The journal of the Institute of Quality Assurance

Vol. 19 No. 2 June 1993








Problem-solving using simple statistical analysis:

A case study





















formerly Quality Assurance


Volume 19 Number 2 June 1993






A case study



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.






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.












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.






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.





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


Data processing

Assembly matrix No.2 (Figure 6)

The overall number of penalty points was reduced from 26 in the former experiment (Figure 4) to 11. As expected, the predominant primary cause of variation was the defective die 'E', which accounted for the minus seven points; despite this, no samples were scrapped.


Figure 6. Assembly matrix No.2



Figure 7. Pareto analysis No.2

Pareto analysis No.2 (Figure 7)

Comparison of these results with those of the original experiment analysis (Figure 5) confirms significant changes for the better:


1 Overall range This was reduced from the former 1.44 points to 0.77.


2 Distribution The difference in distribution about the mean was reduced from 0.56 to 0. 1 0.

These reductions in range and distribution indicate a much improved process capability and corresponding easing of the problems previously encountered in tool-setting. How much easier it would have been if the correction of die 'E' had been carried out will, unfortunately, never be known for sure, but conjecture, based upon the effectiveness of corrective action to the other tooling, suggests that a further dramatic reduction in overall range would have resulted. Nevertheless, this proving experiment had shown that tool-setting to achieve zero rejects was now relatively easy.




Summary and conclusions

Principal benefits

Taking stock of progress thus far, the overall inter-departmental process (consisting of a fluctuating permutation of multiple tooling and two machines) in volume terms had benefited in only a small way, since the success of the exercise was confined to the much smaller permutation bounded by the limitations of the experiments. Nevertheless, its dramatic impact lay in the establishment of a practical system that could both clarify problem root causes and measure the effectiveness of corrective action, thus creating a vehicle for progress through three recognisable stages,



Stage 1 - Status quo

This pre-exercise situation was one of expensive, and frustrating, shop-floor-driven variation containment, depressing in its lack of progress towards the elimination of root causes.



Stage 2 - Interim progress

The discovery of this analysis and monitoring technique opened up the prospect of gradual improvement of tooling, but several of these labour intensive exercises, involving skilled staff, would be necessary to make all tooling used in the process sufficiently compatible to produce zero component rejects. Moreover, in order to maintain the zero reject status, this technique would have to be applied whenever new tooling was introduced.



Stage 3 - The ultimate solution

Perhaps the most significant outcome of all was the confirmation of suspicions that the traditional tooling manufacturing and inspection methods employed were incapable of achieving a sufficiently high level of accuracy in tooling reproduction. The ultimate solution lay in the development of a method of tooling manufacture which would provide 'right first time', zero defect dies and machine jaw sets.





The idea that visual assessment of attributes could he of benefit in the precision-oriented atmosphere of a machine shop seemed

highly unlikely at the outset of the exercise. However, by its conclusion, the feasibility of this technique was beyond doubt.




Response to change

There is an ever-present tendency in manufacturing to become subservient to the sterility of 'custom and practice'; therefore, it was encouraging to witness the enthusiasm of all persons involved in trying out this novel approach to problem-solving. Understandably, there was a great deal of scepticism at first among those who had endured the problem, but this did not impair commitment to the experiments.

Ultimately, acceptance of the technique was demonstrated by requests from machine-tool-setters and toolroom staff to extend its use to all suspect tooling.





Purists might argue that this exercise was not a form of SPC but merely a logical development of common sense. They may well be right, but who is to say where the dividing line between SPC and common sense should be drawn?

If the broad concept of SPC were defined simply as 'the science of process improvement by numerical means' it would certainly embrace the techniques employed in this case; furthermore, it is unlikely that such an effective method of problem-solving could be devised without the influence of statistical training.


Perhaps, upon reflection, it is better to avoid speculation as to boundaries or labels and, accepting the benefits of such techniques, concentrate upon promoting their wider use.


Don Sherratt gained a Diploma in Foundry Technology from the Wulfrun College while serving a patternmaking apprenticeship. He graduated to methods engineering and quality assurance supervisory and managerial roles with the Delta Group, Hamworthy Engineering Group, British Leyland and the Duport Harper Group, prior to joining the Engineering Division of Armitage Shanks Ltd, in November. 1987. As Quality Assurance Manager of the Wolverhampton site operations, he was responsible for implementing the quality improvement programme. He has since been appointed Quality Assurance Manager of the division's Cannock factory where he is engaged in a similar project.