Plot F(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 (all curves should be in one Figure for range of t/C varying from (0+=0.05) to 4). Hint use Normal Distribution Function(select True) of Excel subroutine for Z=-

Mechanical Engineering Department

ME 406- Manufacturing and Design

Project A (Engineering Statistics and Manufacturing)

Title of the Project

Quality Control, Regression Analysis, and Models Fitting

Term 171

Class Section- xx

Project Team – Group X_X

xxxxxxxxx Name 1 (Group Coordinator)

xxxxxxxxx Name 2

xxxxxxxxx Name 3

xxxxxxxxx Name 4

Assigned on 13th November 2017

Due on 4th January 2018 (Before Exam starts)

Note Please Attempt each question as asked using the software where ever mentioned. Full Report generated by STATGRAPHICS Must be included in Problems 1 .All Excel sheets be included in PROBLEMS where Excel has been used such as in Q

Each problem should be started on separate page after pasting the the problem statement at the top of the page. Your Solution will be typewritten.

A hard copy as (WORD +EXCELL SHEETS) be provided along with a Hard copy in PDF format. Plus Software generated reports

A soft copy as a CD (WORD +EXCELL SHEETS) be provided along with a soft copy copy in PDF format. Plus Software generated reports. CD Must have mentioned that it is STSTISTICS PROJECT and it shoulf have All Project students Name and ID mentioned on CD and a on a text file inside the cD.

Project copies both word and PDF will be uploaded on WebCT as will be explained later.

PROBLEM # 1 (1.5 point)

For alpha distribution

Find

a) Plot F(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 (all curves should be in one Figure for range of t/C varying from (0+=0.05) to 4). Hint use Normal Distribution Function(select True) of Excel subroutine for Z=-

b) Find pdf for t varying from -∞ to +∞ ,(note at t=0 function is undefined). Note

where

Z=-

c) Plot f(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 .all curves in one Figure for range of t/C varying from (0+=0.05) to 4 . Hint use Normal Distribution Function (select False) of Excel subroutine for Z=-

d) Median value of T, t0.5

e) Quantile, tp which is the solution of F(tp)=p .

f) Mode of T, (value of t where

PROBLEM # 2 (1.0 point) Use EXCEL and attach all spreadsheet analysis with solution)

Fifty measurements of the ultimate tensile strength of wire are given in the accompanying table.

a) Group the data and make an appropriate normalized histogram (with total area of histogram be 1 ) to approximate the PDF.

b) Calculate and for the distribution from the ungrouped data.

c) Using and from part b, draw a normal distribution through the normalized histogram .histogram.

Ultimate Tensile Strength
103,779	102,325	102,325	103,799
102,906	104,651	105,377	100,145
104,796	105,087	104,796	103,799
103,197	106,395	106,831	103,488
100,872	100,872	105,087	102,906
97,383	104,360	103,633	101,017
101,162	101,453	107,848	104,651
98,110	103,779	99,563	103,197
104,651	101,162	105,813	105,337
102,906	102,470	108,430	101,744
103,633	105,232	106,540	106,104
102,616	106,831	101,744	100,726
103,924		101,598

Source: Data from E. B. Haugen, Probabilistic Mechanical Design Wiley, New York, 1980

(c) Determine the mean, median, and mode from the ungrouped data.

(d) Determine the range and standard deviation from the ungrouped data

(e) Plot the cumulative frequency distribution on normal-probability paper, and determine the mean and standard deviation.

(f), for the data given in Table .what are the 95 percent confidence limits on the mean of the population?

PROBLEM # 3 (1.0 point) (Use EXCEL and attach all spreadsheet analysis with solution)

Three sets of identical twenty five fatigue specimens were tested at the three different level of stresses.. The number of cycles to failure. The results are expressed as log, were as follows.

TABLE 1: FATIGUE LIFE DATA
NUMBER OF CYCLES TO FAILURES
No.	S1	S2	S3
	380 MPa	340 MPa	300 MPa
1	34200	125500	954000
2	37700	156900	959400
3	42000	173600	1194600
4	42300	176900	1240500
5	48200	179400	1250400
6	52500	188500	1285500
7	55900	195100	1410500
8	58300	208100	1495100
9	61700	211900	1518700
10	64700	224100	1544700
11	65000	226000	1551400
12	65500	253000	1585900
13	70400	255500	1639100
14	71000	259000	1683700
15	72400	274000	1926100
16	75200	292000	2011300
17	77400	300400	2171800
18	77800	302300	2391500
19	87800	308300	2569400
20	93400	406300	2674900
21	94000	420700	2921700
22	97200	428500	3046500
23	99600	664800	3105500
24	116700	776100	3523200
25	122500	793900	4311700

Assume that the data at each stress level (S1, S2 and S3) is lognormally distributed.

Using directly the data in table determine

· What is the mean fatigue life ( μ) and its standard deviation (σ )?

· What is the mean Ln of fatigue life ( μlnN) and its standard deviation Ln of fatigue life (σlnN)?

· What are the Parameters of Lognormal distributions at S1,S2and S3.

· Fit lognormal distribution to the data using linear regression model using Excel or Use Statgraphics to fit the lognormal models to data for each stress level and comment on how good the fit is.

PROBLEM # 4 (1.5 point)

Q4. (a) The lifetime of a mechanical switch produced by a company has been determined to have a population mean of μ = 2000 h and σ = 200 h. The temper of a phosphor bronze leaf spring in the switch is changed slightly by the supplier. To determine whether this has changed the product, a sample of 100 switches is tested to give the sample values and . Has there been a change in the product? (0.75 point)

Q4. (b) A vendor of steel wire advertises a mean breaking load of 10,000 lb. A sample of eight tests shows a mean breaking load of 9250 lb and a standard deviation of 110 lb. Do our tests support the vendor’s claim? (0.75 point)

PROBLEM # 5 Control Charts (1 point)

Problem 5-Refer your Text Book above ( See Ebook provided as text book)- -Solve with appropriate calculations, tables and charts

5.1-Problem 8.1 Parts (a) and (b) –P454

5.2 -Problem 8.28 Parts (a) and (b) –P470

PROBLEM # 6

Regression Analysis (MUST USE STATGRAPHICS_ ATTACH COMPLETE REPORT PLUS ONE PAGE SUMMARY OF EACH FITTED MODEL) 2 points

Developing Cutting Forces Empirical Models of a Counter Boring Process in Aluminum.

Counter boring is an operation to enlarge the hole made using drilling. Counter boring or finish boring is a deep hole drilling process that requires a work piece with a pre-existing bore. Counter boring is used to enlarge the drilled hole to the proper depth and machine a square shoulder on the bottom to secure maximum clamping action from the faster. The drilling used to produce a circular hole by removing solid metal. The counter bore tool has a guide, called a pilot, which keep it positioned correctly in the hole. Counter boring tools are often used on low power machines were a small diameter solid boring tool is used for the pre-bore and then a counter boring tool is used to finish the job. Counter boring is also used when there is a heat treat process required after the initial hole is drilled or if a stepped hole is required.  

Pilot of diameter d , which is the predrilled hole size in the workpiece diameter of already drilled hole..

D Dia of the enlarged hole

Visit the link and download STATGRAPHICS FREE FOR 30 DAYS AND USE MULTIPLE REGRESSION MODULE (SEE EXAMPLES ON WEBSITE) TO DEVELOP FOLLOWING MODELS>

http://www.statgraphics.com/centurion-xvii

Regression Analysis http://www.statgraphics.com/regression-analysis

And Quality Control Module (PROICESS CAPABILITY BANALYSIS) from the link http://www.statgraphics.com/process-capability-analysis

Following are the results of Cutting Forces measurements experiments performed at KFUPM Workshop by Professor Anwar K Sheikh. The results are being shared for regression analysis learning objectives.

Cutting Force Fz as a Function of V,D,d and f

Fz Newton	Speed , V mm/minutes	Feed , f Mm/revolution	d mm	D mm	Ln (FZ)	Ln(Speed)	Ln(feed)	Ln(D)
52	2463.007	0.03	3.5	6.5	3.951244	7.809138	-3.50656	1.252763
78	2463.007	0.05	3.5	6.5	4.356709	7.809138	-2.99573	1.252763
104	2463.007	0.08	3.5	6.5	4.644391	7.809138	-2.52573	1.252763
130	2463.007	0.12	3.5	6.5	4.867534	7.809138	-2.12026	1.252763
65	3903.426	0.03	3.5	6.5	4.174387	8.26961	-3.50656	1.252763
78	3903.426	0.05	3.5	6.5	4.356709	8.26961	-2.99573	1.252763
104	3903.426	0.08	3.5	6.5	4.644391	8.26961	-2.52573	1.252763
130	3903.426	0.12	3.5	6.5	4.867534	8.26961	-2.12026	1.252763
65	4948.004	0.03	3.5	6.5	4.174387	8.50674	-3.50656	1.252763
78	4948.004	0.05	3.5	6.5	4.356709	8.50674	-2.99573	1.252763
117	4948.004	0.08	3.5	6.5	4.762174	8.50674	-2.52573	1.252763
130	4948.004	0.12	3.5	6.5	4.867534	8.50674	-2.12026	1.252763
65	6157.516	0.03	3.5	6.5	4.174387	8.725429	-3.50656	1.252763
78	6157.516	0.05	3.5	6.5	4.356709	8.725429	-2.99573	1.252763
104	6157.516	0.08	3.5	6.5	4.644391	8.725429	-2.52573	1.252763
130	6157.516	0.12	3.5	6.5	4.867534	8.725429	-2.12026	1.252763
72	7806.851	0.03	3.5	6.5	4.276666	8.962757	-3.50656	1.252763
85	7806.851	0.05	3.5	6.5	4.442651	8.962757	-2.99573	1.252763
111	7806.851	0.08	3.5	6.5	4.70953	8.962757	-2.52573	1.252763
130	7806.851	0.12	3.5	6.5	4.867534	8.962757	-2.12026	1.252763
78	2463.007	0.03	5.5	10	4.356709	7.809138	-3.50656	1.704748
104	2463.007	0.05	5.5	10	4.644391	7.809138	-2.99573	1.704748
130	2463.007	0.08	5.5	10	4.867534	7.809138	-2.52573	1.704748
182	2463.007	0.12	5.5	10	5.204007	7.809138	-2.12026	1.704748
84	3903.426	0.03	5.5	10	4.430817	8.26961	-3.50656	1.704748
110	3903.426	0.05	5.5	10	4.70048	8.26961	-2.99573	1.704748
143	3903.426	0.08	5.5	10	4.962845	8.26961	-2.52573	1.704748
182	3903.426	0.12	5.5	10	5.204007	8.26961	-2.12026	1.704748
91	4948.004	0.03	5.5	10	4.51086	8.50674	-3.50656	1.704748
117	4948.004	0.05	5.5	10	4.762174	8.50674	-2.99573	1.704748
130	4948.004	0.08	5.5	10	4.867534	8.50674	-2.52573	1.704748
182	4948.004	0.12	5.5	10	5.204007	8.50674	-2.12026	1.704748
78	6157.516	0.03	5.5	10	4.356709	8.725429	-3.50656	1.704748
104	6157.516	0.05	5.5	10	4.644391	8.725429	-2.99573	1.704748
143	6157.516	0.08	5.5	10	4.962845	8.725429	-2.52573	1.704748
195	6157.516	0.12	5.5	10	5.273	8.725429	-2.12026	1.704748
91	7806.851	0.03	5.5	10	4.51086	8.962757	-3.50656	1.704748
117	7806.851	0.05	5.5	10	4.762174	8.962757	-2.99573	1.704748
143	7806.851	0.08	5.5	10	4.962845	8.962757	-2.52573	1.704748
195	7806.851	0.12	5.5	10	5.273	8.962757	-2.12026	1.704748
117	2463.007	0.03	7.5	15	4.762174	7.809138	-3.50656	2.014903
143	2463.007	0.05	7.5	15	4.962845	7.809138	-2.99573	2.014903
195	2463.007	0.08	7.5	15	5.273	7.809138	-2.52573	2.014903
234	2463.007	0.12	7.5	15	5.455321	7.809138	-2.12026	2.014903
123	3903.426	0.03	7.5	15	4.812184	8.26961	-3.50656	2.014903
156	3903.426	0.05	7.5	15	5.049856	8.26961	-2.99573	2.014903
208	3903.426	0.08	7.5	15	5.337538	8.26961	-2.52573	2.014903
234	3903.426	0.12	7.5	15	5.455321	8.26961	-2.12026	2.014903
123	4948.004	0.03	7.5	15	4.812184	8.50674	-3.50656	2.014903
169	4948.004	0.05	7.5	15	5.129899	8.50674	-2.99573	2.014903
208	4948.004	0.08	7.5	15	5.337538	8.50674	-2.52573	2.014903
247	4948.004	0.12	7.5	15	5.509388	8.50674	-2.12026	2.014903
130	6157.516	0.03	7.5	15	4.867534	8.725429	-3.50656	2.014903
169	6157.516	0.05	7.5	15	5.129899	8.725429	-2.99573	2.014903
208	6157.516	0.08	7.5	15	5.337538	8.725429	-2.52573	2.014903
247	6157.516	0.12	7.5	15	5.509388	8.725429	-2.12026	2.014903
143	7806.851	0.03	7.5	15	4.962845	8.962757	-3.50656	2.014903
182	7806.851	0.05	7.5	15	5.204007	8.962757	-2.99573	2.014903
208	7806.851	0.08	7.5	15	5.337538	8.962757	-2.52573	2.014903
247	7806.851	0.12	7.5	15	5.509388	8.962757	-2.12026	2.014903
156	2463.007	0.03	9.5	18	5.049856	7.809138	-3.50656	2.251292
208	2463.007	0.05	9.5	18	5.337538	7.809138	-2.99573	2.251292
260	2463.007	0.08	9.5	18	5.560682	7.809138	-2.52573	2.251292
338	2463.007	0.12	9.5	18	5.823046	7.809138	-2.12026	2.251292
208	3903.426	0.03	9.5	18	5.337538	8.26961	-3.50656	2.251292
234	3903.426	0.05	9.5	18	5.455321	8.26961	-2.99573	2.251292
260	3903.426	0.08	9.5	18	5.560682	8.26961	-2.52573	2.251292
364	3903.426	0.12	9.5	18	5.897154	8.26961	-2.12026	2.251292
208	4948.004	0.03	9.5	18	5.337538	8.50674	-3.50656	2.251292
234	4948.004	0.05	9.5	18	5.455321	8.50674	-2.99573	2.251292
260	4948.004	0.08	9.5	18	5.560682	8.50674	-2.52573	2.251292
364	4948.004	0.12	9.5	18	5.897154	8.50674	-2.12026	2.251292
208	6157.516	0.03	9.5	18	5.337538	8.725429	-3.50656	2.251292
260	6157.516	0.05	9.5	18	5.560682	8.725429	-2.99573	2.251292
286	6157.516	0.08	9.5	18	5.655992	8.725429	-2.52573	2.251292
338	6157.516	0.12	9.5	18	5.823046	8.725429	-2.12026	2.251292
234	7806.851	0.03	9.5	18	5.455321	8.962757	-3.50656	2.251292
286	7806.851	0.05	9.5	18	5.655992	8.962757	-2.99573	2.251292
312	7806.851	0.08	9.5	18	5.743003	8.962757	-2.52573	2.251292

Moment Mz as a Function of V,D,d and f

Mz Newton-meter	Speed , V mm/minutes	Feed , f Mm/ revolution	d mm	D mm	Ln (Mz)	Ln(Speed)	Ln(feed)	Ln(D)
39	2463.007	0.03	3.5	6.5	3.663562	7.809138	-3.50656	1.252763
59	2463.007	0.05	3.5	6.5	4.077537	7.809138	-2.99573	1.252763
72	2463.007	0.08	3.5	6.5	4.276666	7.809138	-2.52573	1.252763
104	2463.007	0.12	3.5	6.5	4.644391	7.809138	-2.12026	1.252763
39	3903.426	0.03	3.5	6.5	3.663562	8.26961	-3.50656	1.252763
52	3903.426	0.05	3.5	6.5	3.951244	8.26961	-2.99573	1.252763
78	3903.426	0.08	3.5	6.5	4.356709	8.26961	-2.52573	1.252763
117	3903.426	0.12	3.5	6.5	4.762174	8.26961	-2.12026	1.252763
39	4948.004	0.03	3.5	6.5	3.663562	8.50674	-3.50656	1.252763
59	4948.004	0.05	3.5	6.5	4.077537	8.50674	-2.99573	1.252763
78	4948.004	0.08	3.5	6.5	4.356709	8.50674	-2.52573	1.252763
117	4948.004	0.12	3.5	6.5	4.762174	8.50674	-2.12026	1.252763
39	6157.516	0.03	3.5	6.5	3.663562	8.725429	-3.50656	1.252763
52	6157.516	0.05	3.5	6.5	3.951244	8.725429	-2.99573	1.252763
78	6157.516	0.08	3.5	6.5	4.356709	8.725429	-2.52573	1.252763
124	6157.516	0.12	3.5	6.5	4.820282	8.725429	-2.12026	1.252763
39	7806.851	0.03	3.5	6.5	3.663562	8.962757	-3.50656	1.252763
59	7806.851	0.05	3.5	6.5	4.077537	8.962757	-2.99573	1.252763
72	7806.851	0.08	3.5	6.5	4.276666	8.962757	-2.52573	1.252763
117	7806.851	0.12	3.5	6.5	4.762174	8.962757	-2.12026	1.252763
52	2463.007	0.03	5.5	10	3.951244	7.809138	-3.50656	1.704748
72	2463.007	0.05	5.5	10	4.276666	7.809138	-2.99573	1.704748
98	2463.007	0.08	5.5	10	4.584967	7.809138	-2.52573	1.704748
163	2463.007	0.12	5.5	10	5.09375	7.809138	-2.12026	1.704748
65	3903.426	0.03	5.5	10	4.174387	8.26961	-3.50656	1.704748
84	3903.426	0.05	5.5	10	4.430817	8.26961	-2.99573	1.704748
110	3903.426	0.08	5.5	10	4.70048	8.26961	-2.52573	1.704748
169	3903.426	0.12	5.5	10	5.129899	8.26961	-2.12026	1.704748
65	4948.004	0.03	5.5	10	4.174387	8.50674	-3.50656	1.704748
98	4948.004	0.05	5.5	10	4.584967	8.50674	-2.99573	1.704748
110	4948.004	0.08	5.5	10	4.70048	8.50674	-2.52573	1.704748
169	4948.004	0.12	5.5	10	5.129899	8.50674	-2.12026	1.704748
65	6157.516	0.03	5.5	10	4.174387	8.725429	-3.50656	1.704748
98	6157.516	0.05	5.5	10	4.584967	8.725429	-2.99573	1.704748
117	6157.516	0.08	5.5	10	4.762174	8.725429	-2.52573	1.704748
169	6157.516	0.12	5.5	10	5.129899	8.725429	-2.12026	1.704748
65	7806.851	0.03	5.5	10	4.174387	8.962757	-3.50656	1.704748
98	7806.851	0.05	5.5	10	4.584967	8.962757	-2.99573	1.704748
130	7806.851	0.08	5.5	10	4.867534	8.962757	-2.52573	1.704748
163	7806.851	0.12	5.5	10	5.09375	8.962757	-2.12026	1.704748
81	2463.007	0.03	7.5	15	4.394449	7.809138	-3.50656	2.014903
130	2463.007	0.05	7.5	15	4.867534	7.809138	-2.99573	2.014903
195	2463.007	0.08	7.5	15	5.273	7.809138	-2.52573	2.014903
260	2463.007	0.12	7.5	15	5.560682	7.809138	-2.12026	2.014903
104	3903.426	0.03	7.5	15	4.644391	8.26961	-3.50656	2.014903
143	3903.426	0.05	7.5	15	4.962845	8.26961	-2.99573	2.014903
195	3903.426	0.08	7.5	15	5.273	8.26961	-2.52573	2.014903
260	3903.426	0.12	7.5	15	5.560682	8.26961	-2.12026	2.014903
117	4948.004	0.03	7.5	15	4.762174	8.50674	-3.50656	2.014903
156	4948.004	0.05	7.5	15	5.049856	8.50674	-2.99573	2.014903
221	4948.004	0.08	7.5	15	5.398163	8.50674	-2.52573	2.014903
260	4948.004	0.12	7.5	15	5.560682	8.50674	-2.12026	2.014903
130	6157.516	0.03	7.5	15	4.867534	8.725429	-3.50656	2.014903
156	6157.516	0.05	7.5	15	5.049856	8.725429	-2.99573	2.014903
195	6157.516	0.08	7.5	15	5.273	8.725429	-2.52573	2.014903
286	6157.516	0.12	7.5	15	5.655992	8.725429	-2.12026	2.014903
130	7806.851	0.03	7.5	15	4.867534	8.962757	-3.50656	2.014903
169	7806.851	0.05	7.5	15	5.129899	8.962757	-2.99573	2.014903
221	7806.851	0.08	7.5	15	5.398163	8.962757	-2.52573	2.014903
299	7806.851	0.12	7.5	15	5.700444	8.962757	-2.12026	2.014903
221	2463.007	0.03	9.5	18	5.398163	7.809138	-3.50656	2.251292
260	2463.007	0.05	9.5	18	5.560682	7.809138	-2.99573	2.251292
357	2463.007	0.08	9.5	18	5.877736	7.809138	-2.52573	2.251292
487	2463.007	0.12	9.5	18	6.188264	7.809138	-2.12026	2.251292
227	3903.426	0.03	9.5	18	5.42495	8.26961	-3.50656	2.251292
325	3903.426	0.05	9.5	18	5.783825	8.26961	-2.99573	2.251292
357	3903.426	0.08	9.5	18	5.877736	8.26961	-2.52573	2.251292
487	3903.426	0.12	9.5	18	6.188264	8.26961	-2.12026	2.251292
195	4948.004	0.03	9.5	18	5.273	8.50674	-3.50656	2.251292
292	4948.004	0.05	9.5	18	5.676754	8.50674	-2.99573	2.251292
357	4948.004	0.08	9.5	18	5.877736	8.50674	-2.52573	2.251292
520	4948.004	0.12	9.5	18	6.253829	8.50674	-2.12026	2.251292
292	6157.516	0.03	9.5	18	5.676754	8.725429	-3.50656	2.251292
445	6157.516	0.05	9.5	18	6.098074	8.725429	-2.99573	2.251292
650	6157.516	0.08	9.5	18	6.476972	8.725429	-2.52573	2.251292
747	6157.516	0.12	9.5	18	6.616065	8.725429	-2.12026	2.251292
357	7806.851	0.03	9.5	18	5.877736	8.962757	-3.50656	2.251292
487	7806.851	0.05	9.5	18	6.188264	8.962757	-2.99573	2.251292
650	7806.851	0.08	9.5	18	6.476972	8.962757	-2.52573	2.251292

Using STATGRAPHICS -MULTIPLE LINEAR REGRESSION MODULE develop the empirical model for cutting force Fz and Torque (Moment) Mz can be writing as following

Find A,f ,b and c d e etc in Fz model using first data table ,and Find B,d,e,f d using second Data table for each of the odel.. Write one page summary based upon completer regression report generated by STATGRAPHICS for each fitted model .Its goodness of fit as measured by R2 values and other important coefficients tabulated and plotted in the report. (Attach PDF copy of each full report of STATGRAPHICS output and your EXCEL File used as input data.

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b

a

V

D

f

A

Fz

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=

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B

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