Question

Pizazz manufactures a 5.0 oz. energy drink of the same name. Because the cans are so small, consumers are concerned that they are not receiving the full 5 ounces in each can. A quality engineer at the company is charged with analyzing the filling process and ensuring accurate readings. On 15 different occasions over the past month, she has taken a sample of 6 energy drinks off the production line and recorded their weight. The sum of the sample means is 80.20 ounces and the sum of the sample ranges is 12.68 ounces (Hint: You are already given the sum. You just have to find the x-double bar and R-bar).
Determine the control limits of an x-bar and R-chart. What is your conclusion?

Answer 1

Answer:

The LCL of  the R-chart starts from the origin ( i.e. zero value ) while the LCL of an X -chart did not start from the origin

LCL of R-chart = 0 * 0.84533 = 0

LCL of R-chart  = 75.128

Step-by-step explanation:

Given data:

number of observations = 15

sample size ( m ) = 6

sum of sample mean = 80.20 ounces

sum of sample range ( R )  = 12.68 ounces

Determine the control limits of an x-bar and R-chart

for an R-chart

LCL of R-chart = D3 * R(bar) ---- ( 1 )

where : m = 6 ,  D3 = 0 , R = 12.68

            R(bar) = 0.84533

back to equation 1

LCL of R-chart = 0 * 0.84533 = 0

for an X-chart

LCL of X-bar) = ( mean ) - (m x R-bar)

                       = 80.20 - ( 6 * 0.84533 )

                       = 75.128

The LCL of  the R-chart starts from the origin ( i.e. zero value ) while the LCL of an X -chart did not start from the origin