Ing-Stat

- statistics for the industry

Ph: +46 70 593 7505

Area for the walk

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We Can...

Together With...

Some Scenarios...

See Variation...

The random walk moves one step 'up', 'right', 'down'
or 'left' with the probability of 0.25. (The walk can be stopped/started by
the 'Stop' and 'Start'-buttons.)

The walk is bounded
and every time it reaches a limit it restarts. Random walks in one, two or three dimensions
play an important role in many processes.

A walk in one dimension can represent a population
or a queue where the size of the population, or the queue, increases or decreases in random steps.
The population or the queue itself can be as real as a fortune or number of Trouble Reports, etc. The random walk
might be bounded – a fortune or a queue cannot be less than 0.

A popular example of a random walk is the famous *Gambler's Ruin* (see the literature.)
Of course, the random steps do not need to be equal-sized or with the same probability and can be more or less complicated.

The three dimensional walk is often used as a model for particles in a fluid and the statistical treatment can be
rather complicated.

(Note: repeated runs of the two dimensional walk
can sometimes show a path that looks far from random.)

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...training, support and consultation within

the area of statistical analysis:

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...the client we look at the current status, the level of understanding and needs.

After this we suggest a tailor-made training or support.

After a training each participant can take part in a world-wide network for questions
within statistics, new approaches and new tricks, etc.

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As a document (En)... As a document (Sw)...

**"Do you say that by exchanging the chemical content we can decrease the manufacturing time?**

Let us perform an experiment to eliminate the uncertainty. Let us do this using statistical
methods and the equipment of our own. By planning it in a smart way we can include many parameters
in few objects. In this way we also eliminate our own opinions and let the process speak for itself!"
(Design of Experiments, DoE).

**"We have received a letter from Volvo about excessive variation of dimensions of our ABC-products**
Volvo has sent us a letter stating that the variation of some of the critical parameters in several
of our products, is too high. They want us to present our own figures together with a basic statistical
analysis by 7QCT (’seven Quality Control Tools’). They also want us to describe a plan of actions and
how we will follow up the improvements." (7QCT analysis).

**"Is there really any correlation between the X- and Y-results?**

On our meetings we often state that there is a correlation between number of particles in the air and number of
incorrect components being produced. Can somebody please perform a trustworthy investigation of this?".

**"What will be the result if we change the electronic component A?**

We have a rather complicated product. Now we have a suggestion stating that if we buy and install a more expensive
component, having a smaller tolerance interval, we will radically decrease the testing time and readjustment work.
I want to see a thorough investigation that shows that the total variation and the costs, decrease!" (As the
component is a part of a relatively complicated product, a computer simulation is simple and cheap way of
investigating the possibilities.)

**"How large should our store of spare parts be?**

We have up-to-date delivered 2700 units and we know that the demand for new sealings is approximately 1 per
two years. I think that our store of spare parts is too large and thus too expensive. On the other hand I
want a small risk for a customer not getting a spare part when needed. I want to design the store getting
this risk, say, 1 in a 1000. Anyone to help me?" (With statistical tools we can give the size of the store
fulfilling the requirements.)

**"We have received new goals from our main office regarding delivery times, from order to delivery**

The other day we received new goals for 2009. As usual they are a little unclear but I thought that we this
time should look at it a little bit closer. It is not obvious what is meant by ’maximum 10 days’. We do
not know if they mean ’on the average’ or that it is valid for all deliveries. Neither do we know how
we will evaluate these goals against the measurements.
We also need to break this goal into sub-goals and follow the progress. I have spoken to some people
that know about statistics and now I have the following suggestion: ...in this way we more easily
can see the progress and not...".

**"Since last autumn we have lots of data. Do we use the data in the right way?**

Our newest machines generate a lot of data that we do not use. You asked for this option in the software and
therefore I suggest that you use the data. I am convinced that many of our problems can be solved or eliminated
if we only cared for own information!" (The data detective at work; ”data mining” is the term.)

**"Every week many diagrams are distributed, but, to be honest, I throw them away**

I have heard that we will put our reports on the intranet in a near future. I have to admit that I think our
graphs neither report or illuminate our problems. A number of percentage bars, one for each quarter, does
not make anybody happy. We ought to begin from scratch and create something that is useful and also shows
our largest problem, namely the variation!"

**"I want to change our process of handling Trouble Reports**

We get a number of complaints about our trouble report handling (TR), it takes too long time. I am convinced
that if we increase the personal we can show decreases in costs in time and fines because of delays. Last
Thursday I met a man that knows how to simulate processes on a computer. He showed me an interesting example
how we can test different options using our own data. Therefore I suggest that we...".

**Customer requirements, supplier requirements, ISO-requirements**

There are usually a number of requirements from e.g. customers, suppliers, authorities, including ISO,
on a company. In order to understand, meet, suggest, fulfil, etc, these requirements the company must
be able to show that it can handle a certain process or commitment. For this a non-trivial level of
understanding of variation, statistics and statistical analysis is a must.

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An ability to understand and measure, discuss, handle, assess, eliminate, variation is important when improving processes and there are many simple and strong tools available. When an organisation starts using statistics, statistical methods and a statistical approach there are many positive effects:

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