# 统计代写|抽样理论作业代写sampling theory代考|STAT392

## 统计代写|抽样理论作业代写sampling theory代考|The Total Sampling Error

We have only looked at the selecting process in general. Now, we shall consider all nonselection operations carried out on the lot and on the successive samples and their increments by various sampling stages. These nonselection operations, or at least some of them, are likely to be present between sampling stages, and we define them as “preparation stages.”

A preparation stage is an error-generating process that may be created by transfers from one place to another, comminution stages, screening operations, mixing attempts, drying, filtration, weighing, packaging, and so on. The generated errors, usually accidental errors, are defined globally as the Increment Preparation Error IPE. We define the Total Sampling Error TSE as the sum of the proper Sampling Selection Error SSE and the Increment Preparation Error IPE, generated for each sampling and corresponding preparation stage:
$$T S E=S S E+I P E$$
Consequently, if we have $N$ sampling stages and preparation stages, $N$ Total Sampling Errors will be generated, and we should write:
$$I P E=I P E_1+I P E_2+\ldots+I P E_n+\ldots+I P E_N$$

Introduction to the Overall Estimation Error
73
$$T S E=T S E_1+T S E_2+\ldots+T S E_n+\ldots+T S E_N$$
Where $n$ is the rank of a sampling or preparation stage $(n=1,2,3 \ldots N)$.
$$\begin{gathered} T S E_n=S S E_n+I P E_n \ T S E=\sum_n\left(S S E_n+I P E_n\right) \end{gathered}$$

## 统计代写|抽样理论作业代写sampling theory代考|A Logical Introduction to the Notion of Heterogeneity

Heterogeneity is a primary structural property of all materials and we cannot ignore it without taking considerable risks that are almost always economically detrimental to any research performed on these materials. There are many examples in various industries using materials of mineral origin such as metallurgy, cements, coal, glass, ceramics, nuclear energy, and so on. There are other examples such as agricultural, food, paper, chemical, and pharmaceutical industries that use mineral, organic, vegetal, and synthetic materials. Without exception, all these industries, and the research programs associated with them, should be affected and extremely concerned by the notion of heterogeneity,
The assessment of the quality of a product and also of the feasibility of a process depend on experimental estimates that always have a certain amount of uncertainty. Two factors contribute to this uncertainty:

1. the measurement or analytical errors
2. sampling errors.
All people involved in research, development, production, quality assurance, and quality control deal directly or indirectly, conscientiously or unconscientiously with sampling problems. These sampling problems exist because all materials are essentially heterogeneous.

Heterogeneity is detrimental to all processes that are regulated in such a way that the optimum output is obtained for a given input material of composition $X$. The output deteriorates in quality and quantity as soon the input raw material has a composition $\mathrm{X}^{\prime}$ different from $X$ which has been set by stringent objectives. The real output becomes different from the optimum output, and nearly always in a negative direction, resulting in a loss directly detrimental to the feasibility of the entire process. The prevention of amounts of energy and time to keep the process at optimum productivity in quantity and quality. To achieve this goal, they have two different strategies at their disposal:

1. acceptance of the heterogeneity, which generates enormous, and not always effective, quality assurance and quality control programs
2. elimination of the heterogeneity through a homogenization process such as bedblending.

The duality between “homogeneity” and “heterogeneity” is not simple, and it cannot be compared to the straightforward kind of duality observed between “black” and “white”.

# 抽样理论代考

## 统计代写|抽样理论作业代写sampling theory代考|总抽样误差

$$T S E=S S E+I P E$$

$$I P E=I P E_1+I P E_2+\ldots+I P E_n+\ldots+I P E_N$$

73
$$T S E=T S E_1+T S E_2+\ldots+T S E_n+\ldots+T S E_N$$

$$\begin{gathered} T S E_n=S S E_n+I P E_n \ T S E=\sum_n\left(S S E_n+I P E_n\right) \end{gathered}$$

## 统计代写|抽样理论作业代写采样理论代考|异质性概念的逻辑介绍

1. 测量或分析误差
2. 采样误差。所有参与研究、开发、生产、质量保证和质量控制的人都直接或间接、认真或不认真地处理抽样问题。这些采样问题的存在是因为所有的材料本质上都是异质的
异质性对所有的过程都是有害的，这些过程是以这样一种方式调节的，即对给定的输入材料的组成获得最佳的输出$X$。一旦输入原料的成分$\mathrm{X}^{\prime}$不同于由严格目标设定的$X$，产出在质量和数量上就会恶化。实际输出与最优输出之间的差异几乎总是负向的，从而导致对整个过程的可行性直接不利的损失。防止大量的精力和时间，以保持过程在数量和质量上的最佳生产力。为了实现这一目标，他们有两种不同的策略:
1. 接受异质性，这产生了大量的，但并不总是有效的质量保证和质量控制程序
2. 通过均匀化过程，如床上混合消除异质性。

“同质性”与“异质性”之间的对偶性并不简单，它不能与“黑”与“白”之间观察到的那种直接的对偶性相比较

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