Task 1: Fundamentals of mathematical statistics (20 points) · 2011/07/26 Page 1 of 25 Task 1:...
Transcript of 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 Page 1 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
0.5 points for the correct
number of classes (3)
Σ =1 point
0.5 points for the correct
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.
0.5 points for the correct
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
0.5 points for the correct
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
1 point for the correct
sample size (25)
Σ =2 points
0.5 points for the correct
answer and
0.5 points for the correct
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
1 point for the correct
formula
0.5 points per correct
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
0.5 points per correct
absolute ranking
0.5 points per correct
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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