There always exist nonzero inspection errors whether inspectors are humans or automatic inspection machines. Inspection errors can be categorized by two types, type I error and type II error, and they can be regarded as either a constant or a random variable. Under the assumption that two types of random inspection errors are distributed with the “uniform” distribution on a half-open interval starting from zero, it was proved that inspectors overestimate any given fraction defective with the probability more than 50%, if and only if the given fraction defective is smaller than a critical value, which depends upon only the ratio of a type II error over a type I error. In addition, it was also proved that the probability of overestimation approaches one hundred percent as a given fraction defective approaches zero. If these critical phenomena hold true for any error distribution, then it might have great economic impact on commercial inspection plans due to the unfair overestimation and the recent trend of decreasing fraction defectives in industry. In this paper, we deal with the same overestimation problem, but assume a “symmetrical triangular” distribution expecting better results since our triangular distribution is closer to a normal distribution than the uniform distribution. It turns out that the overestimation phenomenon still holds true even for the triangular error distribution.

1. Introduction
 2. Problem Statement
 3. Analysis of Model T (R, C)
 4. Analysis of Model T(C, R)
 5. Analysis of Model T (R, R)
 6. Summary
 7. Discussion and Concluding Remarks
 References

• 양문희(Department of Industrial Engineering, Dankook University) | Moon Hee Yang
• 조재형(Department of Industrial Engineering, Dankook University) | Jae Hyung Cho Corresponding Author