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

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## 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

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