A Quality Analyst wants to construct a control chart for determining whether four machines,all producing the same product,are under control with regard to a particular quality attribute.Accordingly,she inspected 1,000 units of output from each machine in random samples,with the following results: What are the control chart upper and lower control limits for an alpha risk of .05?
A).0272 and .0128
B).0289 and .0111
C).029 and .013
D).0303 and .0097
E).0332 and .0068

Question

A Quality Analyst wants to construct a control chart for determining whether four machines,all producing the same product,are under control with regard to a particular quality attribute.Accordingly,she inspected 1,000 units of output from each machine in random samples,with the following results:  What are the control chart upper and lower control limits for an alpha risk of .05?
A).0272 and .0128 
B).0289 and .0111 
C).029 and .013 
D).0303 and .0097 
E).0332 and .0068

Quizplus · Accepted Answer

To find the upper control limit (UCL) and lower control limit (LCL) for the control chart, we need to first calculate the mean and standard deviation for the data.

Mean (x̄) = (11+18+15+16)/4 = 15

Range (R) = Maximum value - Minimum value 
Machine 1: 16-11 = 5 
Machine 2: 25-11 = 14 
Machine 3: 20-11 = 9 
Machine 4: 21-11 = 10

Average range (R̄) = (5+14+9+10)/4 = 9.5

Standard deviation of range (S) = R̄/d2 = 9.5/2.059 = 4.61

Upper control limit (UCL) = x̄ + A2*R̄ = 15 + 0.577*9.5 = 20.52

Lower control limit (LCL) = x̄ - A2*R̄ = 15 - 0.577*9.5 = 9.48

At an alpha risk of 0.05, A2 = 0.577. The closest answer to our calculated UCL and LCL is B (.0289 and .0111).

A Quality Analyst Wants to Construct a Control Chart for Determining