Principle 6: Variability (Item 6)
All systems and processes exhibit variability, which impacts on
predictability and performance.
When you reduce common cause variation, you reduce your major source
of variation. You make your products and services more consistent. That
is you deliver a more consistent product/service to your customers,
who will be more satisfied because your products/services are more reliable.
Your costs go down; because you have less rework. Your customers' costs
go down; because they have less work to do to make your products/services
useable.
Your company is more capable of delivering what it said it would deliver.
And you will be more able to tell if you are achieving your objectives.
(With high levels of variation, you can do neither, even if you wanted
to.)
The major improvement of all systems involves systematic reduction
of common cause variation. No other path can succeed. To make your processes
more capable, reduce your common cause variation.
You can only change common cause variation if you change the system
– Principle 4 (`To Improve the Outcome, Improve the System') again.
If there is a gap between the system average and the target, the only
options are to move the system average towards the target or to change
the target. Changing the target may be an option when it is technologically
impossible to reach the target.
Improvement should proceed by first identifying processes and activities
that contribute most of the significant variation. These are the `low
hanging fruit' and offer good opportunity
for pre-emptive control design. We will see later that errors in early
stages are amplified later. Therefore, the earlier you can intervene
in the system the better. For example:
We recruited ten trainee managers five years ago. We didn't pay too
much attention to our selection criteria at the time. Unfortunately,
none of the ten has proved to be up to our requirements and we have
let them all leave. We are now very short on good management talent
for our expansion.
[If this is too much detail, skip it.]
You have your process producing results that move nicely between the
Control Limits of your Control Chart, all very nice and stable, and
now you want to improve the process. You now want better results. How
will you know that the process has improved? That is anything but a
stupid question.
Let us assume you want a 10% improvement. For example, if your process
produces 100 units per day and you now want to make 110 units per day.
Let us also assume that you are not willing to be wrong more than 0.5
percent of the time, ie you want to be 99.5% confident that when you
say the average has moved from 100 to 110, it actually has moved. (This
is a very high degree of accuracy. However, when you use Control Charts
that use three standard deviations for the Control Limits, this is the
degree of accuracy you have chosen, like it or not.)
The standard deviation of your process must be less than 3.33% of the
process average for you to detect a change of 10% in the average. Or,
around the other way. If the standard deviation of your process is more
than 3.33% of the process average, you cannot pick up a change of 10%
in the average. In our example with the process average at 100 units
per day, if the standard deviation is 4 units, you cannot tell if the
process average shifts to 110 units per day. 100 + 3 * 4 > 110, so
100 and 110 are indistinguishably the same number. Even though you would
like them not to be the same.
This shows another very good reason to reduce the variation of your
process. A smaller variation will allow you to detect a change in the
process average more quickly.
There is nothing magical about three standard deviations being used
as Control Limits in Control Charts. It is just a convention —
mainly used because it is a whole number. Its implied level of confidence
(99.5%) can be a bit restrictive. What if you decide that you can tolerate
a lower level of confidence? 2.75 standard deviations would give a 99%
confidence (ie, you are willing to make an error 1% of the time). 2.5
standard deviations would give a 98% confidence (ie, you are willing
to make an error 2% of the time). Two standard deviations would give
a 95% confidence (ie, you are willing to make an error 5% of the time).
The table below show the minimum percentage change that can be detected
in the average with a variety of error tolerances and a variety of standard
deviations.
| |
Std dev as a % of the average  |
Minimum percentage
change that can be detected in the average |
Control Limit width  |
|
3 std dev |
2.75 std dev |
2.5 std dev |
2 std dev |
| Tolerance for error |
|
0.5% |
1% |
2% |
5% |
| |
1% |
3% |
2.75% |
2.5% |
2% |
| |
2% |
6% |
5.5% |
5% |
4% |
| |
3% |
9% |
8.25% |
7.5% |
6% |
| |
4% |
12% |
11% |
10% |
8% |
| |
5% |
15% |
13.75% |
12.5% |
10% |
| |
6% |
18% |
16.5% |
15% |
12% |
| |
7% |
21% |
19.25% |
17.5% |
14% |
| |
8% |
24% |
22% |
20% |
16% |
| |
9% |
27% |
24.75% |
22.5% |
18% |
| |
10% |
30% |
27.5% |
25% |
20% |
For example, if the standard deviation is 8% of the average (in our
example 8 units per day compared with an average of 100 units per day)
and you are comfortable with a 2% probability of error, then the smallest
change in the average that you can detect is 20%. That is, you would
have to be making more than 120 units per day before you would know
there had been a change.
That is, you need quite a big difference before you would find it.
The good news is that the Control Charts do all the mathematics for
you. You just plug in the numbers and the Control Chart tells you if
a change has occurred.
Can we ask this question the other way around? How small must the standard
deviation be for us to be able to detect a 10% change in the process
average? The table below shows us.
| |
Standard deviation as a % of the process average |
| Control Limit width |
3 std dev |
2.75 std dev |
2.5 std dev |
2 std dev |
| Tolerance for error |
0.5% |
1% |
2% |
5% |
| The Standard deviation cannot be more than this
if we want to detect a change of 10% |
3.33% |
3.6% |
4% |
5% |
For example, if you want to be able detect a 10% change in the average
and you are comfortable with a 2% probability of error, then the standard
deviation cannot be more than 4% of the average (in our example 4 units
per day compared with an average of 100 units per day).
In other words, you would have to have your processes well under control
with very tight variation before you can tell if those processes have
changed.
[The other assumption we have made in these tables is that you have
measured at least 30 points in your process.]
[Statisticians often use 95% confidence. The number has no magic. It
comes from the early days of statistical research when the grandfather
of statistic RA Fisher was doing research on agricultural products.
He wanted to know when one product was better than another. He had 20
plots of land and decided that if one of the twenty was different it
was significant. One in twenty. 5%.]
People forget the simple message of the average. In a team of twenty
people, no matter what, half (ten) will be above average and half (ten)
will be below average. Two will be in the bottom 10%, and two will be
in the top 10%. That is a law of nature – like gravity. If you
chase, hassle or fire the below average and the bottom 10% you are just
fighting gravity. Another half will take their place and you will just
have another ten below average. "Yes but", you cry "I
have raised the average by firing the bottom half and hiring better".
Maybe.
Unfortunately, all systems so much dictate the ability of people to
perform in them, that you will probably never know who your really good
and really bad performers are. Even your really top performers may need
the support of people who may not be so visible. When you fire the support
person (because they look to be below average), you may significantly
weaken the star's ability to perform.
Deming reminded us about understanding the meaning of `average'. Consider
the nonsense of these statements:
- Everyone should come up to the average
- Everybody in our company is above average
- "We have three distributors. One is below average and must
go."
- Half our employees earn less than the average (of course they do!)
- Half the students at this school are below average (of course they
are!)
- An education system puts children of age 15 through examinations
and by design passes 50%. Job adds read `School Certificate required'.
The system of grading has generated half as unemployable.
- To solve this, the examination system is changed so that 80% now
pass. Unemployment is solved. Now students can pass who have not achieved
even minimum levels of competence. The School Certificate now has
no credibility with employers who declare "school leavers do
not have the basic skills we want".
My doctor's surgery is very busy. I am always reluctant to go because
the doctor is always at least 1 hour late and it can be as long as 2
hours. I wouldn't mind so much if she was consistent. I could simply
turn up late knowing that I only have to wait for a short time. It would
be even better if she was on time.
We are always in trouble with our budget performance. Every month
we are way off the forecast, sometimes high and sometimes low. Our typical
monthly performance is + or - 50%. As the year goes on, we seem to get
further and further away from the expected YTD. Over the last five years,
we've been consistently more than 20% above our annual budget.
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