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The purpose of this research is to deepen understanding of variables that impact quality and cost of quality. This research used the prevention-appraisal-failure (PAF) model to evaluate the cost of quality (COQ) and to determine the level of quality that minimizes the total COQ. The PAF models are developed in the framework of three major operational inputs; material, machine, and labor; the model is besides expanded for the company as a whole. This proposed framework presents a first step toward providing researchers and practicing managers with a conceptual view of the cost of quality and quality perspectives. Although the research finds that the shapes of the cost of quality curves in the PAF models for a flower wholesale company are slightly different from the theoretical PAF model, the curves behave in the same manner. They reveal that as appraisal cost plus prevention cost increases, quality enhances and failure cost decreases. Finally, the results provide vital suggestions for investments in appraisal and prevention activities for material, machine and labor in order to achieve a satisfactory level of quality that minimizes total cost of quality.
Keywords: PAF model, Cost of quality, Appraisal cost, Prevention cost, Failure cost
In recent years corporations have been focusing much attention on quality management. There are many aspects on quality management but this research focuses on the cost of quality. The concept of cost of quality originated in manufacturing settings, in the 1950s, as a means of justifying staff functions responsible for quality management . A number of organizations are now seeking both theoretical advice and practice evidence about cost of quality and the implementation of quality costing system . Over the past few decades, the concept of cost of quality has been widely studied and discussed in numerous literature including Crosby , Plunkett and Dale [4,5,6], Diallo, et al., , Willis , Dale and Plunkett [9,10], Zhao , Griffith , Schiffauerova and Thomson , Kulkarni , and Aurora et. al. The costs associated with quality are divided into four categories: prevention, appraisal, internal failure, and external failure (Gryna , Harrington [16, 17,18], Campanella [19,20]). Prevention costs are all of the costs expended to prevent errors from occurring in all functions within a company. They include quality planning cost, new product review cost, process control cost, quality audit cost, supplier quality evaluation cost and training cost. Appraisal costs are the cost incurred to identify poor quality of products before delivery to customers. They normally include incoming inspection and testing cost, in-process inspection and testing cost, final inspection and testing cost, equipment calibration cost, inspection and testing of materials and services cost, and evaluation of stock cost. Internal failure costs are those costs incurred prior to the delivery of the products. These costs include the resources need to complete additional tasks and any costs involved in rework due to inadequate processes. External failure costs arise after a company supplies the product to the customer, such as customer service costs, product recall, and customer returns warranty.
The traditional theory of cost of quality hypothesizes an inverse relationship between quality and failure cost as well as a theory hypothesizes that quality and appraisal cost plus prevention cost are directly related. To further facilitate understanding of cost of quality relationship, the cost of quality model (PAF model) are analyzed and presented in Figure 1 . The basic assumptions of the PAF model are that investment in prevention and appraisal activities will reduce failure costs, and that further investment in prevention activities will reduce appraisal costs. The objective of the model is to find the level of quality that minimizes total cost of quality (Abdelsalam, H., and Gad, M. , Plunkett and Dale [4,5,6], Grimm and Fox , Feigenbaum , Gray ).
Figure1. Cost of Quality Model (PAF) (Gryna, 1999, P8.22)
These models show three curves: failure cost, costs of appraisal plus prevention, and total cost of quality (the algebraic sum of the appraisal cost, the prevention cost and failure cost at each point along the axis). Failure cost is zero when the product is 100% conformance. As nonconformance increases, the failure costs also increase. In order to develop cost of quality strategy, it is vital to seek a balance point at which the cost of quality is minimal. From a prescriptive standpoint, this point could be used to establish and justify the scale of quality assurance and control efforts.
Although there is an enormous amount of cost of quality data being collected in various industries today, the unfortunate fact is that little of it is ever analyzed . In 1985, Rosander  studied the customer costs as a separate COQ category. Heskett et al.  proposed the interpretation of internal and external failure costs to acknowledge the differences between service and manufacturing in 1995. Youngdahl and Kellogg  developed a preliminary classification scheme for customers' costs of service quality that resulted in seven distinct quality assurance behaviors. It provided insight into customers' roles in service quality.
In this research, a correlation analysis is employed to determine the impact of changes in the cost of quality components to the quality using a real data from a flower wholesale company in the United State over a period of 24 months. Furthermore, the data is used to develop the PAF model to identify the right amount of investment in prevention and appraisal activities. In order to apply cost of quality system to improve quality and to reduce cost of quality, there is a need for an analytical framework that explains the relationship between cost of quality components and quality (appraisal cost plus prevention cost and failure cost; appraisal cost plus prevention cost and quality; as well as failure cost and quality) for major operational inputs. Once these relationships are defined and clearly understood, the ability of an organization to make decisions related to improving quality, and reducing cost of quality will be substantially enhanced. In other word, the management enables to create appropriated quality strategy for reducing cost and improving productivity.
This research is intended to apply the PAF model for a wholesale company. It has three main objectives: (1) to test the relationships between the cost of quality components and the level of quality for material input, machine input, labor input, and company as one; (2) to use the PAF model to evaluate the cost of quality; and (3) to determine the optimum value for the cost of quality. Specifically, this research is attempted to answer the following four essential questions:
a) Is there an inverse relationship between appraisal cost plus prevention cost and failure cost for material input, machine input, labor input, and the company as a whole?
b) Is there a direct relationship between appraisal cost plus prevention cost and the level of quality for material input, machine input, labor input, and the company as a whole?
c) Is there an inverse relationship between failure cost and level of quality for material input, machine input, labor input, and the company as a whole?
d) How much the company should be invested in appraisal and prevention activities for material input, machine input, and labor input?
Methodology and Conceptual Framework
This research is concerned with the integration of the concept of cost of quality and the level of quality for four major elements: material input, machine input, labor input, and the company as a whole. In this study, twenty-four months of cost of quality data were collected from a flower wholesale company. The company is located in Miami, South Florida. It had about 27 employees and annual sales of about US$1.2 million per year, at the time of this study. The flowers are imported from Thailand, Europe, and South America to distribute in the USA. The cost of quality system has been established in the company in an attempt to increase the value of the products and services and to enhance customer satisfaction. The company developed the method for estimating cost of quality data for the purpose of a cost of quality program. The method takes into account the number of labor, machine and material involved in any given operation activities. Expenditures are consequently assigned to the cost of quality componenets. The data consist of cost of quality componenets (appraisal cost, prevention cost, internal failure cost, and external failure cost), total sales, and quality performance data for machine, material, labor, and company as a whole. With the aim of measure labor quality performance, a set of questionaire was developed to gather customer attitude associated with both satisfactory and unsatisfactory service encounter. It is important to note that only one question in the questionaire was used this research. This is because the main objective of the questionaire developent was used for another study. For each encounter, the respondents answersed an important question "Please indicate your level of satifaction of the services" (0-none, 1-very little, 2-a little, 3-some, 4-a lot, 5-very much). The question was asked to identify the service performance for the purpose of examining the labor quality. Prior to obtaining the sample data the questionnaire is required to develop and to test for reliability and validity. Personal interviews were conducted to verify respondents's understanding of the survey instrument. Using Cronbach's alpha to test internal consistency, values of 0.87 were obtained. Over 250 samples were conducted for this analysis. The survey data was transformed in to level of labor quality (% of customer satisfaction associated with the labor activities). Minitab software is used to determine the relationship (Pearson Correlation Coefficient Analysis) among the cost of quality components and quality.
The PAF model is selected as a base for this research. This selection is reasoned to: (1) the model is easy to be understood; (2) its ease of application on different company circumstance; and (3) the availability of data needed to apply this model. A conceptual framework is developed by integrating four major elements: material input, machine input, labor input, and the company as a whole with the PAF model. This conceptual framework is presented in Figure 2.
Figure 2. Conceptual Framework for the research
The notations in the analysis are presented as the following:
M = material input
M/C = machine input
L = labor input
O = other inputs
INPUT = M + M/C + L +O
Cost of Quality:
P = prevention costs
PM = prevention cost for material
PM/C = prevention cost for machine
PL = prevention cost for labor
PO = prevention cost for other inputs
P = PM + PM/C + PL + PO
A = appraisal costs
AM = appraisal cost for material
AM/C = appraisal cost for machine
AL = appraisal cost for labor
AO = appraisal cost for other inputs
A = AM + AM/C + AL + AO
Internal failure cost:
IF = internal failure costs
IFM = internal failure cost for material
IFM/C = internal failure for machine
IFL = internal failure cost for labor
IFO = internal failure cost for other inputs
IF = IFM + IFM/C + IFL + IFO
External failure cost:
EF = external failure costs
EFM = external failure cost for material
EFM/C = external failure cost for machine
EFL = external failure cost for labor
EFO = external failure cost for other inputs
EF = EFM + EFM/C + EFL + EFO
Cost of Quality for material (COQM):
The cost of quality for material consists of the combination of appraisal costs and prevention costs (e.g. raw material inspection, supplier quality evaluation, and process control) and failure costs (e.g. decomposition, loss, return, customer complains, and rework) associated with the raw material. The relation can be expressed as the following:
COQM = PM + AM + IFM + EFM
Cost of Quality for machine (COQM/C):
The cost of quality for machine consists of the combination of appraisal and prevention costs (e.g. calibration of machine, preventive maintenance, inspection and test set-up) and failure costs (e.g. repair, and operating cost for rework) associated with the machine. The relation can be expressed as follows:
COQM/C = PM/C + AM/C + IFM/C + EFM/C
Cost of Quality for labor (COQL):
The cost of quality for labor consists of the combination of appraisal and prevention costs (e.g. training, activities to ensure that the most efficient design methods for operations) and failure costs (e.g. labor cost for rework/recheck) associated with the labor. The relation can be expressed as the following:
COQL = PL + AL + IFL + EFL
Cost of Quality for other input (COQO):
The cost of quality for other inputs consists of the combination of appraisal and prevention costs and failure cost associated with other inputs excluding material, machine and labor. The relation can be expressed as follow:
COQO = PO + AO + IFO + EFO
It is important to note that the cost of quality for other inputs is not included in this research. This is because the other input accounts for only 6% of the total inputs. However, the other input is already included in the cost of quality for a company as a whole.
Cost of Quality for company (COQ):
The cost of quality for the company consists of the combination of appraisal and prevention costs (e.g. inspection, quality planning, and training) and failure cost (e.g. scrap, loss, and rework) associated all operations for the company. The relation can be expressed as the following:
COQ = COQM + COQM/C +COQL + COQO
= PM + AM + IFM + EFM + PM/C + AM/C + IFM/C + EFM/C + PL + AL + IFL + EFL + PO + AO + IFO + EFO
The term "quality" in this research is derived from the following definitions:
Quality of Material: The quality of material measured in term of the degree to which the raw material conforms to company specifications (% raw material conformance).
Quality of Machines: The quality of machinery and equipment measured in term of machine availability rate (% machine availability).
Machine availability = Loading time- breakdown - set up time loss
Loading time = planed operation time - breaks - planned maintenance
Quality of Labor: The quality of labor measured in term of a level of customer satisfaction to the service's performance associated with the labor activities (% customer satisfaction).
Quality of Company: The quality of company is measured by the percent of units that conform to specifications (% product conformance).
Results and discussions
The relationship between appraisal cost plus preventive cost and failure cost, appraisal cost plus preventive cost and quality, and failure cost and quality for material input, machine input, labor input, as well as company are presented in table 1. The Pearson Correlation Coefficient value and sign will help in understanding the strength and the direction of the relationship between the two sets of variables.
Table 1. The Pearson Correlation Coefficient among the variables
Appraisal cost + Prevention cost vs. Failure cost
p = 0.000
p = 0.307
p = 0.000
p = 0.000
Appraisal cost + Prevention cost vs. Quality
p = 0.000
Failure cost vs. Quality
p = 0.000
p = 0.003
Hypothesis 1. The Relationship between Appraisal Cost Plus Prevention Cost and Failure Cost is negative.
The results in Table 1 indicate that there is an inverse relationship between appraisal cost plus prevention cost and failure cost for material, labor and company. The degree of the relationship that is measured by the Pearson Correlation Coefficient is found to be -0.629 (p =0.000) for material, -0.522 (p = 0.000) for labor and -0.537 (p = 0.000) for the company. In other words, the failure cost decreases when the appraisal cost and prevention cost increase for material and labor. This means that as an organization expends more of its budget on appraisal and prevention activities for material input and labor input, the failure cost will decrease. However, the relationship between appraisal cost plus prevention cost and failure cost for machine input does not significantly at 95% confident interval.
Hypothesis 2. The Relationship between Appraisal Cost Plus Prevention Cost and Quality is positive.
This research shows the significant relationship between quality and the combination of appraisal cost and prevention cost for all components. The correlation coefficient is found to be 0.620 (p = 0.000) for material, 0.574(p = 0.000) for labor, 0.549 (p = 0.000) for machine and 0.565 (p = 0.000) for the company (Table 1). This indicates that as appraisal cost and prevention cost for material, machine, and labor increase, quality increases. For this reason, if a company spends more of its budget on appraisal cost and prevention cost for material input, the result will be an improved quality of material (% raw material conformance). In the same way, the level of the quality of labor (% customer satisfaction) and machine (% machine availability) increases as a result of increasing in appraisal and prevention activities for labor input and machine input, respectively. Consequently, increasing in appraisal cost and prevention cost for material, machine, and labor would lead to an improvement in the level of quality for the company as a whole (% product conformance).
Hypothesis 3. The Relationship between Quality and Failure Cost is negative.
Similar to the study conducted by Carr and Ponoemon  as well as Vincent, et. al.,  this research shows that the failure cost has a statistically correlation with quality for all components. The correlation coefficient for the relationship is found to be -0.615 (p = 0.000) for material, -0.594 (p = 0.003) for machine, -0.654 (p = 0.000) for labor, and -0.647 (p = 0.000) for the company (Table 1). It can be seen that the level of quality and failure cost bears an inverse relationship. This implies that as failure cost decreases, the level of quality increases. When a company gets a high percent of raw material conformance, a large percent of machine availability for its processes, and a high percent of customer satisfaction, it will experience a reduction in scrap, rework, return, and customer complaints.
Although these relationships follow the same trend for material input, machine input, labor input, and the company, the degree of the relationship varies slightly (as indicated by correlation coefficients). The research also indicates that the relationship between failure cost and quality is the strongest compared to others. Additionally, this study found that there are strong relationships between failure cost and quality for labor, material, and machine, in descending order.
The PAF Model Development
In order to gain better understand of the result implication, the PAF model provides a graphical representation of the relationships. This section compares the PAF model as shown in Figure 1 with PAF models for material (Figure 3), machine (Figure 4), labor (Figure 5) and the company (Figure 6). Although the research finds that the shapes of the cost of quality curves are slightly different from theoretical model (Figure 1), the curves behave in the same manner. In other words, as prevention costs and appraisal costs increase, quality enhances and failure costs slightly decrease for all elements (material, machine, labor, and company).
For instance, with respect to material input (Figure 3), if the company invests US$0.35 in appraisal and prevention activities, failure cost is approximately US$0.85, the total cost of quality is US$1.20 (based on a per US$1,000 product value) and the quality is around 90% raw material conformance. If the expenditures for appraisal and prevention activities raise to US$0.40, failure costs decrease roughly to US$0.60, the total cost of quality reduce to US$1.0 (based on a per US$1,000 product value) and the quality of material increases to about 94% raw material conformance. Moreover, if the expenditures for appraisal and prevention activities increase over US$0.45, the failure cost slightly decrease (lesser than US$0.60) whereas the level of quality increase (greater than 94% raw material conformance). However, the total costs of quality continuously increase (larger than US$1.0). This circumstance implies that the minimum cost of quality for material input is found at approximately 94% of raw material conformance, or the expenses for the appraisal and prevention activities is at US$0.40 per US$1,000 product value. With respect to the PAF model for machine input, the corporation should invest US$0.25 per US$1,000 product value in appraisal and prevention actions, or 94.5% machine availability. Regarding to the labor input, the minimum cost of quality is found at 96% customer satisfaction, or US$0.22 per $US1,000 product value investment for appraisal and prevention activities. Concerning with the company as a whole, the proper expenditure in appraisal and prevention activities is at US$0.90 per US$1,000 product value (the level of quality is 97% product conformance). It can be concluded that to achieve a lower production cost per unit, it is desirable to have the organization operate at this point of minimum total cost of quality.
Implementing the PAF Model: Implications for Decision-Making
The PAF model developed in this research provides a very meaningful guideline for decision-making regarding the operations. As presented in Figure 3, 4, 5 and 6, to minimize the cost of quality, the quality levels should be controlled at 94% conformance for material (approximately US$0.40 expenses in appraisal and prevention activities per US$1,000 product value), 94.5% for machine availability (approximately US$0.25 investment in appraisal and prevention activities per US$1,000 product value) and 96% for customer satisfaction (approximately US$0.22 investment in appraisal and prevention activities per US$1,000 product value). Regarding a company as a whole, the PAF model suggests that the appropriate investment in appraisal and prevention is around US$ 0.90, at 97 % product conformance.
As discussed above, this model makes it possible for management to identify the level of investment required to achieve the desired level of quality. The investments for prevention and appraisal activities may include diagnosis and other forms of analysis, training, redesign of products and processes, testing, quality planning, and equipment calibration (including maintenance for current equipment). Specifically, by increasing prevention cost, the level of quality can be improved due to the training of employees, raw material control, and preventive maintenance of equipment. Also, appraisal cost may be decreased because of reduced inspection level caused by better quality products and equipment. Additionally, less inspection time is required to re input rejected lots because fewer lots are rejected. It is also noteworthy that, if the organization increases both prevention cost and appraisal cost, the internal failure cost and external failure cost decrease because of fewer errors. The returns from such investments should reflect savings in the cost of poor quality, savings in process capability improvement, and increases in sales revenue as a result of a reduction in customer dissatisfaction, and increases in new customers.
The results confirm that as appraisal cost plus prevention cost increases, quality enhances and failure cost decreases. The shapes of the cost of quality curves would be different under different operational environments. Hence, the PAF model should be carefully considered in order to minimize cost of quality and to improve quality. The results significantly indicate the following: (1) there is an inverse relationship between appraisal cost plus prevention cost and failure cost for material, labor, and company; (2) there is a direct relationship between appraisal cost plus prevention cost and quality for all factors; (3) there is an inverse relationship between failure cost and quality for all components; and (4) the PAF models suggest that the appropriate expenditure per US$1,000 product value for appraisal and prevention activities are US$0.40 for material, US$0.25 for machine and US$0.22 for labor. This investment will lead to minimize the total cost of quality for the company. Understanding the cost of quality is extremely important in establishing a quality management strategy. After integrating the PAF model with the major operational inputs, the right amount of money to invest in quality assurance (appraisal and prevention activities) can be defined. Theoretically, the investment in quality assurance is based on the law of diminishing returns, that is, organizations should spend as much as on quality assurance is justified by the cost of the defects being repaired. At the point where the cost of quality assurance exceeds the cost of the defect, the expenditures are too much.
We strongly embrace the usefulness of the typology for exploring the PAF model for three major operational inputs (material, machine, and labor) at a flower wholesale company. This research benefits organization in that it assists management in developing a proper cost of quality strategy. The cost of quality data can be used in an effort to be proactive, and to identify causes of problems. It provides a methodology for pinpointing improvement priorities. Once the causes are resolved, the defects do not occur and failure costs decrease. In summation, understanding cost of quality and PAF model helps companies to develop quality management system as a useful strategic business tool that decreases cost of quality, as well as, improves their products, service and image. This leverage is crucial in achieving the goals and mission of a successful organization.
In essence, it is hoped that this research adds to the existing knowledge regarding cost of quality and quality. In this research, the cost of quality for other inputs was not studied because they are accounted for only 6% of the total cost. Nevertheless, by including the cost of quality for other inputs for the study, the optimum value for investment will be more accurate than the one in this paper. Based on both the experience gained in conducting this study and the literature reviewed, it is felt that more work needs to be done to understand the cost of quality. Consequently, some recommendations for further research are suggested. First, the relationship among cost of quality, quality and productivity for both manufacturing and service sectors should be studied. Second, the PAF model for both profit organization and non-profit organization should be investigated. Finally, other vital inputs, such as energy input must be included in the future study.