

For purposes of better controlling these quality costs, managers and accountants have broken them down into four categories: appraisal costs, prevention costs, internal failure costs, and external failure costs. Internal and external failure costs relate to when the failure is detected, inside the company or by the customer. Internal failure costs include such expenses as material and products scrapped, products reworked, reinspection costs and work interruptions. External failure costs include product warranties, sales returns and allowances, and lost sales. The possibility of incurring internal and external failure costs prompts companies to incur appraisal and prevention costs.

Appraisal costs are referred to as monitoring costs or inspection costs. Typical examples of these costs include the expenses of maintaining the quality control department; evaluation of methods, materials, and processes; and product samples used in testing. To determine when, how often, and how much of the product needs to be inspected, statistical sampling techniques and quality control charts are used. Using these techniques and minimizing appraisal costs were the primary quality control procedures used by accountants until the 1970s. Then, it became apparent that appraisal costs do reduce the number of defective products before they get to the consumer (external failure), but do not reduce the number of internal failures. Thus, the emphasis on appraisal costs focuses on discovery of defects rather than prevention of defects. This realization marked the end of the appraisal cost era and the beginning of the prevention cost era.

An Ounce of Prevention

The prevention cost era began in many other developed nations before the U.S. These nations discovered that emphasizing prevention of defects reduces the probability of producing a defective product. This reduces both internal and external failures, and also reduces appraisal costs. Thus companies began to incur costs for preventive maintenance of equipment, improving manufacturing specifications and procedures, and training personnel. As the popularity of prevention procedures and related costs spread, the cost control emphasis shifted to controlling total quality costs (i.e., the combined internal and external failure costs, appraisal costs, and prevention costs).

Control of total quality costs requires that accountants understand the relationship between internal and external failure costs, and prevention and appraisal costs. These relationships are frequently illustrated as in Figure 1. In this graph, prevention and appraisal costs are added to internal failure costs to obtain total quality costs. Then, the goal of cost management is to achieve the lowest point in the total quality cost curve. This recognizes the trade off between appraisal and prevention costs, and internal and external failure costs. Conceptually, as appraisal and prevention costs increase (the left side of the graph), internal and external failure costs decrease, up to a point. Once this point is reached, additional appraisal and prevention costs do not lower total quality costs (the right side of the graph). In practice, however, it is very difficult to identify this point of lowest total quality cost. The difficulty stems from a lack of proper cost identification and measurement difficulties.

In the past, identification of quality costs was difficult because accounting systems spread the costs out over many accounts (materials, labor, and overhead and divisional accounts). As accountants become aware of these difficulties, accounting systems are redesigned. This is part of the impetus for activity-based costing. However, even if all quality costs are properly identified, a measurement problem still exists.

External Failure Costs, The Measurement Problem

The most significant measurement problem lies in the area of the external failure cost. The more easily measured components include the cost of responding to customer complaints, investigation of customer warranty claims, warranty repairs and replacements, product recalls, product liability, and returns and allowances. Many of these costs are already available in the accounting records. However, the single largest measurement problem in this area is that of measuring the external failure cost associated with lost sales, or customer dissatisfaction.

Customer dissatisfaction is not an expense in the traditional accounting sense. Yet, it is a driving concern in today's quality improvement environment. This opportunity cost is referred to as the cost of poor quality. Today there is no widely accepted means of quantifying this cost.

Companies try to estimate this cost of poor quality in a variety of ways. Research on the cost of quality, conducted by KPMG Peat Marwick, indicates that companies frequently estimate that unobservable costs of poor quality commonly run three times all measurable quality costs, and can run as high as 20% of the cost of sales. The Taguchi approximation gives managers a way to quantify these unobservable external failure costs to more rigorously evaluate quality-improvement projects. Without measuring this potentially substantial opportunity cost, the lowest point on the total quality cost curve can not be correctly identified in practice. Furthermore, as engineers and quality control personnel push towards greater improvements in product quality, a larger capital investment in quality improving technology is required. Accountants are at a disadvantage in making recommendations to management about whether a capital expenditure for a piece of equipment used to improve product quality is cost effective. This problem can be overcome by using the Taguchi method to estimate the elusive external failure cost of customer dissatisfaction.

Explanation of the Taguchi Method

The Taguchi method is a variation of the traditional view of customer dissatisfaction due to poor quality. Under the traditional manufacturing perspective, "quality losses" are incurred when a unit of the product falls outside of the lower or upper limits of some predetermined manufacturing specification range. For example, manufacturing specifications for a widget may require it to be 15 mm. plus or minus 3 mm. Under the traditional manufacturing perspective, if the widget actually produced is less than 12 mm, it must be discarded. The company incurs an internal failure quality cost, that of scrapping the materials that went into producing the small widget. Similarly, if the widget produced is greater than 18 mm, the company incurs internal failure quality costs to rework the large widget into one that falls within the limits. For any widget within the 12 mm to 18 mm range, the traditional manufacturing perspective recognizes no internal failure quality cost. Furthermore, no external failure quality costs are expected as long as appraisal and prevention costs and procedures offer assurance that essentially all widgets sold are within the desired range. In terms of customer satisfaction, the customer is deemed to be satisfied with the product as long as it is within the range. This traditional perspective is illustrated by the box shape in Figure 2. In contrast, the smooth curve in Figure 2 illustrates the Taguchi perspective.

Under the Taguchi perspective, a "quality loss" is incurred whenever the actual widget does not reach the exact target value. Variations from this target value which are still within manufacturing specifications of 12 to 18 mm do not cause the company to incur internal failure costs of scrap or rework. Widgets not reaching the exact target value do however, precipitate customer dissatisfaction because the product performs at less than its designed optimum. This causes the customer to return the product, refuse to buy another, and/or advise others not to buy the product. Thus, the difference between the Taguchi perspective and the traditional perspective is the Taguchi recognizes customer dissatisfaction even when the widget produced is within the specified range. This area of customer dissatisfaction is illustrated by the shaded region in Figure 2.

In quality-loss terms, the shaded areas of Figure 2 indicate that as the distance between the true measurement of the widget and its target value doubles, the quality loss quadruples. This relationship can be expressed in mathematical form. This mathematical form is referred to as the Taguchi loss function (The equation for calculation is available from the authors by writing The CPA Journal). This function can be further developed to obtain an estimate of the average expected cost of customer dissatisfaction from a widget which is not exactly on the target value. A computer program calculates this latter function for a given stable manufacturing process. The average cost calculated can then be multiplied by the total number of widgets produced to obtain an estimate of the total external failure cost attributable to customer dissatisfaction. The resultant total is then added to other external failure costs to obtain total external failure costs.

How the Taguchi Method Affects Total Quality Cost Management

External failure costs, however, are only one component of total quality costs. As discussed earlier, quality-cost management involves balancing internal and external failure costs with prevention and appraisal costs to achieve the lowest total quality cost. Once the external failure costs have been quantified (assisted by the Taguchi method) for the stable process, the company's current position on the total cost curve can be identified. This is accomplished by adding the other quality costs to the external failure cost estimate. Then changes to the process can be considered. Proposed quality improvements to the process, such as the reduction in the variability (or standard deviation) of the actual widget produced from the target value, can be used to project a revised external failure cost estimate. This estimate will be lower than the current external failure cost because it will produce a larger percentage of conforming product (a movement to the right on the internal and external failure cost curve in Figure 1). In terms of the Taguchi method, quality losses are reduced because the actual widget is closer to the target (a movement down both sides of the loss curve in Figure 2 towards the target value).

To obtain this reduction in external failure costs, however, an additional prevention cost must be incurred (movement to the right on the prevention and appraisal cost curve in Figure 1). The additional prevention cost is the capital expenditure needed for the purchase of the quality-improvement technology. From a quality-cost management perspective, the issue is whether such an expenditure would cause total quality costs to rise (a movement too far to the right on the total quality cost curve in Figure 1).

This issue can be resolved by using a traditional capital budgeting technique to evaluate the trade off between the increase in prevention costs (i.e., the capital expenditure) and the reduction in external failure costs. The following illustration shows how an evaluation of the quality improvement proposal is made.

Example of Capital Budgeting Application

Suppose the ACE Widget Company manufactures widgets with a target value of 15 mm. Manufacturing specifications accept widgets produced within the range of |+ or -3 mm (i.e., 12 to 18 mm). The current manufacturing process is producing widgets with an average value equal to the 15 mm target. Quality engineers suggest that replacing a particular machine with a more technologically advanced version would improve product quality by reducing the variability (or standard deviation) of the manufacturing process. The new equipment would not change the average value or the target. It would not produce any savings in operating or production costs (although these savings could easily be incorporated into the analysis). Furthermore, in the short run, no changes in appraisal costs or internal failure costs are anticipated. Thus, the only affected costs are prevention costs and external failure costs.

The increase in prevention costs is measured by the purchase price of the new machine. The external failure cost savings are measured in two steps. First, the Taguchi method is used to produce expected external failure costs for the current level of variability in the process (measured by the current standard deviation). Second, the method is used to estimate external failure costs for the level of variability with the new machine. The difference in these estimates is the reduction in external failure costs attributable to the new machine. To calculate the first and second steps, three pieces of information must be input into the computer program (or the mathematical formula): the standard deviation of the process (current actual and expected new), the total annual production to be obtained from the new machine, and the cost of a customer rejection. This last item, the cost of rejection, is an estimate of the financial cost of one dissatisfied customer. The Taguchi method uses this to estimate the total financial cost of customer dissatisfaction.

The cost of customer rejection may not be easy to estimate. However, some observers have found that 80% of measurable external failure costs come from customer returns. Thus the cost of processing a customer return constitutes a good beginning estimate of the cost of customer rejection.

The present value of the annual reduction in external quality failure cost over the useful life of the new machine is then compared to the purchase cost of the new machine and a decision made. If the present value of the reduction in external failure cost is greater than the cost of the new machine, the purchase is justified. Tables can easily be developed that present the calculations over a range of assumptions as to the level of reduced variability, the cost of customer rejection, and the cost of capital used in computing present values.

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