Problem:

A machine at the Pacific Fruit Company fills boxes with raisins. The labeled weight of the boxes is 9 oz. The quality control department sampled five boxes at two hour time intervals to construct a control chart. Base your analysis on the eight samples below:

Sample        X-bar              R

   1                 8.71           .66

   2                 8.70           .62

   3                 8.66           .59

   4                 8.78            .58

   5                 8.61            .67

   6                 8.72            .55

   7                 8.69             .70

   8                 8.73             .61

Required:

Question 1) Compute the centerline for the x-bar chart. Compute the centerline for the R-chart.

Question 2) Compute the upper and lower control limits for the X-bar chart.

Question 3) Compute the upper and lower AB zone boundary for the x-bar chart.  

Question 4) Compute the upper and lower control limits for the R chart.

Solve the given numerical problem and illustrate step by step calculation.