2005-08-012024-05-16https://scholars.lib.ntu.edu.tw/handle/123456789/666980摘要：工業產品研發初期或其它科學實驗，當實驗變因很多時，&#63847;含重複點的2-變級複因子設計（unreplicated two-level factorial designs），被廣泛用於估計實驗者認為重要&#63847;可忽&#63862;的因子效應（factorial effects）。 但由於實驗未含重複的（replicated）處&#63972;組合（treatment combinations）。因此，實驗機差變&#63842;&#63849;(the variance of experimental error)的估計，僅能借助常態圖（normal plotting）或混合某些高階交感效應 （high order interactions）&#63789;獲得。然而，在很多實驗，以此種有偏（biased）估值當成統計推&#63809;的基礎 常常&#63847;是非常可靠。因此，一方面為&#63930;保持實驗大小(design size or run size)&#63847;至於太大，另一方面又希望 可以獲得機差變&#63842;&#63849;無偏估值(un<br> Abstract: During the initial stages of experimentation, unreplicated two-level fractional factorial designs are commonly used to estimate a set of importantfactorial effects specified by the user. The specification may usually consist of the constant term, all main effects and some two-factor or higher order interactions. See Wu and Chen (1992), Srivastava and Li (1996) and Liao, Iyer and Vecchia (1996). Since each of the treatment combinations is run at most once so that the variance of experimental error cannot be estimated based on the pure replicates, leading to that the estimate may be quite biased in many situations. In order to keep the run size small and hence the cost of experiment affordable, and at the same time to have an unbiased estimate for the variance of experimental error. The two-level fractional factorial designs with partial duplication are in demand. The designs of desire may be used to meet the requirement that the variance of experimental error be estimable subject to relatively little loss of efficiency in estimation for the factorial effects of user-specified resolution. In this research project, we shall extend the results of Liao and Chai (2004) on the partially replicated two-level factorial designs to a more general situation. Liao and Chai (2004) investigate properties of two-level factorial designs generated from the class of f parallel flats designs with two identical flats, abbreviated as f-PFDRs. They focus on the two classes of designs: 3-PFDRs and 4-PFDRs and present a series of partially replicated designs with run sizes N=12, 16, 24 and 32. So their results may still be restricted in practical applications. We shall first investigate the D-optimality of general f-PFDRs for a set of specified factorial effects. Then develop an algorithm for generating the desired designs based on the proposed theorem. Some practical designs generated from the algorithm will be tabularized for the user. Furthermore, we shall explore the possibility of the use of f-PFDRs in screening for dispersion effects. The study on dispersion effects in factorial experiments has been drawn considerable attention recently. The literature pertaining to dispersion effects can be found in Box and Meyer (1986), Bergman and Hynen (1997), Brenneman and Nair (2001), McGrath and Lin (2001a, 2001b), among others.純機差分散效應最適設計平行面設計Pure errorDispersion effectOptimali designsParallel designs