本研究乃探討模糊數學規劃方法在不良數管制圖與道奇─雷敏選剔檢驗計
劃上的應用，以及有關給定兩定點之CSP-1抽樣計劃設計、在檢驗誤差下
設計使平均檢驗比例為最小的CSP-1與CSP-2計劃之研究。綜合各項研究結
論，摘要如下：一、模糊環境下的不良數管制圖經濟統計設計本文以
Lorenzen-Vance (1986)模式為例，考慮模糊環境下儘可能滿足型Ⅰ誤差
與型Ⅱ誤差風險的不良數管制圖經濟統計設計的問題。並將該問題模式化
成模糊數學規劃的模式。研究顯示模糊環境下的管制圖經濟統計設計，它
提供了更多的彈性於統計限制式的經濟模式上，並且較傳統經濟統計設計
模式假設下成本為低。二、模糊環境下的道奇─雷敏選剔檢驗計劃在1992
年 Chakraborty首先提出在模糊環境下儘量能滿足消費者風險的道奇─雷
敏LTPD單次抽樣計劃。本研究繼續推廣至模糊環境下的道奇─雷敏LTPD雙
次抽樣計劃與道奇─雷敏AOQL單次抽樣計劃。研究結果顯示： (i) 就比
較模糊環境下的道奇─雷敏LTPD與AOQL單次抽樣計劃，可以獲知 AOQL的
少量變動對ATI相當敏感，而 LTPD抽樣計劃下的消費者風險的變動相對地
對ATI的敏感度較小。 (ii)就比較模糊環境下的道奇─雷敏LTPD單次與雙
次抽樣計劃，可以獲知雙次抽樣計劃對ATI下降的貢獻程度相當大。三、
連續抽樣計劃問題探討當特定製程平均不良率大於AOQL時，具檢驗誤差的
CSP-1計劃與CSP-2計劃有相同最小的AFI。在相同抽樣成本的情況下，吾
人能使用具檢驗誤差的CSP-1計劃的模式來取代具檢驗誤差的CSP-2計劃的
模式以求解最小AFI的問題，因為CSP-1計劃比CSP-2計劃更容易執行。
This research studies the FMP model applied in the np-control
chart and the Dodge-Romig rectifying inspection plans, the
design of CSP-1 plan with given AQL and LQL points, and the
minimum AFI for CSP-1 and CSP-2 plans under inspection error.
The results of this research are summarized as follows: 1. In
this research, the problem of determining the designs of
economic statistical np-control chart is considered, under the
fuzzy environment that satisfies the risks of Type I and Type
II error as closely as possible. The Lorenzen-Vance''s (1986)
model is used to formulate the above problem as a fuzzy
mathematical programming model. Our research results indicate
that the economic statistical control chart design under fuzzy
environment is superior to traditional economic statistical
designs, because it provides more flexibility on the
statistical constraints in the economic models and is less
costly than the traditional economic statistical models. 2. In
1992, Chakraborty first presented the Dodge-Romig LTPD SSP with
consumer''s risk being satisfied as closely as possible when the
environment is fuzzy in nature. In this research, the following
two sampling plans under fuzzy environments are studied: (1)
Dodge-Romig LTPD DSP, and (2) Dodge-Romig AOQL SSP. The
outcomes of this research reveals that: (i) ATI is more
sensitive to the change of the AOQL in the Dodge-Romig AOQL SSP
than to the change of the consumer''s risk in the Dodge-Romig
LTPD SSP, and (ii) ATI is more sensitive to the Dodge-Romig
LTPD DSP than to the Dodge-Romig LTPD SSP. 3. Both the CSP-1
plan and the CSP-2 plan under inspection error have the same
minimum AFI when the specified process average fraction
defective is larger than the AOQL. Under the same sampling
cost, one can use the proposed model to minimize AFI of the
CSP-1 plan under inspection error to replace that of the CSP-2
plan under inspection error, because the CSP-1 plan is more
convenient to execute than the CSP-2 plan.