Excercises 1

8/13/2019 Excercises 1

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EXERCISE

Exercise 1:The data shown below are chemical process yield on successivedays. Construct a histogram for these data.

94.1 87.3 94.1 9.4 84.! 8".4

93. 84.1 9.1 9#.! 83.! 8!.!

9#.! 9#.1 9!.4 89.1 8".4 91.7

91.4 9". 88. 88.8 89.7 87."

88. 8!.1 8!.4 8!.4 87.! 84.

8!.1 94.3 8".# 8".1 8".1 8".1

9".1 93. 84.9 84.# 89.! 9#."

9#.# 8!.7 87.3 93.7 9#.# 9".!

9.4 83.# 89.! 87.7 9#.1 88.3

87.3 9".3 9#.3 9#.! 94.3 84.1

(Refer Work Sheet Name: Chemical Yield)


2/25

Exercise 2:The time to failure in hours of an electronic component sub$ectedto an accelerated life test is given below. Construct histogram of these data

17 14 11 118

1" 13 13! 131

131 1# 14# 1"

14 119 137 133

19 18 1" 141

11 133 14 1"

14 137 18 14#

1"1 14 19 13

1!# 14 13# 19

1" 13 1 1!

(Refer Work Sheet Name: Failre !ime)


3/25

Exercise ": The tensile strength of a metal part is normally distributed withmean 4# lb and standard deviation 8 lb. %f the lower specification limit is 34 lb

and upper specification limit is 48 lb& 'ind out the ( of parts fail to meet

specification)

Exercise #:The output voltage of a power supply is normally distributed withmean 1 * and standard deviation #.#" *. %f the specification are at 1 #.1 *&

calculate the total ( re$ection)

Exercise $: The life of an automotive battery is normally distributed withmean 9## days and standard deviation 3" days. +hat ( of these batteries would

be e,pected to survive beyond 1### days)


4/25

Exercise %:The following data shows the diameter -in inches of a sample of4# ball bearings manufactured by certain process

#.738 #.79 #.743 #.74#

#.73" #.731 #.7! #.737

#.78 #.737 #.74 #.73"

#.74" #.73! #.78 #.74

#.733 #.74 #.739 #.7"

#.73" #.73 #.734 #.738

#.73 #.73" #.73" #.73!

#.737 #.731 #.733 #.79#.73! #.73" #.738 #.73!

#.73# #.74# #.734 #.733

%f the specification is #.734 #.#& Calculate the process capability inde, Cp /

Cp0)

(Refer Work Sheet Name: &eari' ia)


5/25

Exercise *: The data shown below are the deviations from the nominaldiameter for holes drilled in a carbonfibre composite material used in

aerospace manufacturing. The values reported are deviations in ten thousands of

an inch.

3# "# # 1# 3#

# "# !# # 3#

"# 1# # 3# #

1# 1# 3# # "#

# 4# "# # 1#

# # 4# 4# #

# # # # 1#

7# 3# 3# 1# #

# # # # 1#

1# # 3# 1# "#

%f specifications are at nominal 1##& what you say about the capability of the

process) Calculate Cp and Cp0)

(Refer Work Sheet Name: ia e+iatio')


6/25

Exercise ,: The thic0ness of a printed circuit board is an important 2ualityparameter. ata on board thic0ness -in inches are given below& for # samples

of 3 boards each.

ample 5o. ,1 , ,3

1 #.#!9 #.#!3! #.#!4#

#.#!3# #.#!31 #.#!

3 #.#!8 #.#!31 #.#!33

4 #.#!34 #.#!3# #.#!31

" #.#!19 #.#!8 #.#!3#

! #.#!13 #.#!9 #.#!34

7 #.#!3# #.#!39 #.#!"

8 #.#!8 #.#!7 #.#!

9 #.#!3 #.#!! #.#!33

1# #.#!31 #.#!31 #.#!33

11 #.#!3" #.#!3# #.#!38

1 #.#!3 #.#!3# #.#!3#

13 #.#!3" #.#!31 #.#!3#

14 #.#!4" #.#!4# #.#!31

1" #.#! #.#!44 #.#!3

1! #.#!31 #.#!7 #.#!3#

17 #.#!1! #.#!3 #.#!31

18 #.#!3# #.#!3# #.#!!

19 #.#!3! #.#!31 #.#!9

# #.#!4# #.#!3" #.#!9

et up 6bar charts) %s the process in control)

(Refer Work Sheet Name: -C& !hick'ess)

Exercise .: amples of sie " are ta0en every 4" minutes on cigar lighterdetent. The following results are obtained. et up 6bar chart and e,amine

the process for statistical control)


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ample 5o. ,1 , ,3 ,4 ,"

1 1 3 4 3 3

8 4 3 # 3

3 # 9 # 3

4 1 1 # 1

" 3 # 1 # 4

! 7 # #

7 3 1 1 #

8 # 3 3

9 # 1 3 1

1# # 1 1

11 3 1 1

1 1# # 4 1

13 ! 3 # # 8

14 3 " " # "

1" 1 1 1 1

(Refer Work Sheet Name: /ihter ete't)


8/25

Exercise 10: The data on loose pulp C ( is given below. Construct%ndividual and :oving ange chart)

S/ No ata

1 47."

47."

3 48.#

4 47."

" 47."

! 48."

7 48.#

8 49.#

9 49.#

1# 49.#

11 49.#

1 48."

13 48."

14 49.#

1" 49.#

1! 48."

17 48."

18 47."

19 47."

# 48."

(Refer Work Sheet Name: -l C)


9/25

Exercise 11:The number of nonconforming switches in samples of sie 1"#are shown below. Construct a number nonconforming chart for these data. oes

the process appear to be in control)

ample 5umber 5umber of defective witches1 8

1

3 3

4 #

"

! 4

7 #

8 1

9 8

1# !

11 !

1 #

13 4

14 #

1" 3

1! 1

17 8

18

19 3

# #

(Refer Work Sheet Name: S3itches)


10/25

Exercise 12:; control chart is used to control the number nonconforming fora plastic part manufactured in an in$ection molding process. Ten subgroups of

sie 1## yield the following data. Construct a number nonconforming chart )

ample 5o. 5umber 5onconforming

1 1#

1"

3 "

4 18

" !

! 1

7 "

8 1"

9 8

1# 8

(Refer Work Sheet Name: -lastics)


11/25

Exercise 1": ; process produces titanium forging for automobileturbocharger wheels is to be controlled through use of a p chart. %nitially

samples are collected for # days and is given below.

ay Total %nspected efectives

1 1"# 3

1!"

3 14# 4

4 1""

" 1!# "

! 14# 7 148 1

8 1"9

9 1! #

1# 148 "

11 1"!

1 1"4 4

13 1"# 1

14 1!# 3

1" 1!# !

1! 1" #

17 1"3 1

18 1"4

19 14! 3# 148

(Refer Work Sheet Name: Fori's)


12/25

Exercise 1#: The data below represents the number of defects per 1###meters of telephone cable. 'rom analysis of the data would you conclude that

the process is in statistical control)

ample 5o. 5umber of defects ample 5o. 5umber of defects

1 1 11 4

1 1 !

3 3 13 9

4 7 14 1"

" 8 1" 14

! 1# 1! 8

7 " 17 3

8 13 18 !

9 # 19 7

1# 19 # 4

(Refer Work Sheet Name: !C efects)

Exercise 1$: ;n automobile manufacturer wishes to control the number ofdefects in a subassembly area producing manual transmissions. The inspected

unit is defined as 4 transmissions and data from 1! samples are given below. et

up a control chart for defects)


13/25

ample 5o 5o. of defects

1 1


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3

3

4 1

" #

!

7 1

8 "

9

1# 1

11 #

1

13 1

14 1

1"

1! 3

(Refer Work Sheet Name: 4tomo5ile efects)

Exercise 1%:; company wants touse a control chart for the surface defects inchromium plated parts. The data given below give the number of parts inspected

and the number of defects found. Construct a control chart for defects per part)

ample 5umber 5umber %nspected 5umber of efects

1 1

# "

3 1" 3

4 11 #

" 9


15/25

! 14 1

7 1# #

8 18 4

9 # 4

1# 14

11 13 1

1 1"

13 17 3

14 13 1

1" 1"

(Refer Work Sheet Name: -lati' efects)

Exercise 1*:; company wants touse a control chart for the surface defects ingranite slabs. The data given below give the number of slabs inspected and the

number of defects found. Construct a control chart for defects per slab and

comment.

ample 5umber 5umber %nspected 5umber of efects

1 1

# "

3 1" 3

4 11 #

" 9

! 14 1

7 1# #

8 18 4


16/25

9 # 4

1# 14

11 13 1

1 1"

13 17 3

14 13 1

1" 1"

(Refer Work Sheet Name: 6ra'ite efects)


17/25

Exercise 1,:The diameters of bolts are 0nown to have a standard deviation of#.###1 inch. ; random sample of 1# bolts yields an average diameter of #."4!

inch. Test the hypothesis that the true mean diameter of bolt is e2uals #."" inch

using #".= .

Exercise 1.: Two machines are used for filling plastic bottles with a netvolume of 1! ounces.


18/25

%s there any evidence that the mean titanium content is greater than 9." percent)

(Refer Work Sheet Name: !ita'im Co'te't)

Exercise 2": The time to repair an electronic instrument is a normallydistributed random variable measured in hours. The repair times -in Ars for 1!

such instruments& chosen at random& are as follows.

1"9 8# 1#1 1

4 379 179 !4

3! 1!8 "#

149 !# 48" 17#

oes it seem reasonable that the true mean repair time is greater than "#

hours )

(Refer Work Sheet Name: Reair !ime)

Exercise 2#:The percentage of scrap produced in a metal finishing operationis hypothesied to be less than 7." (. everal days were chosen at random and

the percentage of scrap were calculated.

"."1& 7.3& !.49& 8.81& !.4!& 8."!& ".37& 7.4!

%n your opinion& is the true scrap rate less than 7." percent)

(Refer Work Sheet Name: Scra 7)

Exercise 2$:The following are the burning times -in min of flames of two

different types.

Type 1 Type

!3 8 !4 "!

81 !8 7 !3

"7 "9 83 74

!! 7" "9 8

8 73 !" 8

Test the Aypothesis that two variances are e2ual .>se #".= .

(Refer Work Sheet Name: &r'i' !imes)


19/25

Exercise 2%:; new filtering device is installed in a chemical unit. @efore andafter its installation& a random sample yielded the following information about

the percentage of impurityB

1x ?1."& 17.1#1

1 =s & 1n ?8

x ?1#.& 73.94

=s & n ?9

1 Can you conclude that the two variances are e2ual)

Aas the filtering device reduced the percentage of impurity significantly)

Exercise 2*: The manufacturer of a power supply is interested in thevariability of output voltage. Ae has tested 1 units& chosen at random& with the

following resultsB

".34 ".!" 4.7!

".## "."" "."4

".#7 ".3" ".44

"." ".3" 4.!1

Test the hypothesis that ?#.#". >se 05. .

(Refer Work Sheet Name: 8oltae)


20/25

Exercise 2,: Consider the following two samples& draw from two normalpopulations.

ample 1 ample

4.34 1.87

" 4.97

4." 1.8"

"."" .11

!."" .31

!.37 .8

"."" .#7

3.7! 1.7!

1.91

%s there evidence to conclude that the variance of population 1 is greater than

the variance of population )>se #1.= .

(Refer Work Sheet Name: 8aria'ces)

Exercise 2.:%n a hardness test& a steel ball is passed into the material beingtested at a standard load. The diameter of the indentation measured& which is

related to the hardness. Two types of steel balls are available& and theirperformance is compared on 1# specimens. =ach specimen is tested twice& once

with each ball. The results are given belowB

@all 6 7" 4! "7 43 "8 3 !1 "! 34 !"

@all " 41 43 47 3 49 " 44 "7 !#

Test the hypothesis that the two steel balls give the same hardness

measurement. >se #".= .

(Refer Work Sheet Name: 9ard'ess)


21/25

Exercise "0:The thic0ness of a printed circuit board was measured by si,individuals& using two different 0inds of calipers. The results -in mm are shown

belowB

ub$ect Caliper 1 Caliper 1 .!" .!4

.!" .!"

3 .!! .!4

4 .!7 .!!

" .!7 .!7

! .!" .!8

%s there is significant difference between the mean thic0nesses of measurements

obtained of two calipers)(Refer Work Sheet Name: -C& !hick)

Exercise "1:The number of defective units found each day by an incircuitfunctional tester in a printed circuit board assembly process is shown belowB

5umber of defective per ay Times Dbserved

#1# !

111" 11

1!# 1!1" 8

!3#

313" 19

3!4# 11

414" 4

a %t is reasonable to conclude that these data come from a normal distribution)

>se Chis2uare goodness of fit test.

b Elot the data on normal probability paper. oes an assumption of normalityseem $ustified)

(Refer Work Sheet Name: -C& 4ss)


22/25

Exercise "2: ; pseudo random number generator is designed so that theintegers # through 9 have e2ual probability of occurrences. The first 1###

numbers areB

# 1 3 4 " ! 7 8 99!7 1##8 97" 1# 1##3 989 1##1 981 1#43 1#11

oes this generator seem to be wor0ing properly) FGoodness of fitH

(Refer Work Sheet Name: Ra'dom 6e')

Exercise "":; soft drin0 bottler is studying the internal pressure strength of1litre glass nonreturnable bottles. ; random sample 1! bottles is tested and the

pressure strengths obtained. The data are shown below. Elot these data on

normal probability paper. oes it seem reasonable to conclude that pressurestrength is normally distributed)

!.1! psi 11.14 psi

#. #3.!

19."4 188.1

193.73 4.39

#8.1" 1.31

19".4" #4.""

193.71 #.1

##.81 #1.!3(Refer Work Sheet Name: &ottle -r)

Exercise "#:; company operates four machines three shifts each day. 'romproduction records& the following data on the number of brea0downs are

collectedB

hift:achines

; @ C

1 41 # 1 1!

31 11 9 14

3 1" 17 1! 1#

Test the hypothesis that brea0downs are independent of the shifts.

(Refer Work Sheet Name: &reakdo3's)


23/25

Exercise "$:Eatients in a hospital are classified as surgical or medical. ;record is 0ept of the number of times patients re2uire nursing service during the

night and whether these patients are on medicare or not. The data are presented

hereB

:edicare Eatient category

urgical :edical

es 4! "

5o 3! 43

Test the hypothesis that calls by surgicalmedical patients are independent of

whether the patients are receiving :edicare.

(Refer Work Sheet Name: 9osital)

Exercise "%:Grades in a statistics course and an Dperation esearch courseta0en simultaneously were as follows for a group of students.

tatistics Grade

Dperation esearch

Grade

; @ C Dthe

r

; " ! 17 13@ 17 1! 1" !

C 18 4 18 1#

Dther 1# 8 11 #

;re the grade in tatistics and Dperation esearch related)

(Refer Work Sheet Name: Corse)

Exercise "*:;n e,periment with artillery shells yields the following data on

the characteristics of lateral deflections and ranges. +ould you conclude thatdeflection and range are independent)

ange

-yards

Iateral deflection

Ieft 5ormal ight

#1999 ! 14 8

###"999 9 11 4

!###11999 8 17 !

(Refer Work Sheet Name: eflectio')


24/25

Exercise ",: ; study is being made of the failures of an electroniccomponent. There are four types of failures possible and two mounting position

for the device .The following data have been ta0enB

:ounting position 'ailure type; @ C

1 4! 18 9

4 17 ! 1

+ould you conclude that the type of failure is independent of the mounting

position)

(Refer Work Sheet Name: Failre !e)

Exercise ".: ; random sample of students are as0ed their opinions on aproposed core curriculum change. The results are presented hereB

ClassDpinion

'avoring Dpposing

'reshman 1# 8#

ophomore 7# 13#

Junior !# 7#enior 4# !#

Test the hypothesis that the opinions are independent of the class groupings.

;Chi

(Refer Work Sheet Name: Crriclm)

Exercise #0:'abric is graded into three classificationsB ;& @ and C. Theresults below were obtained from five looms. %s the fabric classificationindependent of the loom)

Ioom5umber of pieces of 'abric in

'abric Classification

; @ C

1 18" 1! 1

19# 4 1

3 17# 3" 1!4 1"8 7

" 18" 1"


25/25

(Refer Work Sheet Name: Fa5ric)

Exercise #1:;n article in the $ournal of :ar0eting esearch reports a studyof the relationship between facility conditions at gasoline stations and the

aggressiveness of their gasoline mar0eting policy. ; sample of 441 gasoline

stations were investigated with the results shown below obtained. %s there

evidence that gasoline pricing strategy and facility conditions are independent)

EolicyCondition

ubstandard tandard :odern

;ggressive 4 " "8

5eutral 1" 73 8!

nonaggressive 17 8# 3!

(Refer Work Sheet Name: 6asole'e)

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Excercises 1