The journal of the
Institute of Quality Assurance
Vol. 19 No. 2 June
1993
_____________________________________________
QUALITY
FORUM
Problem-solving using
simple statistical analysis:
A case study
QUALITY
FORUM
formerly Quality Assurance
Volume 19 Number 2 June 1993
PROBLEM-SOLVING USING
SIMPLE
STATISTICAL ANALYSIS:
A case study
D. SHERRATT
Quality Assurance Manager,
Armitage Shanks Ltd, Cannock
Armitage Shanks Ltd is a traditionally-based manufacturer of kitchen,
bathroom, sanitaryware and laboratory fittings. Although enjoying a long-established
reputation for product and service quality, the Group of Companies is committed
to on-going improvement. A by-product
of this quality initiative is the subject of this paper, which describes how a complex and persistent
problem at the Wolverhampton factory was resolved by the development and application of a simple form
of statistical analysis.
Introduction
The Engineering Division's
Wolverhampton operations consist of a manufacturing facility producing
nickel-chromium-plated brass taps and bidet and mixer units designed to
complement the wide-ranging styles of Armitage Shanks ceramic and plastic
products, but with particular emphasis upon the higher volume 'budget' range
products that face vigorous competition
from low-priced imports.
In order to achieve the corporate
objective of a larger share of this market (in which the pursuit of competitive
pricing must not compromise product or service quality), the manufacturing
operations are subjected to continual review and
development. In line with this
strategy, the Wolverhampton site gained BS 5750
Part 2 registration for its quality assurance system in 1989. Since then, it has undergone a comprehensive
management development programme aimed at improving the identification and
fulfilment of business needs, one of the more obvious being the need to reduce
the wastage of manufacturing materials and resources.
Company production system
The company production system
consists of a series of largely autonomous departments which form a normal
engineering process chain:
FOUNDRY - brass
gravity diecasting and fnishing
MACHINE
SHOP - automatic and semi-automatic machining
POLISHING
SHOP - automatic and manual linishing and polishing
PLATING
PLANT - fully automatic nickel-chromium-plating
ASSEMBLY
SHOP - manual assembly, testing and packaging
This production system is supported
by ancillary services including: drawing office, laboratory, methods engineering, works engineering and
maintenance, purchasing, goods inwards, work study, production control,
toolroom, quality assurance and personnel.
Subject component
The subject, a diecast brass body casting, is the main component of the
relatively high-volume 3/4" bath pillar tap from the 'Silverspa' range of
Armitage Shanks products (Figure 1).
Component manufacture
This brief description of component manufacturing is limited to the
three principal departmental functions involved in the problem causes or
effects.
Figure 1. Silverspa bath
pillar tap
Tooling manufacture
All tooling for both the foundry and
the machine shop was designed and mainly manufactured on site in the toolroom,
and consisted of:
1 Foundry tooling
Cast-iron
coreboxes, each having twin core impressions.
Single impression, hand-cast dies.
2 Machine shop tooling
Steel machine jaw sets. (Eight of
these were used on each of two machines.)
In each case tooling replacement was
on-going. New tooling was checked, as
far as was practicable, in the Quality Assurance Department and approved prior to issue to the relevant production department.
Casting process
During any production day in the
foundry, castings could be simultaneously manufactured from up to six dies,
each using cores produced from either impression of more than one corebox. Each die was uniquely identified inside the
casting cavity, so that all castings could be traced back to source. This was particularly necessary, since the
subsequent finishing operations caused castings, from all dies in use, to
become mixed in the skips in which they were transported to the machine shop.
For the casting process, dies were
hand-clamped and poured, and the casting cavities were cleaned periodically, at
the discretion of the caster, to remove the build-up of carbon-based die
coating.
Machining process
The machining route was through
either of two identical, hand-fed, but otherwise fully automatic, eight-station
indexing machines- producing one fully machined component approximately every
seven seconds.
Skilled machine-tool-setters carried
out the task of setting up the multiple cutting tools and sets of holding jaws,
and supplied proof samples to the section patrol inspector for verification
that the optimum setting conditions had been achieved. During production, machine operators and
patrol inspectors carried out periodic monitoring checks.
The problem
Nature and effects
The problem was one of unpredictable
process variation, manifesting itself in the machine shop, where examination of
fully machined castings revealed inconsistencies in the amount of machining
stock removed from machined faces in the horizontal plane, three of these being
particularly susceptible to variation (Figure 2).
The base face and the critical valve
seat face were dimensionally related by close tolerances and were required
to 'clean up' fully on the removal of a machining stock allowance of
approximately 1.5mm. Failure to do so
would result in the scrapping of the casting. At the
opposite extreme, the removal of more than 2.5mm of material from the valve seat face was undesirable, since
it impaired the operating efficiency of the tap.
In the case of the spigot face there was no specific
requirement for it to 'clean up' by machining; therefore, since the machining
stock allowance was minimal, it often exhibited various stages of a partial
'clean up' condition which served as a convenient indicator of variation.
Traditional countermeasures
The unpredictability of the process
and the resultant scrap rates necessitated constant monitoring by machine
operators and patrol inspectors, resulting in frequent machine stoppages and
the involvement of machine-tool-setters to carry out remedial adjustments to
tool-settings. At best, this action
merely effected a temporary reduction in the incidence of scrap. On other occasions, it brought no
appreciable improvement, and at such times it became necessary to segregate
unmachined castings manually into batches, according to
their die traceability letter, and re-set the machines only when changing over
from one batch to another. This method
improved process capability by the removal of one cause of variation, thereby
making the task of machine-tool-setting somewhat less onerous.
PENALTY POINTS
Key:
1 Valve seat face
a NCU (not cleaned up) = +2*
b Insufficient material removed = +1
c Excessive material removed = -1
· Spigot face
NCU = -1
3 Base face
NCU =
-2*
4 Negligible variation = 0
*Note: The award of plus or minus 2
penalty points denotes the unacceptable variation magnitude of a scrapped
sample.
Figure 2. Diagrammatic
sectional view of the tap body, illustrating the three critical machined faces
and the method of awarding penalty points according to variation magnitude, and
plus or minus status to indicate variation direction
Speculation re causes
The collective measures employed to
minimise the effects of process incapability were clearly expensive, and
addressed only the physical symptoms of the problem rather than the root
causes. They did, however, provide sufficient clues as to the possible origins
of the problem to give rise to much well-intentioned speculation regarding
cause ownership and accountability.
This contributed little towards process improvement!
Business need
The need to resolve the problem had
become urgent. It had reduced what
should have been a capable, cost-effective process to an incapable, labour-intensive
one; furthermore, having achieved a high profile on the shop floor, it was
proving damaging to morale.
Corrective action ownership
The Quality Assurance Department
assumed ownership of the task of directing such management and departmental
resources as might be necessary for problem analysis and subsequent
experimentation, implementation and verification functions. It was well equipped for this task by reason
of its impartial relationship with all of the departments likely to become
involved, and its expertise in the use of SPC techniques.
Causes and experimentation
The hitherto intractability of the
problem stemmed from confusion, brought about by the seemingly illogical nature
of the variation. This defeated all
attempts to assimilate it mentally and deduce a recognisable pattern, based
upon past experience, from which root causes could be diagnosed and remedied.
The apparently illogical variation
could be partly explained, however, by consideration of the multiplicity of
tooling used in the manufacturing process which comprised:
2 coreboxes; multiplied by:
2 core impressions per corebox;
multiplied by:
6 dies; multiplied by:
2 machines; multiplied by:
8 sets of holding jaws per machine.
This produced a possibility of 384 permutations; also the effects of the
human element had to be taken into consideration. Clearly, there was a need to establish a comprehensive list of
process factors and of potential primary and root causes of variation. Moreover, experimentation aimed at proving
which of the many potential causes were actually responsible for variation
would have to be simplified by limiting the number of factors involved, if
confusion was to be avoided.
Possible cause identification
In order to establish the list of
process factors and potential causes of variation, a management 'brainstorming'
session was held by representatives of all associated departments and
functions. From this meeting a 'fish
bone' diagram was drawn up (Figure 3), depicting a clear divergence of the bulk
of factors and potential causes between the two production departments, but
with indications of possible inadequacies in the quality of some ancillary
services.
Experimentation
Planning
Retrospective evidence of machining
variation was discounted as being unreliable due to the lack of planning,
control and recording objectively at the time of the occurrence. Instead, a planned experiment was devised
that would meet these requirements, yielding reliable data that could be
simplified and analysed by some form of statistical processing (yet to be
devised), but whose logic and integrity could be unreservedly accepted by
everyone concerned.
Limitations
The experiment was limited in three
respects:
1 The
two twin-impression coreboxes were considered unlikely to be the cause of
significant variation and were,
therefore,
discounted.
2 The
choice of castings was confined to the typical mix of products from dies 'E'
'F' and 'H', which were
currently in process.
3 Machining was
confined to one of the two machines (C 16).
These limitations simplified the experiment by reducing tooling
permutations from 384 to 48.
Machining method
1 Tool-setting
Machine-tool-setting
comprised machine-head centralisation and locking, followed by setting and
locking of
cutting
tools in the optimum position relative to the eight sets of machine jaws.
2 Verification
Verification checks on a
range of machined castings confirmed the optimum setting conditions.
3 Sampling and machining
From a skip containing a mixture of 'E' 'F' and 'H'
castings, 16 of each identity were randomly taken as
samples.These were segregated by
identification letter and fed into the machine in such a way that each of the eight sets of machine jaws
received two castings of each letter.
Each of the 48 samples was
individually marked with the number of the machine jaw set in which it
was machined, so that resultant data might be processed to reveal the effects
of cross-matching the die letters with jaw set numbers.
Note: *Denotes subsequent
confirmation of the root causes
Figure 3. 'Fish bone'
diagram of potential primary causes and root causes of variation
Variation measurement
and assessment
It was envisaged at the outset of
the exercise that direct measurement of the amount of machining stock removed
from all three critical faces of each of the 48 samples might prove difficult,
protracted and expensive. Having
accrued so much interactive data, it was anticipated that making sense of it
would also present problems. This
assumption proved to be correct in both respects, as will become apparent from
the description of this stage of the exercise.
Direct measurement
In order to make a direct
measurement of the variation in machining stock removal, it was essential that
a reliable, common, horizontal datum face should be established; and then each
of the samples in turn would have to be set up accurately to the datum, and
held in position whilst the measurement readings were taken.
Efforts to find a suitable internal
cored surface to use as a datum face failed, because core form and positioning
both proved to be variable features of the manufacturing process.
Attention was then switched to the
external form in the hope that this would provide a suitable datum face but,
due to the absence of a suitable unmachined horizontal surface, this also
proved impractical. If direct
measurement were to be used, the only recourse would be to devise some kind of
holding fixture with a clamping facility and a built-in datum face. Each sample could then be clamped into the
fixture in a common position relative to the datum face, from where measurement
readings of each critical machined face could be taken. Work on the design and manufacture of such a
fixture was given consideration.
The provision of the fixture, the
time necessary to carry out the individual measurements, and the possibility
that all samples might also have to be sectioned in order to gain adequate
access to the internal valve seat face, promised fulfilment of the prediction
that the exercise might be protracted and expensive. In the mean time. however, there was a different assessment
technique which did not depend upon direct measurement
and which, if feasible, would be quicker and less costly. At that stage of the exercise it was worth
trying.
Visual assessment of attributes
Because it can never be completely
objective, visual assessment of attributes is, by comparison with direct
measurement, relatively crude and inaccurate, resulting in subjective information
rather than precise data. It was,
therefore, appreciated that attempts to make a visual assessment of machining
variation must be effected through the careful and systematic observations of
one person only, in order to achieve a satisfactory level of consistency across
the wide sampling spectrum involved.
Before the task of observation could begin, however, there remained the
question of how to evaluate and express the degrees of variation observed. Having assumed responsibility for the observations,
the writer first addressed the problem of evaluation and expression, conscious
of the need to convert observed information systematically into sufficiently
meaningful, accurate and reliable data to inspire the necessary level of
confidence among the technicians and toolmakers who would have to carry out
expensive remedial work on the tooling.
Several methods were investigated,
leading to the development of a surprisingly simple technique which consisted,
firstly, of the recognition of features which indicated the magnitude and
direction of variation. These were then
categorised and proportionally awarded plus or minus penalty points. This created a system whose resultant data
could be processed to reflect trends in variation magnitude and direction, and
which, by crossmatching, might also indicate primary causes, or even root
causes.
The method of awarding penalty
points (detailed in Figure 2) required that only the most obvious form of
variation observed on each casting needed to be recorded, since, in each case
where more than one indication of variation existed, these reflected the same
trend.
Each sample was duly examined in the
critical areas, and the plus or minus penalty points were awarded and recorded
in readiness for processing.
Data processing
Assembly matrix No. 1 (Figure 4)
As there were two primary factors
comprising this exercise (dies and machine jaw sets), the data were assembled
in matrix form to gain the benefits of cross-referencing.
Figure 4. Assembly matrix
No.1
The double horizontal lines
represent the pairs of castings, identified by the letter of the die from which
they originated.
The vertical columns represent the
machine jaw sets, identified according to their numbers 1 to 8.
Recorded penalty point data were entered
in the appropriate boxes of the matrix and totalled horizontally and
vertically, including the breakdown of each into plus and minus values.
The inference from these totals was
that, for reasons then unknown, dies 'H' 'E' and 'F' and jaw sets 5, 6 and 1
might' require some adjustment. It
appeared that several primary causes of variation had been identified.
At this point it was realised that,
due to an imbalance in the method of sampling (i.e. 16 samples from each die,
compared with six from each set of machine jaws), the results from dies and
jaws were not comparable on the same scale.
Also it was felt desirable to express the data in a graphic form to make
interpretation easier and provide a simple device for the monitoring of
improvements.
Pareto analysis No.1 (Figure
5)
Assembly matrix data were expressed
as average penalty points per die and jaw set, and depicted on a specially
devised form of Pareto analysis chart to compare the magnitude and direction of
variation on the same scale. This revealed
clear (albeit empirical) indications of primary causes of variation.
Conversion of Base Data to Pareto Analysis
Formula 1; machine jaws
Plus and minus variation
Formula 2; Dies
Plus and minus variation
Root causes and corrective action
Where the Pareto chart indicated
average penalty points in excess of ± 0.4, a typical example of each was selected
from among the samples and sectioned; similarly, examples that did not exhibit
signs of variation, and consequently had no penalty points, were
sectioned. These were compared and the
differences measured, revealing confirmation of root causes (Figure 3) and the
nature, amount and direction of adjustment necessary to correct the tooling.
Details of findings are as follows.
Machine jaw sets
Sets 5 & 6 (average = minus 1.0)
All samples machined on these jaw
sets were bodily misplaced during machining, so that the resultant machining
was consistently low. Both jaw sets
were adjusted accordingly in the casting location areas to off-set this trend,
and were then re-set on the machine in readiness for further trials.
Set 1 (average = minus 0.5 & plus 0.33)
No corrective action was considered
necessary at this stage, despite an overall spread of 0.83 points, because:
1 the spread of points
straddled the mean and so posed less of a threat to process capability;
2 reference to the
matrix (Figure 4) shows the minus points all to be related to a probable fault
in die 'E'.
Casting dies
Die 'E' (average = minus 0.56)
The examples exhibited a discrepancy
between the machining location areas and the base and spigot faces, resulting
in a critical shortage of machining stock.
There was no economical way of correcting this die, since it had nearly
reached the end of its useful life; therefore, it was removed from production
and scrapped.
Die 'H' (average = plus 0.44 & minus 0.25)
Close examination of the sectioned
examples suggested that the cored internal form was misplaced in a downward
direction, resulting in a critical shortage of machining stock on the valve
seat face. The die was dimensionally
checked and found to have an error in the positioning of the core location
print.
This was corrected, swnpled and
approved for further trials.
Proving experiment
Sampling and machining
With the completion of the
corrective action to tooling, a proving exercise was carried out to assess its
effectiveness. The limitations,
machining, visual assessment and data processing methods were identical to
those of the former experiment, but sample selection was as follows:
Die 'H' Fresh samples from the corrected die were used,
Die 'F' Samples were taken from existing stocks,
Die 'E' Samples had to be taken again from existing stocks, despite
being seriously defective, since the decision to scrap the die prevented
corrective action and re-sampling.
Visual assessment
As in the former experiment, the
writer carried out the tasks of observation
observation, assessment and
recording of penalty points accrued, during which it
quickly became obvious that variation was less severe.
Figure 5. Pareto analysis
No.1
