Summary by Kellie Quinn
Master of Accountancy Program
University of South Florida, Summer 2002
Constrained Optimization Main Page | Quality Related Main Page
Fargher and Morse discuss the relationship between the four quality costs and explain how to minimize total quality costs by analyzing these four cost functions. The authors argue that the traditional model of quality cost minimization assumes that the manager has already identified the optimal combination of prevention and appraisal activities. They begin by defining each of the four quality-related costs – prevention costs, appraisal cost, internal failure costs, and external failure costs.
Prevention costs and appraisal costs are quality costs inputs. These include costs incurred to produce a product that is not defective. Prevention costs are those costs associated with actions to ensure that defects do not occur in initial production. Costs considered to be preventive in nature include costs to design a higher quality product, training employees on quality activities, purchasing higher quality materials and increased maintenance on production equipment. Appraisal costs, on the other hand, are cost incurred to test and inspect products in order to identify those products that do not meet specifications. The greater the number of tests and inspections, the higher the appraisal costs and the more likely that a defective unit will be identified. Many companies may find that identifying 100% of defective units is very costly, with costs rising sharply as the proportion of defects found approaches 100%.
Internal and external failure costs are considered the quality cost outputs. Internal failure occurs when a product is found to be defective before reaching the customer while external failure occurs when a defect is found after reaching the customer. Internal failure costs include the cost of repairing or replacing a defective product and any discount given to the customer for purchasing the reworked product. External failure costs include all internal failure costs plus the cost of shipping and handling and lost sales due to the effects on the company’s reputation. Since external failure costs include all internal failure costs, it is assumed that external failure costs will be greater than internal failure costs. Therefore, a company would prefer to fix a defective item before it is sold to the customer.
The first step in quality cost minimization is to determine a cost function for each of the four quality activities: prevention, appraisal, internal failure and external failure. After estimating these quality costs, the company needs to determine what level of external failure is acceptable. For example, the company discussed in the article manufactures a chemical used to patch holes in plywood and has decided that a 1% defect rate in products shipped to customers was acceptable. A higher defect rate would be disastrous to the company in terms of lost sales. Companies producing a product that, if defective, may have catastrophic consequences, may decide that there is no room for any external failures and that each and very unit shipped to customers must either be made correctly in initial production or be inspected and re-worked prior to being shipped out.
The next step is for the company to determine the optimal combination of prevention activities and appraisal activities to ensure that the external failure rate does not exceed the acceptable limits. The TQM approach would lead managers towards creating a process where all units are made correctly during the initial production, thereby eliminating the need to re-work defective items. Most companies, however, find that creating such a system is too expensive and will need to rely on the appraisal process to discover and correct defective units. These companies can achieve the most cost-effective combination of prevention and appraisal activities at the point where the marginal cost of prevention is equal to the negative of the marginal cost of internal failure. After this point, it is more costly to make a good unit that to repair a defective unit. The company referred to above determined that the optimal level of prevention occurs at 10% defects in initial production. In other words, it would be more costly for the company to concentrate their efforts on producing less than 10% defects in initial production than to re-work these defective units. The appraisal process must then identify enough defective units to bring the total external failure rate down to the acceptable limits.
The authors recognize that some companies may opt to produce all units correctly the first time as consistent with the TQM approach. For those companies that find this approach to be too costly, the authors have provided guidance on determining the optimal combination of prevention and appraisal activities. By analyzing the cost functions for the four quality activities - prevention activities, appraisal activities, internal failure and external failure - a company can cost-effectively achieve a combination of prevention and appraisal activities that will result in an acceptable external failure rate.
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