---
title: "Continuous process charts"
author: ""
date: ""
output: html_document
---


The construction of charts for a continuous variable relies on

- The value of $c_4(n)$. Available in `qcc` by the function
  `qcc:::.qcc.c4(n)`.
- The value of $d_2(n)$. The vector
  `qcc.options("exp.R.unscaled")` has
  values for n between 2 and 25.
- The value of $d_3(n)$. The vector
  `qcc.options("se.R.unscaled")` has
  values for n between 2 and 50.

```{r,warning=FALSE,message=FALSE}
library(qcc)
c(qcc:::.qcc.c4(5), qcc.options("exp.R.unscaled")[5], qcc.options("se.R.unscaled")[5])
```
The control plan for a production involves taking samples of size 5.
The results for the last 40 samples is summarized by
$\sum_{i=1}^{40} \bar{x}_i=799$, $\sum_{i=1}^{40}  R_i=84.74$ and 
$\sum_{i=1}^{40}  s_i=34.86$. 

* Compute the 3\*sigma limits for the R chart.

* Compute the 3\*sigma limits for the S chart.

* Compute the 3\*sigma limits for the xbar chart using the sample standard deviations.