Assignment 2: Controls As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weights of the boxe

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Unit 4: Module 4 - M4 Assignment 2

 Assignment 2: Controls

As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weights of the boxes. Provide your recommendations to the Operations Manager in a two-three page report. Using the data provided in the Doc Sharing area labeled M4A2Data, create Xbar and R charts.

Your report should indicate the following along with valid justifications of your answers:

a. The control limits of the weights of the boxes.

b. Nonrandom patterns or trends, if any.

c. If the process is in control.

d. The appropriate action if the process is not in control..

Assignment 2 Grading Criteria

Maximum Points

Using the data provided created Xbar and R charts.

15

Set control limits for the weights of the boxes.

15

Established the criteria for nonrandom patterns or trends, if any.

15

Stated whether the process is in control, according to the limits and the criteria established in b and c above.

15

Suggested the appropriate action if the process is not in control.

15

Gave valid and supported reasons for their answer.

15

Used correct grammar, spelling, and word choice and cited all sources using correct APA style.

10

Total:

100

1. Find the mean of each subgroup Xbar(1), Xbar(2), Xbar(3)... Xbar(k) and the grand mean of all subgroups using:

2. Find the UCL and LCL using the following equations:

                               A(3) can be found in the following table:                                n   A(3)      n   A(3)                                2   2.659    6   1.287                                3   1.954    7   1.182                                4   1.628    8   1.099                                5   1.427    9   1.032

3. Plot the LCL, UCL, centerline, and subgroup means

4. Interpret the data using the following guidelines to determine if the process is in control:

· One point outside the 3 sigma control limits

· Eight successive points on the same side of the centerline

· Six successive points that increase or decrease

· Two out of three points that are on the same side of the centerline, both at a distance exceeding 2 sigmas from the centerline

· Four out of five points that are on the same side of the centerline, four at a distance exceeding 1 sigma from the centerline f. Using an average run length (ARL) for determining process anomalies

Example: The following data consists of 20 sets of three measurements of the diameter of an engine shaft.

n

 

#1

 

#2

 

#3

 

StdDev

 

Xbar

1

 

2.0000

 

1.9998

 

2.0002

 

0.0002

 

2.0000

2

 

1.9998

 

2.0003

 

2.0002

 

0.0003

 

2.0001

3

 

1.9998

 

2.0001

 

2.0005

 

0.0004

 

2.0001

4

 

1.9997

 

2.0000

 

2.0004

 

0.0004

 

2.0000

5

 

2.0003

 

2.0003

 

2.0002

 

0.0001

 

2.0003

6

 

2.0004

 

2.0003

 

2.0000

 

0.0002

 

2.0002

7

 

1.9998

 

1.9998

 

1.9998

 

0.0000

 

1.9998

8

 

2.0000

 

2.0001

 

2.0001

 

0.0001

 

2.0001

9

 

2.0005

 

2.0000

 

1.9999

 

0.0003

 

2.0001

10

 

1.9995

 

1.9998

 

2.0001

 

0.0003

 

1.9998

11

 

2.0002

 

1.9999

 

2.0001

 

0.0002

 

2.0001

12

 

2.0002

 

1.9998

 

2.0005

 

0.0004

 

2.0002

13

 

2.0000

 

2.0001

 

1.9998

 

0.0002

 

2.0000

14

 

2.0000

 

2.0002

 

2.0004

 

0.0002

 

2.0002

15

 

1.9994

 

2.0001

 

1.9996

 

0.0004

 

1.9997

16

 

1.9999

 

2.0003

 

1.9993

 

0.0005

 

1.9998

17

 

2.0002

 

1.9998

 

2.0004

 

0.0003

 

2.0001

18

 

2.0000

 

2.0001

 

2.0001

 

0.0001

 

2.0001

19

 

1.9997

 

1.9994

 

1.9998

 

0.0002

 

1.9996

20

 

2.0003

 

2.0007

 

1.9999

 

0.0004

 

2.0003

Sbar chart limits: SBAR = 0.0002

UCL = B(4) x SBAR = 2.568 x .0002 = 0.0005136 LCL =  B(3) x SBAR = 0 x .0002 = 0.00

Xbar chart limits: XDBLBAR = 2.0000

UCL = XDBLBAR + A(3) x SBAR   =   2.000+1.954 x .0002  = 2.0003908 LCL =  XDBLBAR - A(3) x SBAR   =    2.000-1.954 x 0002  = 1.9996092

S-Chart:

Xbar Chart:

Note: The following consists of 12 sets of three box weights in ounces

N

#1

#2

#3

StdDev

Xbar

1

6.3

6.28

6.26

0.02

6.28

2

6.32

6.32

6.33

0.005773503

6.32333333

3

6.29

6.33

6.36

0.035118846

6.32666667

4

6.3

6.29

6.34

0.026457513

6.31

5

6.295

6.315

6.39

0.050083264

6.33333333

6

6.292

6.319

6.33

0.019553346

6.31366667

7

6.289

6.323

6.4

0.0568712

6.33733333

8

6.286

6.327

6.471

0.097161378

6.36133333

9

6.283

6.331

6.498

0.112855365

6.37066667

10

6.28

6.335

6.525

0.128549601

6.38

11

6.277

6.339

6.39

0.056589163

6.33533333

12

6.274

6.343

6.4

0.063095166

6.339