7. THE USE OF STATISTICAL TECHNIQUES IN ENGINEERING A N Cutler GKN Technology Limited, Wolverhampton
7.1 Introduction
GKN plc is a major international industrial organisation whose core businesses are Industrial Services, Defence and Automotive Components. GKN Technology is the research, development and design organisation for the automotive components business and has sites in Wolverhampton, Germany and the USA. GKN Technology provides specialist support to manufacturing companies worldwide for the Company's core "driveline" products: Constant Velocity (CV) Joints and Propeller Shafts.
The Automotive components market is extremely competitive with high standards set by manufacturers (especially the Japanese), short product development times and demanding safety assurance requirements. Market pressure requires continuous product improvement towards longer life; lower noise and vibration; smaller, lighter and more aesthetically pleasing packages; lower running temperatures; greater mechanical efficiency and lower prices.
Statistics is centrally important to delivering cost reduction and quality improvement through its application to product design and manufacture, facilities maintenance and commercial management.
7.2 Product Design
An essential part of product design is the testing and evaluation of new materials. Strength and fatigue properties are of great interest. One frequently encountered material characteristic is the S-N curve (Fig 1). A number of components are tested to destruction at varying levels
of alternating stress. The number of cycles to failure is
recorded and log stress plotted against log cycles. A designer
will want a "safe" curve so that a component will have
a guaranteed life at a given stress. Unfortunately, designers aim
for components with long lives but test engineers dislike lengthy
tests. There is always a temptation to extrapolate from the high
stress, low life region desired by the test engineer and the low
stress, long life region of interest to the designer (Fig 2).
Test engineers are also involved in establishing what stress levels the part will be required to survive. Designers also need statistics in matching part strength to environmental stress where both may be subject to uncertainty, for specifying tolerances on components and in experimenting with alternative designs.
Nothing can be produced with perfect accuracy and design drawings used for manufacture must specify the range of physical dimensions which are allowable for correct product assembly and function. This was traditionally performed by specifying tolerances such that the product was always acceptable for any combination of dimensions which were within their respective tolerance bands. For example, consider the simple peg in a hole in Fig 3.
The peg has diameter a and the hole b. If we make a
too small, it will break; if we make b too large the wall
of this component will be too thin. We also need to control the
clearance between the two parts within defined limits. We can use
this information to produce a plot of the parameter space
defining the allowable region (Fig 4).
We can then specify tolerance bands on a and b such
that the combination of dimensions is always acceptable (Fig 5).
However, examination of data from production reveals that
dimensions often have a distribution peaked around the centre of
the tolerance band (sometimes even approaching a normal
distribution!) and very few parts are near the tolerance limits.
On this basis, the conventional tolerance stack-up looks
pessimistic as there is only a small probability of having both
dimensions at the extremes of their tolerance bands. Furthermore,
we are always looking to loosen tolerances as tighter tolerances
entail higher costs.
One approach is to estimate the standard deviation of the dimensions and hence the overall variability in product function. This approach needs considerable skill in measuring the variability in manufacturing processes (within-batch and batch-to-batch variability) and in identifying correlations between dimensional errors arising from the nature of the manufacturing process or the way the dimensions are specified.
The science of experimental design is massively under utilised in engineering but the difficulties are not always appreciated. When prototype components are manufactured for a new design there is a dilemma between using current in-service production plant or specialist model making workshops. If production plant is used then factors are difficult to control closely and it is hard to achieve an orthogonal experimental layout. Alternatively, if model shops are used, factors can be closely controlled but the processes for manufacture may differ from those likely to be used in future production and some doubt will always be present about the relevance of results. In manufacturing operations, it is often less expensive to perform observational surveys on the natural variability of components in production than costly controlled experiments which involve taking plant off-line and performing a lengthy sequence of machine adjustments and experiments.
Experimentation to improve product life is particularly difficult as even small homogeneous samples can exhibit differences in life of a factor of two. Designed experiments are increasingly important in performing studies using computerised analysis packages as such programs can take several hours to run and there is a demand to minimise computing and human resources.
7.3 Testing
Once a product is designed, it must be tested to ensure that it meets its original specification. Engineers must always be aware that their customer needs a "nice warm feeling" rather than the last word in statistical rigour. Hypothesis testing is often invoked in this situation where the Null Hypothesis is that the product does not conform to its specification. Engineers often refer to the probabilities of Type I and Type II Error as Consumer's and Producer's Risks respectively. Test engineers and project managers need to understand the trade-offs between test cost and the value of the results obtained (confidence, freedom from risk). However, many statistical tests in use have dubious distributional assumptions and engineers need to understand the importance of nonparametric tests. Plotting on Weibull paper is very popular in assessing product life (Fig 6) but is prone to similar problems to the S-N curve.
The test engineer wants a small sample size but the
designer or project manager wants to know the shortest lives of a
large sample of components (eventual production may be millions).
Again the temptation to extrapolate the Weibull plot is only
tempered by doubt in the validity of the distribution.
7.4 Statistical Process Control
In manufacturing, statistics is important in control charting and Statistical Process Control (SPC) and inspection and acceptance sampling by lots (pass/fail, binomial data). The full range of experimental and data exploratory techniques are central to troubleshooting production problems.
Statistics is also important in supporting the customer after-sales. Any problems revealed by field data need to be corrected, especially with the current awareness of legal liability. Field data needs to be carefully analysed but if customers have a perceived problem, they often need to be given reassurance, rather than a lecture on statistical significance.
7.5 Conclusions
Today's engineers need a basic statistical literacy about ideas such as independence. They need to appreciate that not everything is normal and that nonparametric techniques can be very powerful. They must understand what hypothesis tests do, and don't, tell them. They need to understand the dangers of extrapolation. Above all, they need to be convinced of the need for experimental design.