Compute the upper and lower limits for three sigma $\overline{X}$-chart.

Question

A company makes 16 gm toffees (net weight) for sale. As polity, a toffee is considered unacceptable if the net weight is more than 0.1 gm greater or less than this amount. The company took  20 samples of five toffees each (100 in total) from production line when the process was known to be in control. The average weight for 100 toffees was 16.003 gm and the average range for the 20 samples was 0.093 gm.

1. Compute the upper and lower limits for three sigma $\overline{X}$-chart.
2. Compute the upper and lower limits for three sigma R – chart.
3. Based on (i) and (ii) suppose the company now samples 5 toffees from the production line. The net weight of these toffees are 16.018, 15,870, 16.115, 16.002 and 16.005 gm. Determine whether or not the process is in control. If not, specify what the problem is and how you determined this.                                                                                                                        20

[Given that for sample size of 5

d₂ = 2.33

for R chart UCL_R = d₄ $\overline{R}$ and LCL_R = d₃ $\overline{R}$ where d₄ = 2.11 and d₃ = 0]