Modeling and Simulation Using Parallel Computing Question answersAll the questions are in the attached file, its a question answer questions. please no Plagiarism. You can use internet answers but please write on your own words.
Student’s Name…………………………………………………… Grade……………
Morgan State University
Department of Ind. & Systems Engineering
Dr. Anselm Tshibangu, LSSMBB, ASQ-CMBB-SSBB-CQE
11/21/2020
Fall 2020
IEGR 499.150 SPECIAL TOPICS: SIX SIGMA GREEN BELTS
Homework # 6
Question 1 (10 points)
The number of nonconformities in shingles is determined for 20 samples, but
The amount of shingles inspected for each sample varies. Results of the inspection are shown in the table below.
Compute (by Hand) CL, UCL, LCL for the first sample (show all calculations)
Construct a control chart for the number of nonconformities per 100 m2.
Sample, i
Amount Inspected (m2)
Number of Nonconformities
1
200
5
2
300
14
3
250
8
4
150
8
5
250
12
6
100
6
7
200
20
8
150
10
9
150
6
10
250
10
11
300
9
12
250
16
13
200
12
14
250
10
15
100
6
16
200
8
17
200
5
18
100
5
19
300
14
20
200
8
Solution
Question 2 (30 points)
In an assembly manufacturing, joint defects on a sub-assembly (SA) may result from the combination of several specifications of design parameters such as a component pad size, drill hole size, fabrication quality of plated metal surface, and the material and process parameters of the joining equipment. Assuming a 100 PPM sub-assembly process (1 joint defect in 10, 000 joints),
Calculate Cpk (assuming a two-sided specification).
If the joining equipment is a wire bond machine for which it could be assumed that the defects occur due to one side of the specification limits of minimum pull strength. Calculate Cpk in this case.
Assuming you are in a quality team that has to report on their progress toward six sigma using 100 PPM current defect rate, calculate the design specifications expressed in number of sigma for two-sided specifications (in the classical six sigma definition)
Re-do part c) for one sided-specification.
Question 2 (40 points)
A variable control chart for a beam tensile strength was created. There is only one minimum specification for resistance. The (double bar) was 20, 000 kN (kilo Newton) and the UCLx was 23000 kN, with a sample size of 9. A new specification was adopted to keep resistance at a minimum of 16 kN. Assuming that the tensile strength measurement or process average = specification nominal (N),
Compute Cp
Calculate Cpk
Determine rejection rates
Show the R chart limits
A four sigma program was introduced at the company. For the surface resistance process, the lower specification limit (LSL) remained at 16000 kN and the process σ remained the same, redo calculations to compute Cp, Cpk, and reject rates
Show the X-bar and R chart limits, using the same sample size of 9.
Repeat for a six sigma program, with 1.5 σ shift, with the process average and sigma remaining the same. Consider a shift towards the LSL.
A new contract was written with a supplier to deliver parts with the following stipulation: Cpk = 0.85 and part specification = mils. The supplier kept control of their process by using a variable control chart with sample size n =4. Calculate the Cp and the X-bar and variable chart limits.
Question 4 (20 points)
You work at an automobile engine assembly plant. One of the parts, a camshaft, must be 600 mm +2 mm long to meet engineering specifications. There has been a chronic problem with camshaft length being out of specification, which causes poor-fitting assemblies, resulting in high scrap and rework rates. Your supervisor wants to run X and R charts to monitor this characteristic, so for a month, you collect a total of 100 observations (20 samples of 5 camshafts each) from all the camshafts used at the plant, and 100 observations from each of your suppliers.
First you will look at camshafts produced by each Supplier and state your conclusions
Second, suggest a supplier to your supervisor and
Third, what are your observations about the camshaft used in the shop this month.
Length
Supp1
Supp2
601.4
598.0
601.6
601.6
599.8
600.4
598.0
600.0
598.4
601.4
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600.0
600.0
602.8
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598.8
600.8
601.2
598.2
603.6
598.4
599.4
604.2
599.0
599.6
602.4
601.2
599.4
598.4
601.0
599.4
599.6
600.8
600.0
603.4
597.6
598.8
600.6
601.6
599.2
598.4
599.4
599.4
598.2
601.2
599.6
602.0
598.4
599.0
599.4
599.2
599.2
599.4
598.8
600.6
600.8
601.4
598.8
600.8
599.0
598.8
598.6
601.0
599.8
600.0
601.6
599.2
600.4
601.4
599.4
600.8
601.4
600.0
600.8
598.8
600.2
597.2
601.4
600.2
600.4
598.4
599.6
599.8
601.6
599.0
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598.8
599.0
600.4
601.2
599.8
598.2
599.6
600.8
598.6
601.2
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599.6
598.2
598.2
599.0
598.8
600.0
598.2
597.8
599.2
599.4
598.2
599.8
599.4
598.2
601.2
600.2
598.2
600.4
599.0
601.2
600.2
599.4
600.0
599.6
598.0
598.8
599.6
597.6
599.4
599.6
598.0
597.2
600.2
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600.8
599.2
601.2
600.6
599.0
599.0
599.6
599.6
600.4
599.4
600.4
600.6
598.0
600.0
599.0
600.8
599.0
602.2
597.8
599.6
599.8
599.2
599.4
599.8
599.2
599.2
601.0
600.6
597.8
601.6
598.0
600.4
601.6
598.0
599.6
600.2
598.8
600.0
601.8
601.0
600.8
601.2
600.8
600.4
597.6
598.8
599.4
599.8
599.4
599.0
602.8
601.0
598.4
600.0
598.8
599.0
599.6
599.6
599.6
602.2
599.0
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603.8
600.4
599.2
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599.6
601.8
602.2
598.6
602.0
601.0
599.8
603.6
601.4
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600.8
601.0
599.2
600.2
601.2
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600.4
601.4
600.2
600.2
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599.8
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601.6
599.6
598.0
601.0
600.0
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600.2
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601.0
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600.0
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601.4
599.4
602.2
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599.8
600.6
598.8
599.2
596.2
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601.8
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599.6
600.0
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599.4
596.8
Solution
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