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## 统计代写|非参数统计代写Nonparametric Statistics代考|The Markov Chain Approach

Some theory and concepts in the area of what is called a finite homogeneous MC have been applied to derive the run-length distribution and various characteristics of the run-length distribution of some time-weighted charts, such as the CUSUM and the EWMA. The reader can look up, for example, Fu and Lou (2003) and Balakrishnan and Koutras (2002) for a more detailed treatment of the topics; however, most existing SPC books don’t seem to treat this important topic. In this section, some of the basic terminologies, definitions, results, and theorems are provided that give the necessary background for calculating the run-length distribution of some control charts via the $\mathrm{MC}$ approach. These theorems and results are critical to the following chapters; illustrations are provided.

The $\mathrm{MC}$ approach entails that the charting statistic is viewed as following a MC (as a stochastic process), with a state space $S$ and a transition probability matrix $M$. The state space consists of two types of states:

1. one absorbing state (i.e., this state is entered when the chart signals, i.e., when the charting statistic is greater than or equal to the $U C L$, or less than or equal to the $L C L$ for a two-sided chart); and
2. $\nu$ transient or non-absorbing states, so that there are $\nu+1$ states in total.

The $(\nu+1) \times(\nu+1)$ transition probability matrix, $M$, is often written in a partitioned form
where the sub-matrix $Q_{\nu \times \nu}$ contains all the probabilities of going from one transient state to another and is called the essential transition probability matrix. The column vector $\underline{p}{\nu \times 1}$ contains all the probabilities of going from each transient state to the absorbing state; $\underline{0}{1 \times \nu}^{\prime}$ is a row vector of zeros, consisting of the probabilities of going from the absorbing state to each transient state (which are all zero), and the scalar value 1 is the probability of staying in the absorbing state once it has been entered. Note that the key component in using the MC approach is to obtain the essential transition probability matrix $Q_{\nu \times \nu}$.

## 统计代写|非参数统计代写Nonparametric Statistics代考|The Integral Equation Approach

The integral equation approach utilizes mathematics and combinatorics to find a closed form expression of the run-length distribution. This approach is sometimes challenging in that the expression obtained is typically complex or difficult to evaluate numerically. Often, the exact expression of the run-length distribution can be found after a considerable amount of work, but here a simulation is done instead, since it is much easier.

## 统计代写|非参数统计代写Nonparametric Statistics代考|The Markov Chain Approach

1. 一种吸收状态（即，当图表发出信号时，即当图表统计大于或等于在C大号，或小于或等于大号C大号对于双面图表）；和
2. n瞬态或非吸收状态，因此有n+1共州。

，其中子矩阵问n×n包含从一种瞬态到另一种瞬态的所有概率，称为基本转移概率矩阵。列向量p―n×1包含从每个瞬态到吸收状态的所有概率；0―1×n′是一个由零组成的行向量，由从吸收状态到每个瞬态（全为零）的概率组成，标量值 1 是进入吸收状态后保持在吸收状态的概率。请注意，使用 MC 方法的关键部分是获得基本转移概率矩阵问n×n.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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## 统计代写|非参数统计代写Nonparametric Statistics代考|The 1-of-1 Runs-type Signaling Rule

The most commonly used and least complex charts are the usual Shewhart charts, called 1-of-1 charts, which are not supplemented by any runs-rules. However, they are known to be insensitive in detecting small process shifts. These charts signal when the event $A_{1}$ or $A_{2}$, or $\left(A_{1} \cup A_{2}\right)$ occurs, respectively, where

1. The 1-of-1 runs-type signaling rule for an upper one-sided chart: $A_{1}:\left{Q_{i} \geq U C L\right} \leftrightarrow\left{\xi_{i}^{+}=1\right}$
2. The 1-of-1 runs-type signaling rule for a lower one-sided chart: $A_{2}:\left{Q_{i} \leq L C L\right} \leftrightarrow\left{\xi_{i}^{-}=1\right}$.
3. The 1-of-1 runs-type signaling rule for a two-sided chart: $A:\left{Q_{i} \geq U C L \cup Q_{i} \leq L C L\right} \leftrightarrow\left{A_{1} \cup A_{2}\right} \leftrightarrow\left{\xi_{i}^{+}=1 \cup \xi_{i}^{-}=1\right} \leftrightarrow$ $\left{\xi_{i}=1 \cup \xi_{i}=2\right}$
Figure $3.12$ illustrates points (i) and (ii) of the 1-of-1 runs-type signaling rule for an upper one-sided and a lower one-sided chart, respectively. Panel (a) detects an upward shift at time $i=7$ when $Q_{7}$ plots above the $U C L$, whereas Panel (b) detects a downward shift at time $i=7$ when $Q_{7}$ plots below the $L C L$. For each chart the process is declared OOC and a search for assignable causes can be started.

## 统计代写|非参数统计代写Nonparametric Statistics代考|The k-of-k and k-of-w Runs-type Signaling Rules

Several runs-type signaling rules, such as the 2-of-2 and 2-of-3 runs-rules, have been investigated by many authors and proved that their “runs-rules enhanced” charts outperform the 1-of-1 chart.

One-sided $k$-of- $k$ and $k$-of- $w$ Runs-type Signaling Rules To illustrate, we start with the 2-of-2 runs-type signaling rule. This rule uses the last two charting statistics, $Q_{i-1}$ and $Q_{i}$, to determine whether the process is IC or OOC. For the 2-of-2 runs-type signaling rule, an upper one-sided chart signals when event $B_{1}$ occurs and a lower one-sided chart signals when event $B_{2}$ occurs where

1. an upper one-sided chart supplemented by a 2-of-2 runs-type signaling rule: $B_{1}:\left{\xi_{i-1}^{+}=\xi_{i}^{+}=1\right}$
2. a lower one-sided chart supplemented by a 2-of-2 runs-type signaling rule: $B_{2}:\left{\xi_{i-1}^{-}=\xi_{i}^{-}=1\right}$.

Panels (a) and (b) in Figure $3.14$ illustrate these signaling events $B_{1}$ and $B_{2}$, and both signal at time $i=7$ where two consecutive points plots above (below) the $U C L(L C L)$. For each chart, the process is declared $\mathrm{OOC}$ and a search for assignable causes can be started.

## 统计代写|非参数统计代写Nonparametric Statistics代考|The 1-of-1 Runs-type Signaling Rule

1. 上单面图表的 1-of-1 运行类型信号规则：\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别
2. 下单面图表的 1-of-1 运行类型信号规则：\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别.
3. 双面图表的 1-of-1 运行类型信号规则：\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别 \left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别
数字3.12分别说明了上单面和下单面图表的 1-of-1 运行类型信号规则的点 (i) 和 (ii)。面板 (a) 检测到时间上移一世=7什么时候问7地块上方在C大号，而面板 (b) 检测到时间向下移动一世=7什么时候问7下面的地块大号C大号. 对于每个图表，该过程被声明为 OOC，并且可以开始搜索可分配的原因。

## 统计代写|非参数统计代写Nonparametric Statistics代考|The k-of-k and k-of-w Runs-type Signaling Rules

1. 由 2-of-2 运行类型信号规则补充的上单面图表：\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别
2. 一个较低的单边图表，辅以 2-of-2 运行类型的信号规则：\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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## 统计代写|非参数统计代写Nonparametric Statistics代考|Sensitivity Rules

While the Shewhart control chart is effective in detecting large process shifts, it has been shown that it lacks sensitivity in detecting small process shifts. The papers by Koutras, Bersimis, and Maravelakis, (2007) and Park and Seo (2012) present literature reviews on Shewhart charts with supplementary sensitizing rules based on runs and scans to improve the effectiveness of Shewhart control charts for detecting small shifts. Sensitizing rules are signaling rules designed to detect some improbable and/or non-random pattern of the charting statistics on a control chart. We start by discussing the well-known Western Electric rules and, following this, we discuss other supplementary sensitizing rules based on runs and scans.
The Western Electric rules make use of warning limits, typically set at a distance of 1-sigma or 2-sigma from the $C L$ to determine whether the process is IC or OOC. The Western Electric rules (Western Electric Company, 1956) are listed below. The chart will signal if any one of these conditions is met.

1. One or more points on or outside the control limits.
2. Two of three consecutive points plot outside the 2-sigma warning limits but still inside the control limits.
3. Four of five consecutive points above the 1-sigma limits.
4. A run of eight consecutive points on one side of the CL.

## 统计代写|非参数统计代写Nonparametric Statistics代考|

The repeat construct is less frequently used, but adds flexibility as termination will always depend on a call to break(), which can be located anywhere within the compound statement that forms the body of the loop. To achieve conditional end of iteration, function break() must be called, as otherwise, iteration in a repeat loop will not stop.

approach of adding print() statements, as described on page $101 .$
Although repeat loop constructs are easier to read if they have a single condition resulting in termination of iteration, it is allowed by the R language for the compound statement in the body of a loop to contain more than one call to break(), each within a different if or else statement.

## 统计代写|非参数统计代写Nonparametric Statistics代考|Sensitivity Rules

Western Electric 规则使用警告限制，通常设置在距离控制器 1-sigma 或 2-sigma 的位置。C大号判断流程是IC还是OOC。西部电气规则（西部电气公司，1956 年）如下所列。如果满足这些条件中的任何一个，图表将发出信号。

1. 一个或多个点在控制限之上或之外。
2. 三个连续点中有两个位于 2-sigma 警告范围之外，但仍在控制范围内。
3. 连续五个点中的四个超过 1-sigma 限制。
4. 在 CL 的一侧连续八个点。

## 统计代写|非参数统计代写Nonparametric Statistics代考|

repeat 构造的使用频率较低，但增加了灵活性，因为终止将始终依赖于对 break() 的调用，它可以位于构成循环体的复合语句中的任何位置。要实现迭代的条件结束，必须调用函数break()，否则重复循环中的迭代将不会停止。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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## 统计代写|非参数统计代写Nonparametric Statistics代考|STATS205 Design of Control Charts

avatest非参数统计Nonparametric Statistics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest™， 最高质量的非参数统计Nonparametric Statistics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此非参数统计Nonparametric Statistics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在网课代考方面已经树立了自己的口碑, 保证靠谱, 高质且原创的网课代修服务。我们的专家在非参数统计Nonparametric Statistics代写方面经验极为丰富，各种非参数统计Nonparametric Statistics相关的作业也就用不着 说。

## 统计代写|非参数统计代写Nonparametric Statistics代考|Sample Size, Sampling Frequency, and Variable Sample Sizes

The sample size and the sampling frequency (the length of time between two consecutive samples) must be specified before a chart can be implemented. These depend on considerations such as time and cost, and the size of the shift to be detected. Both can impact the statistical performance of the chart. Larger samples can detect smaller shifts but are more expensive and time consuming, whereas smaller samples can be sufficient if the expected shift is large

Frequency of sampling, that is, how often to collect data, is impacted by conditions on the ground, so to speak, that is, again, time and cost and expected shift. Obviously, it is desirable to take large samples as frequently as possible, but this is probably not going to be feasible. We can generally take smaller samples at shorter time intervals (more frequency) or larger samples at longer time intervals (less frequently). Current industry practice favors the former approach. Automated data collection facilities have made this process much easier, so much so that it is not uncommon to sample and inspect every item that is produced.

The appropriate sample size can be determined by looking at the underlying process variability and the size of the shift. Generally, a process with a relatively large inherent variation requires reasonably larger samples to detect an OOC condition as opposed to a process with a relatively small inherent variation. In general, it is also easier to detect a small shift using larger samples as opposed to when the process shift is relatively large, for which smaller samples would be sufficient.

## 统计代写|非参数统计代写Nonparametric Statistics代考|Variable Control Limits

Although the former approach to variable sample sizes makes the calculations and interpretation of the control charts easier, with the availability of current computer technology it is natural to try to calculate the exact control limits based on the actual size $n_{i}$ of each sample. Here, the control limits are calculated separately for each subgroup based on the subgroup size $n_{i}$. This implies that the spread between the $U C L$ and the $L C L$ will vary (increase or decrease) as the sample size varies. However, the varying width is merely an indication of the varying amount of information available from each sample, as portrayed by the different sample sizes. Consequently, the visual representation of these control limits is not as attractive as those based on the average sample size with constant control limits. On the one hand, having fixed rather than varying control limits is definitely more pleasing to the eye. On the other hand, the interpretation of these variable control limits is still the same. If a point plots on or above the $U C L$ or on or below the $L C L$, it is regarded as a signal of a possible OOC process, whereas a point that plots between the two control limits is regarded as no signal and is associated with an $\mathrm{IC}$ process.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Nonparametric Statistics, 统计代写, 统计代考, 非参数统计

## 统计代写|非参数统计代写Nonparametric Statistics代考|STATS205 Sample Size or Subgroup Size

avatest非参数统计Nonparametric Statistics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest™， 最高质量的非参数统计Nonparametric Statistics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此非参数统计Nonparametric Statistics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在网课代考方面已经树立了自己的口碑, 保证靠谱, 高质且原创的网课代修服务。我们的专家在非参数统计Nonparametric Statistics代写方面经验极为丰富，各种非参数统计Nonparametric Statistics相关的作业也就用不着 说。

## 统计代写|非参数统计代写Nonparametric Statistics代考|Sample Size or Subgroup Size

Data must be collected before a control chart can be implemented. In practice, the data are usually collected in batches or samples, each typically with $n$ observations, taken at random at equally spaced time points. The batches are also called subgroups and such data are referred to as subgrouped data. The sample size $n$ generally is a small number, around five, although there are applications in the modern environment where every individual data point can be and is inspected. Such data are commonly referred to as individual data. In this case $n=1$. Some cases where individual values are monitored include, for example, where:

• Production may be extremely slow and collecting more than one observation is not practical.
• There is no rational way for subgrouping the data.
• It may be that a sample of more than one is not justified economically.
We will treat the individual observations case later under control charts for individual observations.

## 统计代写|非参数统计代写Nonparametric Statistics代考|Rational Subgrouping

A rational subgroup is a sample or a subgroup taken from the process so that the variation among the measurements, or observations within the sample, is only due to the inherent or natural variability of the process, and no additional variation due to any special causes is present within the sample measurements. Rational subgroups are those subgroups that contain or enclose only the common/chance causes. The variation among the readings should be due to the natural process variation. There should be no opportunity for assignable/special causes to add to this variation.

## 统计代写|非参数统计代写Nonparametric Statistics代考|Sample Size or Subgroup Size

• 生产可能非常缓慢，收集多个观察结果是不切实际的。
• 没有合理的方法对数据进行分组。
• 一个以上的样本可能在经济上是不合理的。
稍后我们将在个别观察的控制图下处理个别观察的情况。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Nonparametric Statistics, 统计代写, 统计代考, 非参数统计

## 统计代写|非参数统计代写Nonparametric Statistics代考|CSTAT6610 onstruction of Control Charts

avatest非参数统计Nonparametric Statistics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest™， 最高质量的非参数统计Nonparametric Statistics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此非参数统计Nonparametric Statistics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在网课代考方面已经树立了自己的口碑, 保证靠谱, 高质且原创的网课代修服务。我们的专家在非参数统计Nonparametric Statistics代写方面经验极为丰富，各种非参数统计Nonparametric Statistics相关的作业也就用不着 说。

## 统计代写|非参数统计代写Nonparametric Statistics代考|Construction of Control Charts

The charting statistic has been mentioned previously, and statistical considerations such as unbiasedness, minimum variance, robustness, and efficiency are generally employed in the choice of this statistic. In order to monitor the central tendency or the location of a process, for example, the sample mean (X¯) or the sample median (X~) is often used. Alternatively, the sample range (R), the sample standard deviation (S), and the sample variance (S2) are used to monitor the process spread, standard deviation, or variance, respectively. Once a charting statistic is chosen, we use its probability distribution, along with some desired chart performance criteria, to be discussed soon, to set up the control limits. Many of the classical control charts have been developed under the assumption that the process distribution is normal. Sometimes, the charting statistic is an average or a statistic for which the central limit theorem can be used to invoke approximate normality without an explicit normality assumption about the process distribution. When normality or some other distributional assumption (such as exponentiality) is made about the process, the control chart is called parametric. When such a distributional assumption cannot be made or justified, alternative control charts are available, which are called nonparametric or distribution-free. Such charts are discussed in detail in Chapter 4.

## 统计代写|非参数统计代写Nonparametric Statistics代考|Variables and Attributes Control Charts

Variables are characteristics that we are interested in monitoring. In order for a variable to be monitored, it must be measurable. There are mainly two types of variables: quantitative and qualitative (categorical). Quantitative variables can be continuous or discrete. In SPC, the terminology variables data refers to measurements on quantitative continuous variables. Examples include data on variables such as length, width, temperature, weight, volume, etc., each of which is a continuous variable. Depending on the parameter, the charting statistic can be the sample mean (X¯), the sample median (X~), the sample range (R), the sample standard deviation (S), or the sample variance (S2). For a variables control chart, the charting statistic follows a continuous distribution.

Conversely, the terminology attributes data refers to recordings or measurements on quantitative discrete variables. Examples include the number of errors or mistakes made in completing a loan application, or the number of medical errors made in a hospital. For an attributes control chart, the charting statistic is discrete and follows a discrete distribution, for example, the charting statistic can be the fraction nonconforming (p), the number nonconforming (np), the number of nonconformities (c), or the average number of nonconformities per unit (c).

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。