一種非參數性推斷理論及其紡織應用

On a Non-parametric Theory of Inference and its Applications in Textile Industries

紡織工業常用的各種參數性檢定法都需要假定母體成為常態分佈或他種確定的分佈。但母體實在成為何種分佈往往並不能準確斷定。因此需要一種不論母體成为何種分佈都能適用的方法。本文討論一种检定兩子樣是否來自同一母體的方法,祇需要假定母體分佈為連續函數而可不問它是什麼樣的分佈。這種方法適合紡織工業之用,因其不仅適用範圍極為廣泛,且用法之简便還超過常用的參數性检定法。首先我们推導了拉潑拉斯的廣義貝斯定理。然後在這定理的基礎上建立了一種適合紡織机件製造工業用的檢定兩子樣來自的母體的次品率是否相同的方法。編製了一種表格以備工廠撿查,並計算了這種检定法的功效函數。然後闡明檢定兩子樣來自的母體的頻率分佈是否相同的非參數性檢定法可以看作上述方法的一種擴展。對於這種方法也編製了一張表格,並舉了縷紗强力試驗及人造絲單纖維强力試驗的兩個例題。

The parametric methods of significance test commonly used in textile industries are based on the assumption that the parent population were distributed normally or in some other definite form. Yet in textile industries exact informations about the population distribution are hardly accessible to us. Hence a test independent of the nature of the population distribution is needed in these industries. In this paper we first discuss a non-parametric method of testing whether two samples of machine parts are from populations with the same fraction defective. A table has been constructed giving the critical values of the defectives in a second sample after a first sample, both random, has been drawn in which the number of defectives is known. If the number of defectives in the second sample does not exceed the critical value corresponding to that of the first sample at prescribed significance level a, then we may conclude that in 1—a of the cases the fraction defective of the population from which the second sample is drawn is not greater than that of the first. Further, an extension of this method may be established for testing whether two samples are from populations with the same distribution function, for which the only assumption is the continuity of the distribution. A table has also been constructed giving the lower and upper critical values at preassigned confidence level a. If the number of observed values in the second sample, which are smaller than (or larger than) the median of the first, lies between the corresponding critical limits, then we may conclude that in l—a of the cases the two samples are from populations with the same distribution function. Power function of the test has been calculated and examples for testing rayon filament strength and lea strength have been given for illustrative purposes.