e xtracting characteristic functions from growing populations – examples from reliability,...

EXTRACTING CHARACTERISTIC FUNCTIONS FROM GROWING POPULATIONS – examples from reliability, epidemiology, climate and traffic safety research

Örjan Hallberg, Hallberg Independent Research

OBJECT

To predict the future outcome based on reported response to growing populations. By population is here ment a measure of any

physical object or activity capable of causing an effect.

Examples from the following areas will be given Product reliability The Mad Cow disease Traffic death statistics Global warming The melanoma epidemic

BACKGROUND

If you sell 100,000 products at one occasion the number of returned products per month will give you the reliability information.

AN EXAMPLE OF PRODUCTS INSTALLED DURING A SHORT PERIOD

WE WANT TO FIND THE LIFE DISTRIBUTION THAT BEST MATCHES REPORTED DATA

THE SUPERPOSITION PRINCIPLE FOR LINEAR SYSTEMS

The net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.

WE ADD ALL FAILURE CONTRIBUTIONS OVER TIME TO GET THE TOTAL FAILURE LEVEL

RETURNED PRODUCTS COME FROM THE TOTAL INSTALLED VOLUME

COMMENTS ON PRODUCT RELIABILITY

The failure rate is normally decreasing by time and good products become virtually failure-free after 4 years in use.

Sometimes production process errors or design errors may cause the failure rate to start to increase after some years of use. Such problems may cost millions or even 100 millions SEK to correct. Fortunately not common in telecommunication business, but it has happened.

THE MAD COW DISEASE Cows became infected since early 1980s and got

sick from end of 1980s

MANY OF THEM ENDED UP ON THE KITCHEN TABLE

AND SOME ENGLISHMEN DIED, THE FIRST ESTIMATE DONE IN 1996 POINTED AT 160 DEATHS IN TOTAL

TODAY 164 HAVE DIED…

DISCUSSION REGARDING MAD COWS

A simple physical model was in 1996 able to give a very good estimate of future deaths at a very early stage.

The application of a death risk function following a normal distribution in 2002 gave a similar result as in 1996 but at even better fit to reported data.

This simple way of analyzing medical data was never used by professional statisticians at that time, as far as I have seen.

TRAFFIC DEATHS IN SWEDEN

What is the single most important factor behind a lethal car crash?

Inexperience!

EVERY YEAR THE TOTAL POPULATION OF REGISTERED CARS IS INCREASING

AND EVERY YEAR MANY PEOPLE DIE IN TRAFFIC ACCIDENTS

YOUNG PEOPLE ARE AT HIGHER RISK FOR INJURIES

KEY INPUT: ANNUAL INCREASE IN CAR POPULATION. BEST FIT TO 1975-1985 WAS USED TO DETERMINE PARAMETERS.

DISCUSSION ON TRAFFIC DEATHS

Traffic safety is mainly depending on driving experience.

The risk of being involved in a lethal traffic accident is decreasing by age and experience

An increased number of registered cars also means an increase of inexperienced young drivers

It appears as this simple physical model can explain most of traffic deaths in Sweden

The traffic safety has further improved during the last 10 years due to regulations and technical arrangements

CLIMATE CHANGE AND GLOBAL HEATING

Here the causing factor is the release of green house gasses (GHG) like CO2 in the atmosphere.

And as a response to that we can measure temperature increase, melting ice, sea level increase and more.

What does an analysis of the temperature response to increasing CO2 levels indicate?

GLOBAL HEATING – WHAT WILL IT BE IF WE COULD STOP CO2 INCREASE RIGHT NOW?

PRINCIPLES AND ASSUMPTIONS

A step-wise increase in the CO2 contents of 1 ppm will result in a corresponding, delayed temperature increase.

The superposition principle is again used to calculate the total temperature increase over time.

Already reported increase of CO2 and temperature since 1850 is used to extract the step response function.

This function is used to project future increase of global temperature.

IPCC SAYS +1.1C BUT HISTORIC DATA POINTS AT +3.5C IN YEAR 2100

IN A LONGER PERSPECTIVE

DISCUSSION ON GLOBAL TEMPERATURE

Our analysis points at 5,45 oC increase from 100 ppm of CO2 increase. This is also consistent with geologic records since 600 000 years back.

Our analysis points at a characteristic delay (to 50%) of 113 years, consistent with other reports.

The new IPCC report does not match historic data since 1850 and assumes the characteristic delay to be 37 years. The response to 100 ppm is assumed to be only 1,1 oC.

Unfortunately, the situation looks much worse than what IPCC are forecasting.

MELANOMA OF THE SKIN

Melanoma is a deadly skin cancer that suddenly started to increase after 1955 in Western countries.

It mainly affects grown-up people. And mostly on sun-protected areas of the

body. Even more on the left side of the body. The incidence in Japan is only 3% of

Sweden’s.

MORE!

Strong geographical differences in Sweden People who often are exposed to the sun

have less of melanoma! Southern Europe have less than Northern People under 50 years of age have stable

rates Older people still show increasing rates The authorities blame this to increasing sun

tanning habits and artificial sun tanning.

WE NEED TO UNDERSTAND THIS!A PHYSICAL MODEL SHOULD BE ABLE TO EXPLAIN IT ALL!

A PHYSICAL MODEL CAN MANAGE WELL BY VARYING ONLY TWO PARAMETERS. (HALLBERG Ö. A REDUCED REPAIR EFFICIENCY CAN EXPLAIN INCREASING MELANOMA RATES. EUROPEAN JOURNAL OF CANCER PREVENTION. 2008;17:147-152.)

One probability function describing cancer risk over time if no skin damages are being repaired at all (F)

Another function describing how fast skin damages are being repaired before (Sn) and after (Sd) an environmental change.

The dispersions of the two functions F and Sd are varied to fit age-standardized rates with reported data.

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AN INCREASING RISK OVER TIME IF THE DAMAGE IS NOT BEING REPAIRED

REPAIR PROBABILITY OVER TIME

CALCULATE THE INCIDENCE OVER TIME FOR ONE BIRTH COHORT

REPEAT IT FOR ALL BIRTH COHORTS BETWEEN 1860-1980

VARY TWO KEY PARAMETERS TO FIT THE AGE-STANDARDIZED RATES

TEST THE RELEVANCE OF THE MODEL BY COMPARING AGE-SPECIFIC DATA

CAN INCREASING SUN TANNING EXPLAIN?NO! CALCULATED DATA DOES NOT FIT REPORTED

Calculated Reported

DISCUSSION ON MELANOMA

A reduced repair efficiency from around 1955 can explain the increasing melanoma rates noticed in many Western countries.

Increasing sun tanning habits can not explain the trends reported.

CONCLUSIONS DRAWN FROM THESE EXAMPLES

1. A model that is relevant and has a clear physical meaning may be useful for prediction purpose

2. Only a small number of parameters need to be varied to fit reported data

3. If a model does not have a realistic physical base it will not fit reported data.