Quante^xRESEARCH Work Page

	Introduction  What we don't do  Application areas  Engineering statistics  General work  Computing  Commercial  Examples  Engineering ...  General ...  Computing ...  Working methods  Contact

Introduction (next)

Sir Ronald Fisher - one of the founding greats of the discipline - wrote in 1925 that "The science of statistics is essentially a branch of Applied Mathematics, and may be regarded as mathematics applied to observational data" (Statistical Methods for Research Workers). It may therefore be defined as the theory and practice of collecting, analysing and summarising data in order to make inferences or take decisions in practical situations where uncertainty is involved - ultimately it may be viewed as the quantification of uncertainty. In some areas statistics is extremely difficult to penetrate and it is little wonder that some people are puzzled or threatened by it since it can be and is used to change our lives in some way or another.

There is a fashion today of indicating the statistical part to a subject area by appending 'metric' to the discipline title. Thus we have everything from biometrics to econometrics via chemometrics, infometrics, scientometrics, psychometrics and many more. These disciplines - as well as those such as neural networks and epidemiology for example - sound much sexier than statistics yet their practices are fundamentally statistical.

What we don't do (next) (top)

1. We do not provide information on companies, economic statistics, etc. In general such information may be found in libraries, on the Internet or from economic and social research foundations.

 

 
 
 

2. We do not involve ourselves in an individual's research where the work is towards a qualification since we consider this unethical.

 

 
 
 

Application areas (next) 1234 (top)

While many problems may appear to be soluble by fairly standard approaches, few real data issues are actually so simple. Specialist knowledge in the applications area is very helpful. Because of the breadth of subjects covered within engineering and industry, it is therefore sensible to focus on certain areas where the main experience lies, while not excluding statistical general work. There are three main platforms for Quante^x RESEARCH:
 
 

1. Engineering statistics 23 - with particular emphasis on the problems of power engineering. This implies trying to make sense out of plant or laboratory measurements, in which Quante^x RESEARCH has many years experience.

 

 

 Statistical issues of interest include:
 

• analysis of errors conditional on the deterministic parts of the predictive model eg the laws of physics possibly represented by mathematical models. These are generally much better known (or believed) than in the soft sciences

 
• unbalanced data - experiments are rarely planned and the data to be analysed are unlikely to represent the various categories equally

 
• censoring - tests removed before failure or that failed well before removal

 
• measurement errors that may be either systematic (possibly common to a number of transducers) or random

 
• prior knowledge for example from laboratory studies

 
• correlated measurements

 
• coefficients that are fundamentally random in nature rather than being fixed values for which we do not have precise knowledge

 
• hierarchical or multilevel data - some measurements may be on replicate samples from a batch which would be expected to yield similar responses while others may from different batches

 
• repeated observations on the same variable (which can be regarded as a special case of hierarchical data)

 
• data that is not normally distributed and may have a theoretically based distributional form

Most work is done for the nuclear industry on material science data such as in corrosion, weld cracking, failure rates etc. but the skills are immediately applicable in conventional power plant areas as well as in industries such as oil, petrochemical, aerospace and marine.

Particular areas of application include:
 

• Analysis of performance data - the investigation by statistical and deterministic models of the plant measurements in order to optimise the operating regime for safety, reliability and/or output

 
• Calculation of damage fractions, remanent life etc from temperature/stress histories

 
• Risk assessment using statistical and probabilistic calculations to assist in determination of failure probabilities

 
• Longitudinal modelling - that is representing the effect of a process with time eg from corrosion measurements

 
• Analysis of failure time data from accelerated and other tests or from plant measurements

 
• Spatial statistics - probabilities of events in an area - eg cracks on a pipe

 
• Extreme value techniques - statistics of data which is essentially largest or smallest in nature rather than average

 
• Analysis of categorical and ordinal data such as counts of weld failures - leading to log-linear models

 
• Analysis of multivariate data from balanced or unbalanced experimental designs with hierarchical or cross classification - leading to multilevel analysis or random effects models

 
• Multivariate techniques can be used to some benefit since data is frequently high-dimensional. Graphical models are a powerful tool in this context

 
• Expert peer review of documents and verification. Resources are frequently stretched and therefore unavailable for such work. The eye of an experienced analyst is invaluable in ensuring that results and calculations are fit for purpose.

 
The increasing sophistication of statistical techniques tends to integrate some of these areas and the future holds considerable challenges as more complex problems become soluble.
 
 
1. General work 3 is also welcome. This work is usually much simpler to do than the engineering work above and may consist merely of tabulation or presentation of the results of client surveys. Survey analysis has been carried out for various organisations both large and small, as seen in the examples below.

 

 

Interpretation may also use some of the advanced techniques mentioned above - log-linear models, graphical models etc. The aim of quality is the same whatever the problem.
 
 

2. Computer applications 4 in various operating systems and languages - Unix (particularly x86 Linux), DOS/Windows, OS/370, Fortran, Pascal - as well as many statistical programming tools.

 

 

Many people think that statistical analysis is merely a case of selecting a spreadsheet, clicking the mouse and out pops the answer. Would that it were as simple. While it is understandable that the innumerate view statistics in this way, it is also perpetrated by people who should know better. The truth is far removed from this for two reasons - firstly the best model nearly always has to be tailored to the data and secondly data rarely arrives in anything like the right format - even from computer literate clients.

Therefore computing is frequently required as part of routine analysis as the data has to be rendered into a suitable format for the computing or statistical tools used. In addition it is necessary to understand the algorithms employed in the solution. Thus a substantial part of all work is computational in nature.

While computing is frequently treated as a clerical tool - which in many ways it is - where data is being analysed there are good reasons for using the skills of an analyst who has a full appreciation of how the data was measured, what it means and how the results are to be used. For situations where statistical analysis is part of the function, it may be essential to employ such skills to ensure that the calculations are done correctly and it is frequently easier to use a statistician (who must almost by definition be an expert in many aspects of computing) in critical phases of software development.

Quante^x RESEARCH is frequently asked to develop or verify software in this area.

Commercial (next)  work is also of interest.  Many statistical techniques can be applied to purely commercial data - sales and marketing for example.  The world is fast moving to a state where, from individual purchases and other characteristics, businesses can apply data mining techniques to their data  wharehouses (a picturesque name for a large amount of data) held primarily in relational databases and target their marketing activities.  This principally uses cluster analysis (both heirarchical and non-heirarchical) but more complex models can be developed using graphical models and complex longitudinal approaches.  Another application can be seen on the Organise  web page where optimal structures can be elicited particularly in high skill industry.

Examples (next) 123 (top)

1. Engineering ... 23

 
• The corrosion properties of 9%Cr superheater boiler tubing were not initially appreciated. The oxidation mode could change from safe protective behaviour to a type of corrosion known as breakaway oxidation where the tube wall could be consumed in a few thousand hours. The materials on test were of various geometries, silicon contents and manufacturers. Analysis of the protective corrosion rates enabled identification of the important causal factors and quantification of the plant risk.

 
• Inspection revealed occasional deep cracks in a transition weld assembly and it was necessary to assess the depths and lengths of the cracks from semi-regular inspections, including observation uncertainties. A model enabled quantification of the risk of a through-wall crack within pre-set times, thus justifying the inspection intervals for return to service. The weld design was eventually changed.

 
• The (still) present ISO standard for high temperature, high stress creep failure has a number of predominantly statistical weaknesses by present standards. An analytical technique was developed along likelihood-based statistical lines within a generalised linear model using a gamma error distribution with censoring. This work has been furthered at Lancaster University Centre for Applied Statistics both as a new British Standard (PD6605) and as a candidate European Standard. Quante^x RESEARCH has been involved in the computing side of this exercise (see below).

 
• If a major boiler tube leak were ever to occur in a Magnox power station, it would lead not only to immediate increase in pressure from the evaporating steam but also to corrosion of the magnesium part of the fuel can in the moist hot atmosphere. The resultant friable product could affect the safety relief valve discharge rates by impeding filter flow. A model was evolved that quantified this effect based on available codes and laboratory measurements. This work led to a program of relief valve filter testing and in some cases replacement to ensure continued safe operation of the plant under this unlikely fault scenario.

 
• The probability of pin-hole failure in some of the older mild steel radioactive waste disposal tanks used on nuclear power stations has been calculated using an intricate model of the corrosion and pitting processes. While the implications of a tank leak are not severe, it was still necessary to quantify the risk and identify the major factors.

 
• A periodic review of a reactor pressure vessel integrity identified a shortcoming in the estimates for failure rate from a penetration weld. The only easily available data was a contingency table in the public domain and a model was generated from this data to calculate the probability of failure for the (large) pressure vessel which had many penetrations. This included implementation for the target vessel but application to similar vessels is immediate.

 
• Examination of reactor channel gas outlet tempertures to estimate the size of the uncertainty for unmeasured channnels. This was collaborative work with the Mathematics and Statistics Department at Lancaster University. By using kernel smoothing techniques and examining the residual distribution tails, it enabled the Health and Safety Inspectorate to verify the present procedures and potentially enables the Licensee to optimise the reactor output.

 
• The reactor pressure vessel temperature is an important parameter since irradiation damage raises the ductile transisition temperature. Accurate calculation is therefore important and work has been done to estimate the likely uncertainties in such results from deterministic models. The work also identified the statistical linkages between the main parameters by using multivariate analysis and statistical graphical models.

 
• Some cracks were noted in flanges of an assembly that were initiated at the internal corners of cut-outs made at the time of manufacture and which conventional crack growth models could not explain.  Many of the sites did not initiate any cracks but some of the cracks proceeded all through the flange within a single observation period.   Using non-parametric maximum likelihood, a compound model was built that characterised both the crack probability and the crack growth rate.  This approach was able to identify new sites at risk for the next observation.

 
• A cracked weld was found in an assembly that was made of the wrong material.  There were a large number of other welds, most of which could be checked but some were inaccessible.  A second crack was also found.  These welds were made many years ago and no documentation existed to indicate which welds were made when and from which roll of filler.  A comprehensive model was generated that took all the information available, including soft opinion, and estimated the probability of these unobservable welds also being constructed of the wrong material.  The techniques used included acceptance sampling, meta analysis and logistic ridge regression.

 
• Measurements were available of oxidation rates for high tensile steels which had historically been used to evaluate strains in bolted assemblies.   Some of the measurements were from destructive tests - therefore end of life and only one per assembly - while others were repeated measurements of extension.  Using the latter, a random effects model was built to estimate the strain rate and uncertainties to be applied.  The results showed that the original approach was considerably inaccurate but also pessimistic.

 

 

2. General ... 3

 

 
 
 

• Analysis of a survey for the CER (Centre for Employment Research) at Manchester Metropolitan University dealing with the use of telematic facilites by international trade union organisations

 
• Analysis of a survey by a medical practice wanting to evaluate patient satisfaction with out-of-hours services

 
• Checking lottery results for randomness

 
3. Computing ... (next)

 

 
 
 

• The sensitive boiler design of two of the AGR stations meant that the thermal hydraulic boiler model was also very sensitive and difficult to align with the plant. A major role was taken in implementing this from design measurements and data from the operating reactors. It involved carrying out plant tests to establish parameters to the model, integration with plant data extraction tools as well as making extensive modifications to the computer model so that model-plant alignment was more automated.

 
• Various cases of design and implementation of software for routine data extraction from source and presentation to end users for examination.

 
• Algorithms have been developed to analyse further creep failure data using the GLIM program. These are for Weibull and log-logistic distributions in the presence of both censoring and variance heterogeneity. This was carried out for the Centre for Applied Statistics at Lancaster University as part of BS PD6605 mentioned above.

 
• Assessment of mild steel oxidation allowances. The older nuclear stations were made predominantly of mild steel and an extensive assessment methodology had already been developed, based on older approaches and using main frame programs. The calculation approach has been verified and the programs ported to a PC environment. Verification and substantial development of the programs has been carried out. The calculation route is being simplified to enable assessment to be carried out much more speedily.

 
• The innovative analysis for the UK Foresight Technology programme required some programming effort to create the chain lists of nominees and co-nominees and prepare the input matrices for the main analysis program used to identify the national expert groups . This software development was carried out for PREST (Policy Research in Engineering, Science and Technology) at Manchester University. More recently, the software has been modified for the South African Foresight Technology programme.

 

Working methods (next) (top)

Statistical problems are frequently self-contained and do not require continuous presence at the client's premises. New technology - personal computers and workstations - as well as telematics - electronic mail, hypertext, video conferencing etc - can all be used to avoid the problem of excessive travel which wastes time and resources.

Such high skill technical work is therefore moving away from formal structures to a freer and more independent approach. The increasing complexity of knowledge combines with today's technological changes to enable specialist consultants to work independently, freeing the work place, ensuring that their services are available to a wider audience while not insisting that an employer should find them continuous work. The direct consultant-client contact enables close control by both parties and ensures a mutually successful outcome.

A statistical consultant will then have the advantage of continuous technical contact with a wide variety of problems, as well as with other people within the statistical community. The freedom offered by working as a consultant also means that conferences, courses, lectures and seminars can be attended without particular reference. Continuing contact with academia offers support in depth for particularly intricate problems and facilities for continuing training.

Quante^x RESEARCH has academic statistical contacts at Lancaster University - one of the premier statistical groups in the UK - with the Centre for Applied Statistics and the Mathematics and Statistics Department, with both of whom collaborative work has been done.  Other work has been carried out with the  Statistical Advisory Unit at UMIST . Clients include some of the main UK power generators, various local small businesses, PREST (Policy Research in Engineering, Science and Technology) at Manchester University and CER (Centre for Employment Research) at Manchester Metropolitan University.

Quante^x RESEARCH has no interest in becoming an agency, managing third party work unless specifically required by a client, nor of becoming a large organisation of partner consultants and employed support staff. But it is in touch with other consultancies and is interested in all types of collaborative working arrangements.

Contact (top)

Quante^x RESEARCH has an open-door philosophy. Brief enquiries are encouraged and may well be serviced without charge - for example advice on a simple statistical programming problem. A client will be told if a piece of work is chargeable. Extra work, additional travel, subsistence and excessive telecommunications costs can incur supplementary charges.

While some work can be done on a daily basis - particularly where Call-Off Contracts are involved, fees are generally not by time but by project. The project fee will be negotiated at the outset - perhaps with some contingency or staging on both sides. Complex projects may be split up and in general, projects of over a month will require regular staged payment.

In general, work is carried out at Quante^x RESEARCH offices with client visits as required. It is possible to offer ISDN dialin to minimise travelling if it is necessary to access client's computers. While it is not policy to charge specifically for site meetings, where site work is required, sensible extra charges are involved to reflect the time away from base. This approach has evolved over a period of time and has proved satisfactory to all concerned.

If you or your organisation have problems to solve and these arrangements seem sensible, do not hesitate to contact Quante^x RESEARCH via email John Logsdon or telephone +44 (0) 161 445 4951.