Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are in control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results.

Machine 1 Measirement 17 15 15 17
Machine 2 Measurement 16 25 18 25
Machine 3 Measurement 23 24 23 22

What are the Mean chart three-sigma upper and lower control limits?

a. 22 and 18
b. 23.16 and 16.84
c. 22.29 and 16.71
d. 23.5 and 16.5
e. 24 and 16

Sagot :

Tundexi

Answer:

b. 23.16 and 16.84

Explanation:

Mean (X-bar) = Sum of observations / No of observations

Range (R) = Highest observation - Lowest observation

Machine 1

Mean (X-bar) = (17 + 15 + 15 + 17) / 4

Mean (X-bar) = 16

Range (R) = (17 - 15)

Range (R) = 2

Machine 2

Mean (X-bar) = (16 + 25 + 18 + 25) / 4

Mean (X-bar) = 21

Range (R) = (25 - 16)

Range (R) = 9

Machine 3

Mean (X-bar) = (23 + 24 + 23 + 22) / 4

Mean (X-bar) = 23  

Range (R) = (24 - 22)

Range (R) = 2

Mean of means (X-double bar) = Sum of X-bar / Number of samples = (16 + 21 + 23) / 3 = 20

Mean of ranges (R-bar) = Sum of R / Number of samples = (2 + 9 + 2) / 3  = 4.33

From table of constants for calculating the 3-sigma upper and lower control limits, For n = 4, A2 = 0.729

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

UCL = 20 + (0.729 x 4.33)

UCL = 23.1566

UCL = 23.16

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

LCL = 20 - (0.729 x 4.33)

LCL = 16.8434

LCL = 16.84

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.