[Type text]
[Type text] [Type text]
USE OF
STATiSTiCS
AT
Every single engine we make at Rolls-Royce needs to be perfect. There is no
room for error. We measure 1000’s of locations over every surface on every
part in an engine...and they all have to be perfect.
It is impossible to do this manually when over the next 20 years Rolls-Royce
are required to make on average 20 engines per day.
A simple statistical method is used to highlight how accurately we are
manufacturing our engines.
Very little deviation from ‘perfect’ is allowed at Rolls-Royce. As an example,
the tolerance of a Fan Disc’s Slot Depth is ± 0,1mm. That’s a max allowance of
200 microns, 100 above and 100 below the nominal – bear in mind that a sheet
of paper is normally 100 microns thick. (You can see the Fan Disc on the front of the engine below).
So, The Maths: SPC stands for Statistical Process Control. We use this to
identify problems on our engines and to make sure the manufacturing process
is operating at its best. Fewer errors, means less scrap and less money wasted.
Feature X
Individual Value
I Chart
Capability Histogram
UCL=0.06508
LSL
S pecifications
LS L 0.03
U S L 0.07
_
X=0.05013
0.05
2
0.04
LCL=0.03518
4
7
10
13
16
19
22
25
28
0.0300 0.0375 0.0450 0.0525 0.0600 0.0675
Moving Range Chart
Normal Prob Plot
0.02
Moving Range
USL
0.06
1
A D: 0.380, P : 0.382
UCL=0.01836
0.01
__
MR=0.00562
0.00
LCL=0
1
4
7
10
13
16
19
22
25
28
0.030
Last 25 Observations
0.045
Within
S tD ev 0.00498288
Cp
1.34
C pk
1.33
0.05
0.04
10
15
20
Observation
Jonathon Cooper
0.060
Capability Plot
0.06
Values
All of the data is passed
through the SPC software
and a 6-Pack Chart is
created.
25
30
Within
O v erall
S pecs
O v erall
S tD ev 0.0059465
Pp
1.12
P pk
1.11
C pm
*
Jonathon Cooper
[Type text]
[Type text] [Type text]
Feature
A perfect spread of values
on theXhistogram would show the highest quantity
I Chart
Capability
Histogram
on the
nominal (centre) with a few anomalies
either side
– well USL
away from the
LSL
UCL=173.93834
tolerance boundaries. In the above chart the values tend towards the
lower
S pecifications
LS L 173.915
_
limit.
U S L 173.945
X=173.92689
1
4
7
In the bottom right there are numbers; these
are
telling
us6 the
Process
6
0
4
8
2
0
4
LCL=173.91544
91 .92 . 92 .92 .93 . 93 .94 .94
.
3 73 73 73 73 73 73 73
7
Capability.
This
is
a
complicated
word
for
something
simple.
It
tells
us how
10
13
16
19
22
25
28
1
1
1
1
1
1
1
1
consistent
our work is. The Process Capability Index
(Cpk Prob
– eqnPlot
below) is a
Moving
Range Chart
Normal
A D:
: 0.106number):
single number that tells us ifUCL=0.01407
it’s good (high number)
or0.604,
bad P(low
1.33 or above is good.
__
MR=0.00431
Cpk can determine short-term
capability and Ppk for long-term capability.
LCL=0
1
4
7
Just13to16clarify
we are making parts 173.92
almost exactly173.93
to the
19 good
22
25means
28
173.94
specification
every time – in every million we make Capability
on average
63 are rejected
Last
25 Observations
Plot
(0.0063%). Bad means it’s
Within
Within
O v erall
S tD ev 0.00381817
S tD ev 0.00406213
different every time and nowhere
Cp
1.31
Pp
1.23
O v erall
C
pk
1.04
P
pk
0.98
near the target (nominal).
10
C pm
10
*
S pecs
Cp15 tells us20 how well
fits in
25 the data
30
theObservation
limits and Cpk tells us how
centred the data is. In a perfect world everything would be bang on centre –
nominal every time.
The mean, variance and standard deviation are calculated and used to model
the variability from nominal distribution (a bell curve) by determining the Cp,
Cpk and Ppk. The normal probability plot shows how the actual values differ
from the predicted variation – the straight line being perfectly distributed.
By using basic statistical equations I learnt at college, I am able to assist with
the production of faultless aircraft engines. Ultimately, a strong mathematics
foundation allows me to tailor and interpret these charts and use them to
improve the way we manufacture engines.