QUESTION 15 Information for problems 15-19. Mom\'s Favorite Macaxlamia Nut cooki

Question

QUESTION 15 Information for problems 15-19. Mom's Favorite Macaxlamia Nut cookies have an average of 8 chunks of Macadama nut in each cookie for the perfect taste Too itthe amount of nut degrades the taste of the cookie and too many chunks of Macadamia nut adds cost to the coove The quality control manager takes a sample of 12 cookies each day and records the number of Macadamia chunks in each cookie for 10 days. The average (x bar) and the range of the number of Macadamia chunks of the 12 cookies for 10 days are recorded in the table below bar Range what is the lower (3-?) control limit for the x-bar chart? O 7.114 7.168 7.204 7.276 QUESTION 16 What is the upper (3. ?) control limit for the x-bar chart? 7.924 7.996 8.032 8.086 Stop sharing Proctorio is sharing your screen QUESTION 17

Explanation / Answer

Solution:

Number of observations in each sample (n) = 12

From the given information on X-bar and Range for each day, mean X-bar and mean range are calculated below:

X-double bar = Sum of X-bar / Total Number of days

X-double bar = 76 / 10 = 7.6

R-bar = Sum of Range / Total Number of days

R-bar = 18 / 10 = 1.8

The Upper Control Limit (UCL) and Lower Control Limit (LCL) for x-bar chart is calculated as:

LCL = X-double bar - (A2 x R-bar)

UCL = X-double bar + (A2 x R-bar)

The Upper Control Limit (UCL) and Lower Control Limit (LCL) for R-bar chart is calculated as:

LCL = (D3 x R-bar)

UCL = (D4 x R-bar)

From the 3-sigma chart of constants,

For n = 12 (Number of observations = 12)

A2 = 0.27, D3 = 0.28, D4 = 1.72

Putting these values in the above formulas, we get,

For x-bar chart:

LCL = 7.6 - (0.27 x 1.8) = 7.114

UCL = 7.6 + (0.27 x 1.8) = 8.086

For R-bar chart:

LCL = 0.28 x 1.8 = 0.504

UCL = 1.72 x 1.8 = 3.096

Answers are summarized below:

15) 7.114

16) 8.086

17) 0.504

18) 3.096

19) On the basis of the UCL and LCL of x-bar chart and r-bar chart, we can say that the process is out-of-control because only x-bar chart is out of control.

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