Problem:

Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows:

Sample Number                                    Readings (in ohms)
                          
  1                       1010                   991           985             986
  2                        995                    996          1009            994  
  3                        990                  1003          1015          1008
  4                       1015                  1020         1009            998
  5                       1013                  1019          1005           993
  6                        994                   1001           994          1005
  7                        989                     992           982          1020
  8                       1001                   986            996            996
  9                       1006                   989          1005          1007
10                        992                 1007          1006            979
11                        996                  1006           997            989
12                       1019                   996           991          1011
13                        981                   991           989           1003
14                        999                   993           988             984
15                       1013                  1002       1005            992
                                           
Required:

Develop an X-chart and an R-chart and plot the values. From the charts, what comments can you make about the process? Solve the given numerical problem and illustrate step by step calculation.