Introduction
In inferential statistics, sample data is analyzed to make general assumptions and estimate a population parameter. The confidence interval provides the probability of accuracy, which falls between the range of interval of numbers, the upper boundary, and the lower boundary. For example, suppose we have 100 samples, we do not know the population means μ, but we know that the population standard deviation (σ) is = 1. Then, by the central limit theorem, the standard deviation (SD) of the sampling distribution of the sample means is σ/√(n)= 1/√100=0.1. The empirical rule applies that 95% of the sample distribution will be within or approximately two standard deviations of the population mean ©. That mean two SD from the mean will be μ = mean ± 2(σ/√100), at 95% confidence intervals.
Figure 1.
Confidence level and accuracy table
Figure 2.
Distribution graph
Process Control
A control chart (Shewhart Chart) is a graphical representation of process behavior using the data point obtained from a process. Benchmark or centerline (Average) is set or created from the available datasets to represent a model or target variable, with upper and lower limits as cut-off points to the expected result from the process. With the mean representing the desired outcome, an assumption can be made that that population means is equal to the sample mean when using a large selection (>30 data points).
When and why to use a control chart
1. Monitor process
2. Establish predictions for a process
3. Diagnose a process (common or natural cause, random cause or special cause, or sporadic cause)
The process graph limits provide a standard for measuring process stability, control, consistency, or out of control (affected by special causes)
Are rea between UCL and LCL: 99.73% confidence intervals (3 STDs)
Uploading python library
Figure 3
Code
