A soft drink bottle filling facility has been operating in the region PIKE for the past three decades Recently, the facility replaced the existing filling systems with new systems While the contractor firm who was responsible for the replacement project promised the machine will be functioning really really well, the firm needed to know more about the characteristics of the process There were total two machines replaced The process characteristics study data are provided in a separate Excel spreadsheet Their primary customer is looking for the following specifications 16 9 0 18 For question 1) 3), please complete in Excel, then fill in all the answers in the table comes in the next page In your submission, please also attach your Excel file as a reference Please analyze each column of data separately Please construct the histograms for each column to discuss what is the mean, standard deviation, and the shape of the distribution Hint one of the machines is operating more like a uniform distribution In case of a uniform distribution, its mean is1 2(max min , the variance is 1 12(max min) 2 Assuming the sample results are a very good representation of the actual working condition, what is the DPMO for both systems Also, for both systems, please find out the C pk (Hint the specifications are provided in the description) Assuming the loss function constant is k 8, which machine will generate a greater loss Please fill all the blanks in the table below (You should have already calculated all of them) Machine A Machine B Mean SD Shape LSL USL C pk C pu C pl Proportion Defect Too small Too big DPMO k Variance Deviation 2 Expected Loss Which system is a better system What is your conclusion when you compare two systems using the C pk Does that conclusion sustain when DPMO is being used for the comparison What about when the expected loss is being used for the comparison Please briefly discuss this issue by explaining the definition of C pk , DPMO, and EL in your own words and advise me on which measurement should be used in order to determine which one is a better system

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Oct 06, 2024

A soft-drink bottle filling facility has been operating in the region PIKE for the past three decades. Recently, the facility replaced the existing filling systems

A soft-drink bottle filling facility has been operating in the region PIKE for the past three decades. Recently, the facility replaced the existing filling systems with new systems. While the contractor firm who was responsible for the replacement project promised the machine will be functioning really really well, the firm needed to know more about the characteristics of the process. There were total two machines replaced. The process characteristics study data are provided in a separate Excel spreadsheet. Their primary customer is looking for the following specifications: 16.9 0.18

For question 1) ~ 3), please complete in Excel, then fill in all the answers in the table comes in the next page. In your submission, please also attach your Excel file as a reference.

Please analyze each column of data separately. Please construct the histograms for each column to discuss what is the mean, standard deviation, and the shape of the distribution. Hint: one of the machines is operating more like a uniform distribution. In case of a uniform distribution, its mean is1/2(max+min , the variance is 1/12(max-min)^2
Assuming the sample results are a very good representation of the actual working condition, what is the DPMO for both systems? Also, for both systems, please find out the C_pk. (Hint: the specifications are provided in the description)
Assuming the loss function constant is k = 8, which machine will generate a greater loss?

Please fill all the blanks in the table below

(You should have already calculated all of them)

	Machine A	Machine B
Mean
SD
Shape
LSL
USL
C_pk
C_pu
C_pl
Proportion Defect
Too small
Too big
DPMO
k
Variance
Deviation^2
Expected Loss

Which system is a better system? What is your conclusion when you compare two systems using the C_pk? Does that conclusion sustain when DPMO is being used for the comparison? What about when the expected loss is being used for the comparison? Please briefly discuss this issue by explaining the definition of C_pk, DPMO, and EL in your own words and advise me on which measurement should be used in order to determine which one is a better system.