A perspective of quality costs in a two-parameter framework.

Author:Chang, Chiaho

    Recent development in management accounting literature emphasizes the importance of non-financial indicators as opposed to the traditional, bottom-line approach to performance evaluation. One such indicator, quality measure, has been well accepted and widely applied to quality control field in general and quality cost literature in particular. One result of this line of research, ranging from Juran (1951), Morse and Roth (1987), Edmonds, Tsay and Lin (1989) to Heagy (1991), is to accept a non-zero level of defect rate as an optimal way of doing business.

    On the other hand, Crosby (1979) and Deming (1982) argue that only zero defect can survive competition. Recently, Fine's (1986) quality-based learning model and Ittner's (1993) empirical results provide some support for zero-defect argument. However, the debate goes on.

    The first purpose of this paper is to take a second look at the concept of quality as a non-financial measure of performance and to develop a two-parameter framework on quality, which effectively makes the traditional, one-parameter model a special case. We hope that implications from this new development may help direct future research on quality costs and resolve the debate.

    The second purpose of this paper is to impose quality-related costs on this framework and to consider the fiscal responsibility of quality improvement. For that, we only model the behavior of a single firm with one period to act.

    The remainder of the paper is organized as follows. Section 2 describes the setting for the two-parameter framework on quality and its features. Section 3 considers quality costs in a world without budget constraint, followed by a comparison with a world where the budget constraint is binding. Section 5 concludes this paper with a discussion of some possible extensions.


    We first divide all quality improvement activities into two categories: prevention and appraisal. Prevention effort (or activities) includes R&D, product design, quality engineering, worker education and training, process control, and supplier support, etc. It determines a "default" quality ([delta], [delta] [member of]e [0, 1] ), which represents the proportion of the output that will work properly in the hands of the customers. Appraisal effort (or activities), such as materials inspection, component testing, in-process inspection, final product inspection, and reliability testing, determines an "appraisal effectiveness" ([gamma], [gamma] [member of] [0, 1]), which indicates the proportion of defective units that will be picked up before they reach the customers. Note that the presence of uncertainty is assumed away here in the sense that the prevention (appraisal) effort will lead directly to improvements in default quality (appraisal effectiveness) without noise (i.e., free of the influence of random factors).

    With the distinction between prevention and appraisal in place, we can look at a simple manufacturing environment in which a batch of x units of outputs is produced. Then [delta] x units, on average, should be defect-free (good units). On the other hand, (1- [delta])x units are defective (bad units), out of which [gamma] (l - [delta])x units will be screened out and become part of the internal failure. The remaining (l - [gamma])(l - [delta])x units pass inspection, get delivered to the customers, and eventually become part of the external failure (we assume that any defect will be detected and reported by the customers shortly after their purchases). Exhibit 1 shows the impact of default quality and appraisal effectiveness on internal and external failures.


    By assuming that all defective units caught in appraisal are reworked and become good units, we can work out an "outgoing" quality (q, q [member of] [0, 1]) that represents the quality level of outputs actually delivered to the customers. That is, the outgoing quality is the proportion of good units among all units shipped out, or

    q [equivalent to] [delta]x + [gamma](1- [delta])x / x = [delta] + [gamma] (1 - [delta]

    Observation 1. Improving either default quality or appraisal effectiveness will shore up the outgoing quality. Mathematically, q is increasing in both [delta] and [gamma], or

    [partial derivative]q / [partial derivative][delta] = 1 - [gamma] [greater than or equal to] 0 and

    [partial derivative]q / [partial derivative][gamma] = 1 - [delta] [greater than or equal to] 0.

    With the risk of stretching economic terminology too far, we can define the "iso-quality" curve as the curve that traces combinations of default quality and appraisal effectiveness producing equal outgoing quality level, whose slope can be derived by first totally differentiating q, or

    dq = [partial derivative]q / [partial derivative][delta] d [delta] + [partial derivative]q / [partial derivative][gamma] d [gamma] = (1 - [gamma])d [delta]+ (1 +[delta] d[gamma].

    Since the outgoing quality level remains constant along an iso-quality curve, dq = 0 . Thus



    [d.sup.2][delta] / d [[gamma].sup.2] = - 1 - [delta] / [(1 - [gamma]).sup.2]

    Observation 2. As far as the quality technology is concerned, [delta] and y may be deemed substitutes in determining the outgoing...

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