Twelve​ samples, each containing five​ parts, were taken from a process that produces steel rods at Emmanual​ Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results​ were:
Sample Sample Mean​ (in.) Range​ (in.) Sample Sample Mean​ (in.) Range​ (in.)
1 11.204 0.033 7 11.201 0.041
2 11.204 0.041 8 11.203 0.034
3 11.189 0.034 9 11.197 0.027
4 11.208 0.051 10 11.201 0.029
5 11.195 0.031 11 11.201 0.039
6 11.197 0.036 12 11.206 0.047
For the given​ data, the x ​= nothing inches ​(round your response to four decimal​ places).
Based on the sampling​ done, the control limits for ​3-sigma x chart​ are:
Upper Control Limit ​(UCLx​) ​= nothing inches ​(round your response to four decimal​ places).
Lower Control Limit ​(LCLx​) ​= nothing inches ​(round your response to four decimal​ places).
Based on the x​-chart, is one or more samples beyond the control​ limits? ▼ Yes No .
For the given​ data, the R ​= nothing inches ​(round your response to four decimal​ places).
The control limits for the ​3-sigma​ R-chart are:
Upper Control Limit ​(UCLR​) ​= nothing inches ​(round your response to four decimal​ places).
Lower Control Limit ​(LCLR​) ​= nothing inches ​(round your response to four decimal​ places).
Based on the​ R-chart, is one or more samples beyond the control​ limits? ▼ Yes No .