workbook programming and supervision of cnc … · the functions of the cnc software, which will be...

WORKBOOK

PROGRAMMING AND SUPERVISION

OF CNC MACHINES

LUBLIN 2014

Projekt wspó finansowany ze rodków Unii Europejskiej wł ś ramach Europejskiego Funduszu Spo ecznegoł

Author: Radosław Cechowicz

Desktop publishing: Radosław Cechowicz

Technical editor: Radosław Cechowicz

Figures: Radosław Cechowicz

Cover and graphic design: Radosław Cechowicz

All rights reserved.

No part of this publication may be scanned, photocopied, copied or distributed in any form,

electronic, mechanical, photocopying, recording or otherwise, including the placing or

distributing in digital form on the Internet or in local area networks,

without the prior written permission of the copyright owner.

Publikacja współfinansowana ze środków Unii Europejskiej w ramach Europejskiego

Funduszu Społecznego w ramach projektu

Inżynier z gwarancją jakości – dostosowanie oferty Politechniki Lubelskiej

do wymagań europejskiego rynku pracy

© Copyright by

Radosław Cechowicz, Lublin University of Technology

Lublin 2014

First edition

Projekt wspó finansowany ze rodków Unii Europejskiej wł ś ramach Europejskiego Funduszu Spo ecznegoł

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TABLE OF CONTENTS

1. THE NC PROGRAMMING LANGUAGE.............................................................................2

1.1. Selected functions of the NC programming language...............................................................2

2. WORK STAND..............................................................................................................6

2.1. Description of the CNC control software.................................................................................6

2.2. Function codes handled by the software...................................................................................8

2.3. Programming the drilling cycles...............................................................................................9

2.4. NC code format accepted by the machine...............................................................................10

2.5. Programming the milling cycles.............................................................................................11

3. REPORTING THE RESULT OF THE PHYSICAL QUANTITY MEASUREMENT.........................12

3.1. The rules for stating the result of the measurement................................................................12

3.2. The construction of the stem-and-leaf and the histogram diagram..........................................12

3.3. Deming's experiment..............................................................................................................13

4. DESCRIPTIVE STATISTICS AND THEIR PRESENTATION...................................................13

4.1. Construction of a histogram. Box-plot diagrams....................................................................13

4.2. Pareto analysis........................................................................................................................15

5. PROPERTIES OF A NORMAL DISTRIBUTION AND ITS USAGE.........................................15

5.1. The Central limit theorem.......................................................................................................15

5.2. Estimating of the non-conforming fraction. Process capability..............................................16

6. TEST OF THE STATISTICAL HYPOTHESES....................................................................17

6.1. Determination of the sample size; Power of a statistical test;.................................................17

Projekt współfinansowany ze środków Unii Europejskiej w ramach Europejskiego Funduszu Społecznego

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1. THE NC PROGRAMMING LANGUAGE

1.1. Selected functions of the NC programming language

NOTE: Bold font has been used for the commands defined in ISO6983-1:2009

Default power-on commands according to ISO6983-1:2009 are on grey background.

Turning Milling Description Example M1

Program and block numbering

O O Program number O0122

N N Block number N0010 ...

Machine measurement units, coordinate system and reference points (program zero)

G53 G53 Program reference point reset G53 M1

G54, G55,

G56...G59

G54, G55,

G56...G59Reference point set (program zero coordinates) G54 M1

G50, G92 G92Sets program zero coordinates; used in machines that do

not have G54..G59. Works like G54...G59 and G41..G44G92 X10 Y20 Z15 L

G20, G70 G20, G70 Inch mode (coordinate values are in inch) G20 M2

G21, G71 G21, G71 Metric mode (coordinate values are in milimeters) G21 M2

G90 G90 Absolute mode (all dimensions refer to program zero) G90 M3

G91 G91 Incremental mode (dimension chains) G91 M3

-- G17 Sets work plane to XY G17 M4

-- G18 Sets work plane to XZ G18 M4

-- G19 Sets work plane to YZ G19 M4

Cutting parameters

G96 --Constant cutting speed (Cutting speed value in m/min or

ipm is set using the S command)G96 S150 M5

G97 --Constant spindle rotating speed (Rotating speed value in

rpm is set using the S command)G96 S2000 M5

G93 G93Programs feed speed by setting the time of the operation

(Inverse time). Ex: G93 F1 sets operation time to 1minG93 F10 M6

G98 G94 G94 Feed set in mm/min or ipm G98 F100 M6

G99 G95 -- Feed set in mm/rotation or ipr G99 F100 M6

1 Function type according to ISO6983-1:2009:

M – Modal – after calling remains active until modified or replaced by another command from the same

group (groups are designated with numbers – M1, M2, etc.)

L – not modal – active only in a block where called


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Turning Milling Description Example M

F -- Feed value (used in conjunction with G98/G99) G98 F100 M

-- F Feed value (in milling centres in mm/min or ipm) F100 M

S -- Spindle speed value (used in conjunction with G96/G97) S1300 M

-- S Spindle speed value (in milling centres usually in rpm) S1300 M

T -- Tool change (followed by tool nr and wear offset nr) T0202 M

-- T Tool change (followed by tool number)T2

or T2 M06M

Tool movement - basic

G00 G00 Rapid motion G00 X15.2 Z1.5 M7

G01 G01 Linear motion (linear interpolation; used with F) G01 X1.5 Y12.0 F80 M7

G02 --Circular interpolation, clockwise (used with F and

appropriate parameters, ex: X, Z, R or X, Z, I, K)

G02 X2.0 Z4.0 I-12.5

K2.5

or G02 X5.0 Z4.0 R5.0

M7

-- G02Circular interpolation, clockwise (used with F and

appropriate parameters, ex: X, Y, R or X, Y, I, J)

G02 X2.0 Y4.0 I-12.5

J2.5

or G02 X5.0 Y4.0 R5.0

M7

G03 --Circular interpolation, anticlockwise (used with F and

appropriate parameters, ex: X, Z, R or X, Z, I, K)

G03 X2.0 Z4.0 I-12.5

K2.5

or G03 X5.0 Z4.0 R5.0

M7

-- G03Circular interpolation, anticlockwise (used with F and

appropriate parameters, ex: X, Y, R or X, Y, I, J)

G03 X2.0 Y4.0 I-12.5

J2.5

or G03 X5.0 Y4.0 R5.0

M7

G04 G04Dwell. Dwell time can be defined by parameter X, F or P

(units: seconds or milliseconds)

G04 X2.0 (2s)

or G04 F20 (20ms)M7

G06 G06Parabolic interpolation. Parameters I, J, K are used to

define vertex coordinates

G06 X2.0 Y4.0 I-12.5

J2.5M7

G33 G33 Threading, constant pitch. M7

G34 G34 Threading, increasing pitch. M7

G35 G35 Threading, decreasing pitch. M7

Tool movement - advanced

G09 G09

Exact stop. Operation ends after the tool comes to a

complete stop. Used to improve accuracy, slows down

the program execution. NON-MODAL version.

G09 L

G60 G60

Exact stop function. Operation ends after the tool comes

to a complete stop. Used to improve accuracy, slows

down the program execution. MODAL version.

G60 M8

G64 G64 Exact stop reset (cancellation) – see G60 G64 M8

G63 G63

Sets the threading mode. In threading mode the

„Feedrate Override” control on the operator's panel is

disabled, feed cannot be controlled manually. Used for

threading with taps.

G63 L


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G40 G40

Resets tool radius compensation (see G41, G42)

According to ISO6983-1:2009 this function also resets

tool length compensation (see. G43, G44).

Fanuc controllers use G49 to reset toll length

compensation.

G40 M9

G41 G41

Sets tool radius compensation (cutting on the right side

of tool path). Tool radius is read from the pre-set D

register.

G41 D... M9

G42 G42Sets tool radius compensation (cutting on the left side of

tool path). Tool radius is read from the pre-set D register.G42 D... M9

G43 G43Sets tool length compensation (toll length is a positive

number). Tool length is read from the pre-set H register.G43 H... (M9)

G44 G44Sets tool length compensation (toll length is a negative

number). Tool length is read from the pre-set H register.G43 H... (M9)

G49 G49Resets tool radius compensation in Fanuc controllers

(see G40)G49 (M9)

Fixed cycles2

G28, G74 G28, G74Machine reference point return (tool change point

return)G91 G28 Z0 L

G80 G80 Cancels all fixed cycles (see G81..G89) G80 M10

G81 G81 Sets the fixed cycle – drilling M10

G82 G82Sets the fixed cycle – drilling with dwell

(counter-boring)M10

G83 G83Sets the fixed cycle – deep hole drilling (with tool

withdrawal)M10

G84 G84 Sets the fixed cycle – tapping M10

G85 G85 Sets the fixed cycle – boring (rough) M10

G86 G86 Sets the fixed cycle – boring with dwell (rough) M10

G87 G87 Sets the fixed cycle – boring (finishing) M10

G88 G88 Sets the fixed cycle – boring with dwell (finishing) M10

G89 G89 Sets the fixed cycle – reaming M10

Machine functions3

M00 M00 Stop (unconditional) M00 A L

M01 M01Optional Stop (active only if “Optional Stop” switch in

ON position)M01 A L

M02 M02Program end. Stops the spindle and other devices (like

coolant pump). Used for machine reset.M02 A L

2 Application examples are presented during classes

3 Function type according to ISO6983-1:2009:

A – Function activated after tool stops (tool movement completed before function)

B – Function activated parallel to tool movement (function engaged during tool motion)

M – Modal – active until modified or cancelled by a function from the same group

L – Not modal – active only in the block where was called


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M03 M03 Spindle start clockwise M03 M

M04 M04 Spindle start anticlockwise M04 M

M05 M05 Spindle stop M05 M

M06 M06Tool change. Coolant pump may be switched off on

some machines.M06 L

M07 M07 Coolant on (mist)

M08 M08 Coolant on (coolant pump on) M08

M09 M09 Coolant off M09

M10 M10 Material hold (engage material holding system) M10 L

M11 M11 Material release (disengage material holding system) M11 L

M20 -- Tailstosk disengage M20

M21 -- Tailstock engage M21

M30 M30

End of data. Like M02 but machine returns to the

beginning of the active program (so it can be re-started

with green button)

M30 A L

M41 --Spindle speed ranges – sets the first speed range (usually

used for rough machining)M41

M42 -- Spindle speed ranges – sets the second speed range M42

M43 -- Spindle speed ranges – sets the third speed range M43

M44 -- Spindle speed ranges – sets the fourth speed range M44

M48 M48Enables spindle speed and feedrate control with the

operator's panel controls (see M49)M48

M49 M49Disables spindle speed and feedrate control with the

operator's panel controls.M49 A B

M60 M60Pallet change or part setup change. Stops spindle and

coolant M60 L

M98 M98

Sub-program call

(U – program number, L – number of program

executions)

M98 U123 L3

M99, M17 M99,M17 Sub-program end – return to the main program M99

Notes:

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2. WORK STAND

General view of the work stand with the C-type milling machine is shown on Fig. 1.

2.1. Description of the CNC control software

The functions of the cnc software, which will be used during the laboratory exercises can be

accessed from the main screen (Fig. 2), the programming screen (Fig. 4) and the manual operations

screen .

The function keys in the main screen have the following assignments:

• Esc (koniec) – end of task (exits the program or returns to main screen)

• F1 (pomoc) – help (in Polish)

• F2 (programy) – access to file operations menu (also allows to create new program)

• F3 (parametry) – edit or manage machine parameters (like the scaling factor)

• F4 (inne funkcje) )- other functions

• F5 (bazuj) – homing (must be executed after the machine is switched on)

• F6 (wykonaj) – execute the active program (program must be loaded with F10 first)


Fig. 1:Work stand with the CNC milling machine

spindle controller

C-frame milling machine

main switch

control computer

emergency switch

axis controller

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• F7 (reczna) – manual control mode (see Fig. 3)

• F8 (symuluj) – program simulation mode (program must be loaded with F10 first)

• F9 (popraw) – edit the active program (quick alternative to F2)

• F10 (ładuj) – choose and load the program into machine memory


Fig. 2: Main screen of the controlling program (before homing the machine)

current tool position

active program name, scaling factor

coordinates of the program zero

machine coniguration parameters

function keys

Fig. 4: New program window (available after pressing F2 on the main screen). Program editing window

becomes available after the creation of a new program or after pressing F9 on the main screen.

program edit operations

create new program

Fig. 3: Manual control screen

current tool coordinates

axis speed value

axis speed controls

Y axis controls (Left/Right arrow)

Z axis control (Page Up/ Page Down)

X axis control (Up/Down arrow)

Tool change menu

Spindle control (I nsert)

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After the NC code has been written, the program has to be tested with the simulation functions

(main screen: Fig. 5). The following functions are available in the simulation screen menu:

PodPliku - the preview of all the tool paths (the entire program)

DefMater - sets of the size and position of the material (a grey rectangle on the preview screen)

DoMater - sets the program zero point in the upper-left corner of the defined material (all axes)

DefOffset - manual entering of the coordinates of the program zero point

ZerOffset - sets the program zero point in the machine reference point (machine zero; all the axes)

Stan - screen displaying the information on the range of the axes movement (Fig. 7)

TrajPow - draws the programmed tool path (full screen)

TrajRze - draws the programmed tool path (against the machine work area)

Symuluj - simulation of the machining (requires the correct setting of the work-piece dimensions

and program zero point)

Kolory - configuration of colours assigned to particular tools

Koniec – quits the simulation mode.

2.2. Function codes handled by the software

Machine functions Preparatory functions

M0, M1 - program stop,

M2, M30 - program end,

M3, M4 - spindle on

M5 - spindle off

M99 - end of the sub-program

F - feed rate in mm/min

T - tool change

% - this symbol is obligatory at the beginning and

at the end of each program

G0 – rapid motion

G1 – linear interpolation

G2, G3 – circular interpolation

G4 – dwell (argument: code X__[ms])

G22 – sub-program call (P__)

G40 – tool radius compensation off

G41, G42 – tool radius compensation

G80 – cancel canned (fixed) cycle

G90, G91 – absolute and incremental positioning

Fixed cycles: G61, G77, G78, G79, G81, G82,

G83, G87, G88, G89

Full description of the CNC software can be found in the documentation of the machine.


Fig. 5: Main screen of the simulation mode (can be accessed from the main screen after pressing F8).

machine zero point

simulation screen menu

axis Z range (of the active program)

axes X and Y range (of the active prgm)

position of program zero on Z axis

program zero position on XY plane

machine workspace (green rectangle)

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2.3. Programming the drilling cycles

The milling machines in the CNC machine laboratory have the following fixed cycles:

No. G-code Name Description

1 G81 Drilling Syntax: G81 Z... W...

Z – depth of a hole – relative (incremental) negative value,

calculated from the retraction plane (see Fig. 6).

W – distance to the retraction plane – positive incremental value

measured from the initial tool position (see Fig. 6).

2 G82 Chip-breaking

drilling

Syntax: G82 Z... W... B... D... K...

B – time for chip breaking in seconds

D – value by which successive K-steps are decreased (positive)

K – length of a single drilling step between the successive

intervals for the chip-breaking (positive; see Fig. 7)

Other parameters as in G81

3 G83 Peck drilling

(with breaking

and removal of

chips)

Syntax: G83 Z... W... B... D... K... A...

A – time for chip removal in seconds (tool dwells at the retract

plane)

Other parameters as in G81 and G82


Fig. 6: Initial and tool retract planes in fixes cycles programming

initial plane ZB

tool retraction plane ZR

rapid motion traverse

programmed end position ZS

ZB

initial tool position

ZR

ZS

WZ machining with programmed feed

Fig. 7: Programming the chip-breaking cycle and pocket machining

Płaszczyzna początkowa ZB

Płaszczyzna wycofania ZR

Przejazd ruchem przestawczym

Pozycja końcowa ZS

ZB

Narzędzie w pozycji początkowej

ZR

ZS

WZ

Pierwszy przejazd ruchem roboczym (K)

Kolejny przejazd ruchem roboczym (K-D)

K

K-D

K-D

initial tool position

initial plane ZB

rapid motion traverse

retract plane ZR

drilling/ milling depth (irst tool entry)

drilling/ milling depth (successive entr.)

programmed end position ZS

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4 G79 Execution of

a programmed

cycle in a single

point

Syntax: G79 X... Y...

X, Y – coordinates of the point in which the hole is to be made

5 G78 Execution of

a series of

programmed

cycles along a

straight line

Syntax: G78 X... Y... I... J... S...

or G78 X... Y... A... D... S...

X, Y – coordinates of the first hole to be made

I, J – relative distance to the next hole along the X and Y axes

A - inclination angle of a line in relation to axis X (positive in the

1st and the 2nd quadrant)

D – distance to the next point along the line

S – number of repetitions (number of holes to be made)

6 G77 Execution of

a series of

programmed

cycles along an

arc

Syntax: G77 X... Y... A... B... D... S...

X, Y – coordinates of the centre of the arc (relative to the

program zero point)

A – angle between axis X and the radius indicating the first hole

B – the radius of the arc on which the holes are to be made

D – angular distance (in degrees) between the succeeding holes

S – number of repetitions (number of holes to be made)

2.4. NC code format accepted by the machine

When writing the program in the NC language, the following rules have to be respected:

• A program has to begin and end with the "%" symbol.

• At the end of the program, the line before the "%" symbol has to contain the "M30" command,

which ends the program; previously, the spindle has to be turned off with the "M5" command.

• At the beginning of the program, a tool has to be set (even if it has already been mounted in the

spindle; the "T___" command) and moved along all the axes (X, Y and Z). It is recommended to

move the tool to the program zero point on the X and Y axes and up to the safe position over the

material on the Z axis.

• Whenever radius compensation is used, the first and last sections of the tool path should be

programmed as straight lines (G0 and G1 commands).

• Arcs can be programmed through setting the radius "R" (positive or negative value) or the

coordinates of the centre (I and J; the coordinates should be absolute).


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2.5. Programming the milling cycles


1 G87 Rectangular

pocket milling

Syntax: G87 X... Y... Z... I... K... W...

X, Y – dimensions of a pocket along the X and Y axes

Z – depth of a hole – relative (incremental) negative value,

measured from the retraction plane (as in Fig. 6).

W – distance to the retraction plane – positive value measured

incrementally from the initial tool position (as in Fig. 6).

I – depth of cut on the XY plane in the percentage of the width of

the tool – positive value (as in Fig. 8).

K – depth of cut along the Z axis – positive incremental value as

shown on Fig. 7

2 G88 Circular pocket

milling

Syntax: G88 B... Z... I... K... W...

B – radius of the pocket

Other parameters as in G87

3 G89 Milling of a

circular pocket

with a bos

Syntax: G89 B... C... Z... I... K... W...

C – radius of the bos

Other parameters as in G87 and G88

Notes

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Fig. 8: Pocket milling cycles available on the machines in the laboratory

XY

I

G87 G88 G89

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3. REPORTING THE RESULT OF THE PHYSICAL QUANTITY

MEASUREMENT

3.1. The rules for stating the result of the measurement

Problem 1: The result of the measurement indicates that the frequency of string vibrations equals

210 Hz. The uncertainty interval for the measurement was established as the following: 200-220 Hz.

Write down the result of the measurement using the standard form.

Problem 2: The result of the measurement determined the vibration frequency to be 230±15Hz.

Establish the uncertainty interval for the given outcome. How to interpret the record of the

measurement result?

Problem 3: Write down the uncertainties of the following measurements:

the best approximation uncertainty interval

34,8 km od 34,2 do 35,4 km

23,12 MPa od 20 do 26 MPa

112 V od 108 do 116 V

Problem 4: Write down the following results of the measurements in a proper form:

p = 7,123476 ± 0,02345 MPa;

x = 4,2345*104 ± 2 m;

q = 2,45678*10-7±3*10-9 F;

x = 0,000000567± 0,00000003 m;

p = 4,345* 103±22 kPa;

t = 1,6234 ± 1 s;

t = 3,8932 ± 3 s;

3.2. The construction of the stem-and-leaf and the histogram diagram

Problem 1: The results of the measurements are organised into a table (Table 1) and show the

percentage of cotton in a textile material.

Design the stem-and-leaf display and, on the basis of the obtained diagram, determine the mean

value, median, upper and lower quartiles and the interquartile range.

Verify the results of the calculations using the STATISTICA software.


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34,2 37,8 33,6 32,6 33,8 35,8 34,7 34,6

33,1 36,6 34,7 33,1 34,2 37,6 33,6 33,6

34,5 35,4 35 34,6 33,4 37,3 32,5 34,1

35,6 34,6 35,4 35,9 34,7 34,6 34,1 34,7

36,3 33,8 36,2 34,7 34,6 35,5 35,1 35,7

35,1 37,1 36,8 33,6 35,2 32,8 36,8 36,8

34,7 34 35,1 32,9 35 32,1 37,9 34,3

33,6 34,1 35,3 33,5 34,9 34,5 36,4 32,7

Table 1: Measurement results of the percentage of cotton in a textile material.

3.3. Deming's experiment

Problem 1: Create a new variable of a Statistica spreadsheet and name it as D.

Using the RndNormal(x) function of the Statistica software, generate a sequence of 100

pseudo-random numbers, whose mean value is 50 and standard deviation equals 2.

Afterwards, generate a sequence of numbers that constitutes the difference between the mean

value (50) and the previously generated variable.

Record the result of the calculations in the next variable – DR symbol.

Calculate the backward differences for the original D sequence and DR variable, and assign the

result to the next variable W, then calculate its standard deviation.

Which of the considered variables D and W shows greater dispersion? Explain the obtained result.

4. DESCRIPTIVE STATISTICS AND THEIR PRESENTATION

4.1. Construction of a histogram. Box-plot diagrams

Problem 1: Multiple measurement samples of the post-mould shrinkage of the moulded pieces are

organised in a table (Table 2). Complete the following steps:

Using the STATISTICA software, prepare a box-plot diagram, which compares the results of the

measurements obtained in particular samples s1 ÷ s10. Then, make a consolidated histogram including

all the results of the measurements (s variable). Compare the box-plot diagrams for s1 ÷ s10 variables

with the result of the histogram for the s variable. Is there a substantial difference between the results

of the measurements?

Calculate the mean value and standard deviation for particular s1 ÷ s10 variables. Afterwards,

calculate the mean value of means and the standard error. Compare the obtained results with the result

of the calculation of the mean value of the s variable. Comment on the obtained results.


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Assess the goodness of fit of the distribution of the s variable measurements to the normal

distribution using the probability-probability plot;

Establish the fraction of defectively manufactured moulded pieces, assuming that the distribution

of the post-mould shrinkage fits the normal distribution. Assume that the lower and upper

specification limit equals 3.2 and 7.7 (%), respectively.

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

4,5 6,2 5,4 4,8 3,6 4,7 5,1 4,8 4,4 5,5

5,1 4,2 5,0 5,4 7,1 6,1 6,0 5,5 6,4 6,5

4,3 4,2 4,1 5,0 3,7 5,8 5,7 5,7 6,1 4,7

4,6 4,3 6,5 7,7 4,4 4,9 4,9 4,6 6,1 5,6

5,7 4,2 6,6 4,8 5,0 6,8 3,7 3,9 4,9 5,9

5,5 4,6 4,7 6,0 6,4 7,0 6,1 6,5 5,1 5,5

6,1 3,8 5,7 6,7 6,3 5,2 5,5 6,5 5,2 7,5

5,1 4,0 7,0 5,8 7,0 5,9 6,0 5,6 5,5 4,2

6,5 7,3 5,9 6,0 7,3 5,4 4,6 6,6 5,4 3,8

5,3 6,3 5,7 5,4 5,6 5,8 4,7 4,9 6,3 3,6

Table 2: Measurement results of the post-mould shrinkage of the moulded pieces. Comment: a table header row

shows a symbol of a sample, while a corresponding table column organises the results of this sample

Problem 2: Multiple measurement samples of the voltage on the battery terminals are organized

into a Table Table 3. Prepare a histogram (empirical distribution) of the analysed variable and then

calculate and mark the following descriptive statistics: the mean value, median, mode and the upper

and lower quartile.

A1 A2 A3 A4 A5 A6

12,62 12,74 12,7 12,63 12,63 12,66

12,59 12,68 12,79 12,68 12,65 12,56

12,59 12,63 12,61 12,56 12,65 12,66

12,68 12,61 12,75 12,56 12,62 12,71

12,66 12,59 12,68 12,59 12,71 12,73

12,68 12,67 12,63 12,57 12,64 12,6

12,64 12,62 12,73 12,64 12,67 12,71

12,67 12,69 12,58 12,62 12,61 12,73

12,64 12,65 12,61 12,69 12,63 12,61

12,66 12,67 12,63 12,61 12,69 12,72

Table 3: Measurement results of the voltage taken on the battery terminals. Comment: a table header shows a

symbol of a sample, while a corresponding table column organizes the results of this sample


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4.2. Pareto analysis

Problem 1: The results of the moulding process observation were presented in relation to the

registered defects and the expenses borne during the production of the moulded pieces (see Table

Table 4). Fill in the table columns (percentage of defects, percentage of expenses). Given so, prepare

two independent statements: the first concerning the percentage of defects and the second regarding

the percentage of the expenses, according to the defect type. In order to reduce the loss sustained

during the manufacturing, take advantage of the Pareto Analysis and establish which of the defects

should be eliminated first?

Type of

defect

Flaw

description

No. of

defects

[-]

Perc. of

defects

[%]

Expenses of

materials,

[zł]

Expenses

of labour

[zł]

Expenses of

manufacturing

[zł]

Total

expenses

[zł]

Perc. of

expenses,

[%]

1 underflowing 59 11,8 7,25 23,52 42,57

2 tension 21 194,67 15,14 48,69 258,5

3 line of flows 20 181,8 11,08 35,43 228,31

4 shrinkage 2 0,38 1,14 3,64 5,16

5 overflowing 60 11,4 8,08 26,34 45,82

Table 4: Results of the moulding process observation

5. PROPERTIES OF A NORMAL DISTRIBUTION AND ITS USAGE

5.1. The Central limit theorem

Problem 1: Launch the program named "The Central Theorem Limit.exe", attached to the script,

familiarise yourself with the content of the exercise and carry out the following instructions:

1. Choose the normal distribution form the "Population distribution" list. Select 5 as the number

of measurements in a sample. Next, choose the mean value as the statistic and generate 1000

samples (measurements). Are the mean value of means and the standard error consistent with

the population parameters ? What can be thought of the obtained distribution of the sample

statistics.

2. Repeat the instruction (1) but choose the standard deviation (SD) as the analysed statistic and

generate 1000 samples. Is the mean value of the calculated SD statistic consistent with the

value of the population parameter?


16

___________________________________________________________________________

3. Repeat the instruction (1), though change the distribution function to the exponential

distribution. The number of measurements in a sample is to be n = 5. What is the distribution

form of the values of the statistic from the sample ?;

4. Repeat the instruction (3), though increase the number of measurements in a sample to 20;

5. Repeat the instruction (3), though increase the number of measurements in a sample to 20 and,

simultaneously, change the form of distribution to the uniform one;

6. Repeat the instruction (5), though increase the number of measurement in a sample to 100.

Interpret the obtained results of the calculations.

5.2. Estimating of the non-conforming fraction. Process capability

Problem 1: In many cases of the industrial use of the SPC, it is required to estimate the proportion

of the production which does not meet the expected specification. Assume that the technological

process consists in dividing the product and final packaging of its portions. 100 portions of this

product were randomly chosen and weighed. It turned out that the observations belonged to the normal

distribution (Fig. 9). The mean value of the measurement was 255g, while the standard deviation

equalled 4.73g. 250±10 g was adopted as the upper and lower specification of a single portion. How

many portions were produced outside the limits of specification? How will the non-conforming

fraction change if the mean value of the portions is consistent with the aim of the process?

Fig. 9: Probability distributions illustrating the measurement results with the limits of specification being

highlighted


y = n o r m a l ( x ; 2 5 5 ; 4 , 7 3 )

2 3 0 2 3 5 2 4 0 2 4 5 2 5 0 2 5 5 2 6 0 2 6 50 , 0 0

0 , 0 2

0 , 0 4

0 , 0 6

0 , 0 8

17

___________________________________________________________________________

6. TEST OF THE STATISTICAL HYPOTHESES

6.1. Determination of the sample size; Power of a statistical test;

Problem 1: The melting point measurement carried out on n=10 units of the connectors used in

the fuel production process equalled T=154.2oC. It was established that the temperature measurements

belong to the normal distribution with the standard deviation σ=1.5oC.

1. Carry out a statistical test comparing the results of the measurement of the connectors’ melting

point with the referential value T0=155oC, assuming the value of I-type error, α=0.05, as

defining for the level of statistical significance. How to interpret the test results?

2. What is the value of the probability P of the conducted test;

3. What is the value of a second-type error β, assuming that the population mean is μ = 150?;

4. What would be the required n sample size if the II-type error was limited by a condition:

β<0.1. Assume that the I-type error equals α=0.05.

Problem 2: Assume that the quality characteristic R describes the wear of the new construction of

the drive-train element, measured after 25 000 km mileage, and is an important aspect associated with

the warranty repairs. 17 drive-train units were examined and the mean value was determined to be

4.42 (units). The previously performed tests proved that the analysed quality characteristic belongs to

the normal distribution and the standard deviation value equals σ=0.7.

On the basis of the given information, carry out a statistical test in order to find out whether the

drive-train new construction meets the requirements included in the design (specification) of the

drive-train R0=3.8. Assume that the I-type error equals α=0.05. What is the power of the test ?

What should be the sample size if a quality engineer would like to detect a change in a

construction wear dR = 1.25 σ (units). The power of the test is assumed to be 0.95?


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