You\'re managing an assembly line that produces high quality 1 liter insulated b

Question

You're managing an assembly line that produces high quality 1 liter insulated bottles that can be used for hot or cold beverages. You sell your products on Amazon and other retail outlets known for high quality and excellent customer service. You produce 1,000 bottles per day and are concerned about the number of defects that result in scrapping the material. Using a sample size of 100, you've collected the following data over the past 30 days) You remember something about defect charts from your OM 370 class and want to determine if your process is in control. a. using the data provided, calculate p bar and your upper and lower control limits. (use 3) b. Based on your answer in part a, is your process in control? c. If your answer to part b. is no, which sample(s) are considered assignable cause variation? (there is no requirement to create a p chart) Day Defects 1 10 2 5 3 15 4 2 5 4 6 7 7 15 8 5 9 17 10 7 11 16 12 6 13 20 14 5 15 13 16 13 17 17 18 21 19 16 20 2 21 3 22 2 23 18 24 16 25 3 26 2 27 4 28 18 29 15 30 10 You're managing an assembly line that produces high quality 1 liter insulated bottles that can be used for hot or cold beverages. You sell your products on Amazon and other retail outlets known for high quality and excellent customer service. You produce 1,000 bottles per day and are concerned about the number of defects that result in scrapping the material. Using a sample size of 100, you've collected the following data over the past 30 days) You remember something about defect charts from your OM 370 class and want to determine if your process is in control. a. using the data provided, calculate p bar and your upper and lower control limits. (use 3) b. Based on your answer in part a, is your process in control? c. If your answer to part b. is no, which sample(s) are considered assignable cause variation? (there is no requirement to create a p chart) Day Defects 1 10 2 5 3 15 4 2 5 4 6 7 7 15 8 5 9 17 10 7 11 16 12 6 13 20 14 5 15 13 16 13 17 17 18 21 19 16 20 2 21 3 22 2 23 18 24 16 25 3 26 2 27 4 28 18 29 15 30 10

Explanation / Answer

Back-up Theory

p-Chart

Central Line: CL = pbar …………………………………………………….(1)

Lower Control Limit: LCL = pbar - 3{pbar(1 - pbar)/n} …………………..(2)

Upper Control Limit: UCL = pbar + 3{pbar(1 - pbar)/n} …………………..(3)

where pbar = mean sample proportions = (1/kn)[1,n](xi) …………………(4)

n = sample size

k = number of samples

xi = number of defectives in the ith sample.

Part (a)

n = 100, k = 30

Central Line: CL = pbar = 303/3000 = 0.101[vide (1) above]

Lower Control Limit: LCL = 0.101 - 3{(0.101 x 0.899)/100}[vide (2) above]

= 0.101 - 30.000908

= 0.101 – (3 x 0.0301)

= 0.101 – 0.0903

= 0.0107

Upper Control Limit: UCL = 0.101 + 0.0903 [vide (3) above]

= 0.1913

Thus, pbar = 0.101, LCL = 0.0107, UCL = 0.1913 ANSWER

Part (b)

Viewing given xi’s against the above limits, it is seen that

Process is out of control. ANSWER

Part (c)

2 points , namely, x13 (20) and x18 (21) are above the UCL ANSWER

Going beyond the asked questions,

Part (d)

Since 2 points are out of limits, it is necessary to revise the control limits after eliminating these out of control points;

CL = 262/(28 x 100) = 0.0936, LCL = 0.0063, UCL = 0.1809

Viewing given xi’s against the above limits, it is seen that Process is under control and hence the above limits can be used for future control. DONE

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