Task 1: Fundamentals of mathematical statistics (20 points) · 2011/07/26 Page 1 of 25 Task 1:...

Quality Management Exam

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2011/07/26 of 25

Task 1: Fundamentals of mathematical statistics (20 points)

1.1 Basics of statistics (5.5 points) (E3-4, 6, 10)

Table 1-1: Different types of statistics

Type of statistics Description

A Descriptive

Statistics

Characteristics to describe the population or the

sample

B Inductive

Statistics

Statistical inference of the sample data to the

population

Please sketch the distribution function F(x) corresponding to the probability density function of a

normal distribution f(x) shown in picture 1-2.

Picture 1-2: Normal distribution

Table 1-2: Influence of the different experimental setups

Experiment Influence to the spread of the measured data

A For the first experimental setup the standard deviation is

significantly higher than for the second setup because the

natural spread is enlarged by the systematical readjustment

of the process (systematical spread) after every throw.

B Because the experimental setup is readjusted after n

throws (here 10), the systematical spread does not affect the

distribution of the measured data as much.

1 point for each

explanation

Σ =2 points

1 point for each

correct description

Σ = 2 points

1 point for F(x)

Σ =1 point


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Why does it make more sense not to readjust a process immediately after each measurement?

Answer:

A single measurement does not give a correct statement of the process.

The natural spread of measured data has to be considered before changing or improving a

process.

1.2 Calculation of the variance and the standard deviation (3.5 points) (E3-14)

mms

mms

mmx

248

²61714

73172

==

=

1.3 Histograms (4 points) (E3-18-20)

Hint: k

xxH

)( width Class minmax −==

k= 346.312 ===n

2503

)70007750( =−=H

0.5 points

1 point for each correct

formula (formula for mean

value was not expected)

Σ =2 points

0.5 points for each correct

result

Σ =1.5 points

Σ =3.5 points

0.5 points for the correct

formula and


number of classes (3)

Σ =1 point


class width


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Table 1-4: Data needed to create a histogram

Class No. Class limits (range) Absolute frequency

1 7000 ≤ xi < 7250 5

2 7250 ≤ xi < 7500 4

3 7500 ≤ xi ≤ 7750 3

Table 1-5: Median and mode

Median (7250+7251)/2=7250.5

Mode (7000+7249)/2=7124.5

1.4 Confidence intervals (3 points) (E3-25-26)

mms

mms

mmx

248

²61714

73172

==

=

2012975,0;11

2

α 1 ;1

,ttn

==−−

Or (with given values)

There are different influences on the size of the confidence interval. Please fill in the blanks:

A) The smaller the sample, the larger the size of the confidence interval.

B) The larger the probability of an error, the smaller the size of the confidence interval.


class limits (range)

Σ =1.5 points

1 point for the correct t

1 point for the correct

confidence interval

0.5 points for each correct

answer

Σ =1 point


median and mode

Σ =1 point

12

248201,27317

12

248201,27317 +≤≤− µ

74747159 ≤≤ µ 76407360 ≤≤ µ

n

stxµ

n

stx

αn

αn

21;1

21;1 −−−−

+≤≤−


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1.5 Sample size (4 points) (E3-27-28)

Hint :

2

21;1

*

∆=

−−

µ

α

α

st

nn

Security = 90 % � Probability of an error (α) = 10 % � 796,1

95,02

1

95,0;11

2 1;1

==

=−

−−tt

nα

α

255.2490

248*796.12

==

=mm

mmnα

Or (with given values) 2027.1990

220*796.12

==

=mm

mmnα

Is the current sample size sufficient?

Answer: no

Reason: Because of the demanded accuracy of 90 mm together with a security of 90 % (two

sided test), a minimum sample size of 25 (20) has to be taken in order to be able to make a

significant statement about the process.

1 point for the correct t

1 point for the correct result

(24,5) and


sample size (25)

Σ =2 points


answer and


reason

Σ =1 point


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Table 1-6: Distribution function of the t-distributions


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Task 2: Quality in the early phases – focus product (20 points)

2.1 Balancing targets and risks in product development (15 points) (L7-32/35)

Table 2-1: Pairwise comparison of targets

Formula: relative ranking 1*4minmax

min +

−−

=xx

xxRd oder 1

15

1*4 +

−−x

Rd

Table 2-2: Pairwise comparison of risks

Attracting attention

Dynam

ic appearance

Low risk of injuries

Low production costs

Absolute ranking

Relative ranking

Attracting Attention X 0 0 1 1 1

Dynamic appearance 2 X 0 1 3 3

Low risk of injuries 2 2 X 1 5 5

Low production costs 1 1 1 X 3 3

2 - more important than1 - as important as0 - less important than

Tim

e-to-Market

Feasibility

Bad for business

Absolute ranking

Relative ranking

Time-to-Market X 0 0 0 1

Feasibility 2 X 0 2 3

Bad for business 2 2 x 4 5

2 - more important than1 - as important as0 - less important than

0.5 points per correct

relative ranking


formula


relative ranking


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Table 2-3: Evaluation of product ideas

Targets/Risks Ideas

Relative ranking

AA

A-S

lots

Pedals

Candles

Hiking boots

Targets

Attracting attention 1

Dynamic appearance 3

Low risk of injuries 5

Low production costs 3R

isks

Time-to-Market 1

Feasibility 3

Bad for business 5

Absolute ranking Targets 58 48 36 52

Relative ranking Targets 10 5,9 ≈ 6

1 7,54 ≈ 8

Absolute ranking Risks 27 33 55 19

Relative ranking Risks 3 4,5 ≈ 5

10 1

Legend: = 1

= 3

= 9


absolute ranking


relative ranking


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Alternative solution:

Targets/Risks Ideas

Relative ranking

AA

A-S

lots

Pedals

Candles

Hiking boots

Targets

Attracting attention 2

Dynamic appearance 1

Low risk of injuries 3

Low production costs 5

Risks

Time-to-Market 5

Feasibility 3

Bad for business 1

Absolute ranking Targets 45 29 51 35

Relative ranking Targets 7,54 ≈ 8 1 10 3,45 ≈ 3

Absolute ranking Risks 27 57 23 11

Relative ranking Risks 4,13 ≈ 4 10 3,35 ≈ 3

1

Legend: = 1

= 3

= 9


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Picture 2-1: Targets/risks-portfolio

Alternative solution:

According to the portfolio in picture 2-2, which product idea should not be realized by the

Worldcar Corp.?

Answer: candles (alternative solution: pedals)

0 5 10

5

10

?

Targ

ets

Risks

AAA-Slots

Pedals

Candles

Hiking boots

0 5 10

5

10

?

Targ

ets

Risks

AAA-Slots

Candles

Pedals

Hiking boots

0.5 points per correctly

allocated product idea

0.5 points for the correct answer


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2.2 Over- and under-fulfillment of quality expectations (5 points) (L7-10)

Picture 2-2: Grades of customer expectations

Under-fulfillment: Under-fulfillment will be severely punished, in the worst case the customer

will not buy the product.

Over-fulfillment: Over-fulfillment will only be rewarded to a minor degree. The customer won’t

pay for something he doesn’t need.

100%

150%

50%

Value

Velocity

Expectationsfor a town car

Expectationsfor a sports car

Over-fulfillment

Under-fulfillment

0.5 points per correct description

1 point per correctly

indicated area of over-

/under-fulfillment

1 point per correct value

function (steeper till

100 %)


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Task 3: Quality in the early phases – focus deviation (20 points) (L9/E9)

3.1 FMEA (8 points)

Name the formula to calculate the risk priority number (RPN). (1 point) (E9-11)

___________RPN = RNS x RNA x RND__________________

Name all possible measures for risk minimization and the corresponding risk number (RNX).

(3 points) (E9-16)

Tab. 3-1: Measure types for FMEA

Measure type Risk number

Effect limiting measure RNS

Detection measure RND

Remedial measure RNA

(0.5 points for each correct entry)

Which measure would you choose in the given example? (1 point)

Tab. 3-2: Risk numbers

RNA RNS RND

2 4 8

_________ cause/effect detecting measure______________________________________


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Calculate the missing values (one decimal place) and insert them into the table. (1 point)

Tab. 3-3: Analysis of failure numbers

Position Number Failure

numbers

[%] Sum [%]

1 2 200 42.6 42.6

2 1 140 29.8 72.4

3 5 80 17.0 89.4

4 4 35 7.4 96.8

5 3 15 3.2 100

470 100

(0.5 points per correct column) (E9-15)

Transfer the calculated values from the table into the Pareto diagram below. (1 point) (E 9-15)

Picture 3-1: Pareto analysis

(0.5 points fort he correct bars; 0.5 points for the summed line)


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Choose the products, for which – based on the Pareto analysis – measures have to be initiated.

Mark each chosen number with a cross in the table below. (1 point)

Tab. 3-4: Products

No. 1 No. 2 No. 3 No. 4 No. 5

X X X

(1 point for all three crosses)

3.2 Definitions and terms for methods of quality assurance before start of serial production (12 points)

a) (4 points) (L9-12, 15)

Method: Quality Assessment

Definition: QA accompanies the development of a product through different stages.

Goal:

- detection and assessment of failures by systematically questioning the

departments involved in the product development process at an early stage prior

to start of production

Methode: Fault Tree Analysis

Definition: FTA is a method to determine all logical combinations of

component or system failures that lead to an unwanted event.

Goals:

- Recognize failures at an early stage

- Calculate system reliability characteristics

- Avoid failure causes

(1 point per correct definition and 0.5 points per correct goal)


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b) (5 points) (L9-8)

Complete the table according to picture 3-2.

Picture 3-2: Phases and items of types of Design Reviews

(1 point per correct element)

1 PDR

2 Functional spec.

3 Development

4 Lab sample (component)

5 Qualification

6 Prototype

7 Pre-series

8 FDR

9 Pilot lot

10 Production processes


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c) (3 points) (L9-12)

Name the three steps of a Quality Assessment and the respective review item. (3 points)

Tab. 3-5: Steps of the QA

Name of the step Review item

QA 1 Concept selection

Concept

QA 2 Development prototype contract

Development prototype

QA 3 Release of series production

Intermediate and first prototype

(0.5 points for each correct entry)


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Task 4: Quality Management in Procurement (20 points)

4.1 Procurement Strategies (3 points) (L10-7)

Please fill in the missing strategies (1 to 3). (3 points)

Picture 4-1: Portfolio of different types of suppliers and procured goods

1: Procuring efficiently (1 point)

2: Securing the availability (1 point)

3: Supplier management in partnership (1 point)


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4.2 Procurement and supply strategies (8 points)

Single & Local Sourcing (4 points) (L10-12)

Quality advantage for the procuring company:

1: Creation of long-term business connections (1 point)

or: Marginal risk of communication problems

or: Reduction of transportation risks (only Local Sourcing)

Quality disadvantages for the procuring company:

1: Dependence on suppliers (1 point)

2: Low flexibility for changing suppliers (1 point)

3: Loss of technology know-how (1 point)

Just in Sequence (4 points) (L10-15)

Quality advantage for the procuring company:

1: Very fast reaction time (1 point)

or: Very slight chance of transportation damage

or: Highly reduced stocks

Quality disadvantages for the procuring company:

1: Very high dependence on suppliers (1 point)

2: Production stops when supply chain fails (1 point)

3: Very long setup time (1 point)


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4.3 Continuous supplier assessment (9 points)

Key performance index for “Procurement”:

Calculation of the sub-category “Price“ (3 points):

Comparison to other suppliers:

25/30 = 83.3% --> 100%-83% = 17% cheaper --> 100% (picture 4-2) (1 point)

Comparison to target: Target price (picture 4-2):

25/28 = 89.29% --> 95% (1 point)

Assessment of the sub-category „Price“ as a whole:

85% * (65%*95% + 25%*100% + 10%*96%) = 81.9% (1 point)

Calculation of the sub-category “Initiative for cost reduction“ (1 point):

15%*100% = 15% (1 point)

Final calculation of the category “Procurement” (1 point):

81.9% + 15% = 96.9% (1 point)

Key performance index for “Quality”:

Calculation of the sub-category “Quality performance“ (2 points):

Recognized failures during assembly:

1/20,000 = 50 ppm

Picture 4-4 at 50 ppm --> 90% (1 point)

Field failures (picture 4-5): for the 4th quarter of the year --> 2 failures

--> 2/20,000 = 100 ppm

--> Picture 4-6 at 100 ppm --> 90% (1 point)

Calculation of the sub-category “QM system“ (1 point):

10%*95% = 9.5% (1 point)

Final calculation of the category “Quality” (1 point):

90% * (80%*90% + 20%*90%) + 9.5% = 90%*90% + 9.5% = 90.5% (1 point)


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Task 5: Quality programs and quality management systems (20 points)

5.1 Quality management and standards (6 points)

The DIN EN ISO 9000 ff. is the most popular series of standards for quality management

systems. Please name the three essential standards (0.5 points each) and give short explanations

of their content in table 5-1 (0.5 points each):

Table 5-1: The three essential standards of the DIN EN ISO 9000 ff. series of standards

Name Content DIN EN ISO 9000 Fundamentals and vocabulary

DIN EN ISO 9001 Quality requirements

DIN EN ISO 9004 Guidelines for performance improvements

The DIN EN ISO 9000 contains eight quality management principles which can be used by

management to improve the performance of an organization. Please name six (0.5 points each; 3

points max.) of the eight principles (table 5-2):

Table 5-2: The principles of quality management

1 Customer orientation

2 Leadership

3 Involvement of employees

4 Process approach

5 System approach to management

6 Continuous improvement

Alt. Factual approach to decision making

Alt. Mutually beneficial supplier relationship


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5.2 Process-based quality management (4 points)

Please complete the model of process-based quality management (picture 5-1) by naming the

numbered fields in table 5-3 (0.5 points each):

Picture 5-1: Process model of DIN EN ISO 9001

Table 5-3: Elements of the DIN EN ISO 9001 process model 1 Management responsibility

2 Resource management

3 Product realisation

4 Measurement, analysis and improvement

5 Product

6 Satisfaction

7 Continuous improvement of the quality management system

8 Requirements


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5.3 Process-Structure-Matrix (7 points)

For each correctly answered line in the Process-Structure-Matrix you receive 1 point. Lines filled

out incorrectly receive 0 points.

5.4 Multiple Choice (3 points)

Each correct answer leads to 0.5 points, incorrect as well as no answers lead to 0 points.

Correct?

yes no

1 The DIN EN ISO 9001 contains requirements for the product. X 2 The certification of a quality management system is based on a first-party audit. X 3 The DIN EN ISO 9001 indicates industry-sector-specific requirements. X 4 The ISO-9001-certificate is valid without any time limitations. X 5 The ISO TS 16949 contains requirements for a quality management system for

the automotive sector. X

6 “Management decision“ and “Identify requirements“ are steps of the top-down-

approach during the implementation of a quality management system. X


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Task 6: Quality management in manufacturing (20 points)

6.1 Process variation (1 point) Please calculate the value 3s missing in table 6-1!

( ) ( ) ( ) ( ) ( )4

44.6533.6544.6546.6544.6585.6544.6557.6444.6599.65 22222

3

−+−+−+−+−=s

557.03 =s

Result 3s : formula given; 557.03 =s (1 point)

6.2 Process capability (8 points)

[ ]693.0571.0691.0648.0701.0468.0807.0557.0782.0801.010

11

1

+++++++++⋅=⋅= ∑=

n

iis

ns

672.0=s (formula 0.5 + correct result 1; in case of consistence 1)

940,0

672,0ˆ ==

na

sσ

715.0ˆ =σ (formula given; correct result 1; in case of consistence 1) (E6-15)

( ) ( )715.032

6268ˆ32 ⋅⋅

−=⋅⋅

−=σLTLUTL

cp (E6-14)

399.1=pc (formula 0.5 + correct result 1; in case of consistence 1)

[ ]12.6544.6443.6533.6501.6534.6529.6544.6577.6414.6510

11 10

1

+++++++++⋅== ∑=i

ixn

x

130.65=x (formula 0.5 + correct result 0.5) (E6-15)

{ } { }145.2

870.2

715.03

62130,65;130,6568minˆ3

;min =⋅

−−=⋅

−−=σ

LTLxxUTLcpk (E6-14)

338.1=pkc (formula 0.5 + correct result 1; in case of consistence 1)


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Result pc : 399.1=pc (4 points)

Result pkc : 338.1=pkc (2.5 points)

Process capability including justification

This process is capable, (0.5 points) because the minimum requirement pc and pkc > 1 is fulfilled. (1 point)

(1.5 points)

6.3 Control limits (4 points)

715.05

576.2130.65ˆ

576.2 ⋅+=⋅+= σn

xUALx

(E6-15)

954.65=x

UAL (formula given; correct result 1; in case of consistence 1)

715.05

576.2130.65ˆ

576.2 ⋅−=⋅−= σn

xLALx

(E6-15)

307.64=x

LAL (formula given; correct result 1; in case of consistence 1)

672.0089.2 ⋅=⋅= sbUAL ns (E6-15)

403.1=sUAL (formula given; correct result 1; in case of consistence 1)

672,0000,0 ⋅=⋅= scLAL ns (E6-15)

000,0=sLAL (formula given; correct result 1; in case of consistence 1)

Result x

UAL : formula given; 954.65=x

UAL (1)

Result x

LAL : formula given; 307.64=x

LAL (1)

Result sUAL : formula given; 403.1=sUAL (1)

Result sLAL : formula given; 000.0=sLAL (1)


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6.4 Mean/standard-deviation control chart (1 point)

1. (L6-30): Exceeding control limit (0.5 points)

2. (L6-30): More than 7 values on one side of mean (run);

alternatively: More than 7 values with the same direction of slope

(trend)

(0.5 points)

6.5 Prevention of waste (2 points)

1. (L6-3): Overproduction; alternatively: qualification of employees (0.5 points)

2. (L6-3): Failures/repair; alternatively: Transports (0.5 points)

3. (L6-3): Waiting periods; alternatively: Areas (0.5 points)

4. (L6-3): Stocks; alternatively: Distances (0.5 points)

6.6 Stocks (1.5 points)

1. (L6-5): Cover problems; alternatively: Cause costs (0.5 points)

2. (L6-5): Require storage area/depots; alternatively: Hamper work flow (0.5 points)

3. (L6-5): Prevent real control of the processes; alternatively: Mislead to

routine and comfort; alternatively: Prevent the possibility for

improvement

(0.5 points)

6.7 5S (2.5 points)

1. (L6-9): Sorting is taking out of unnecessary items and disposing of them (0.5 points)

2. (L6-9): Systematizing is arranging necessary items in good order (0.5 points)

3. (L6-9): Sweeping is cleaning the workplace (0.5 points)

4. (L6-9): Sanitizing is maintaining high standards of housekeeping (0.5 points)

5. (L6-9): Self-discipline is doing things spontaneously without being told (0.5 points)


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Task 1: Fundamentals of mathematical statistics (20 points) · 2011/07/26 Page 1 of 25 Task 1:...

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