Analysis and Probability of Overestimation by an Imperfect Inspector with Errors of Triangular Distributions

• 발행기관: 한국산업경영시스템학회
• 저자명: Moon Hee Yang(양문희) Jae Hyung Cho(조재형)
• 간행물 정보: 『산업경영시스템학회지』제41권 제2호, 117~132쪽, 전체 16쪽
• 주제분류: 경제경영 > 경영학
• 파일형태: PDF
• 발행일자: 2018.06.30

영문 초록

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.

목차

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

키워드

Imperfect Inspection Overestimation Triangular Error Distribution