# 1. Introduction
## 1.1. General
Most organizations are involved in
producing some kind of output, be it in the form of manufacturing, assembling
bought components and selling them as a system, or combining ‘old’ knowledge to
new approaches to name just a few.
Every process has a Yield.
Yield in the context of this paper is defined as process-inherent output (before
any quality control, auditing or testing) that meets specifications or customer
expectations.
To keep the terminology simpler,
this paper deals only with manufacturing despite the fact that the results are
universally applicable.
## 1.2. Importance of Yield
Your customers expect a certain
level of quality. A number of products even require some sort of certification.
Quality control, auditing, or testing are common tools to reach the required
levels of quality, but they add costs to the process (e.g. additional rework
and/or scrap, higher shipment and restocking fees for returns or the costs
associated with warranty and reduced customer satisfaction). Most of these costs
can not be properly tracked, they disappear somewhere in the overall costs of
doing business.
**1.3. Elements **
Manufacturing in the broadest
sense is assembling (self manufactured and/or purchased) components to a final
product. Each of these components has its specifications (or drawings) and has
to be assembled in a defined way in order for the final product to work as
required. In the context of this paper, each parameter of the individual
specification and each assembly instruction for each component is considered an
“Element”.
This paper looks into the
correlation between Yield and number of elements on a purely mathematical basis.
Even if organizational reality is the result of countless dimensions, looking at
the relationship between two specific ones helps to better understand what to
expect.
# 2. Yield
## 2.1. Some Math basics
To understand the
mathematics, let’s look at tossing coins. Heads is the ‘required’ result.
With one coin, the
probability of the ‘right’ result is 50 % (if one neglects the possibility of
the coin coming to rest on its edge).
With two coins, the
probability of two ‘Heads’ reduces to
0.5 x 0.5 = 0.25
(or 25%)
Adding a third coin reduces
the probability of an all ‘Heads’ result further to
0.5 x 0.5 x
0.5 = 0.125 (or 12.5 %)
In general the Yield (in the case
of this example the probability of having an ‘All Heads’ result) is calculated
with the formula:
**Y = (1 –
E) **^{n}
Where: Y
is the Yield
E is the error rate or the probability of an
individual coin showing ‘Tail’
n is the number of coins
## 2.2. Yield of a Process
The above formula can be used to
calculate and graph the Yield of a manufacturing process for different Error
Rates per Element (an error rate of 1 / 1000 Elements is a ‘good rate’ of 99.9%,
5 / 1000 is 99.5% good elements, etc).
Fig. 1 Yield = f (Number of Elements per Product and Error
Probability per Element)
**3. Discussion of
Results**
Today’s products are more
complex than yesterday’s and tomorrow’s will be even more complex than today’s.
Increased complexity of products means nothing else but an increased number of
elements per product.
The above graph shows that
even with a constant Error Rate, the yield will drop with an increasing number
of elements. If you think that your organization does not perform as well as
just a few years ago, you are probably right; not because your employees are
less diligent, but because of the nature of the beast.
Throwing more Quality Control
(QC) at the problem is probably not the most cost effective solution. Not only
because QC has a yield too (QC only finds a certain percentage of non
compliances), but rather because the mistakes have already happened and
correcting them costs more money.
The errors responsible for
your Error Rate happen throughout the process, from the moment a new order comes
through the door or even earlier. Every step along the way adds errors to your
Error Rate.
*What you want to
achieve is minimal costs per unit to provide your customer with the quality
product he/she requires*. It does not matter where
you spend the money, up front in the administrative steps, QC of parts
(purchased or manufactured) or at the end of your process with Quality Control
and rework, as long as your costs per unit are minimized.
Unless your products don’t change,
review the way your organization operates every few years. How you generate and
handle data and information has to be part of this review, because this is an
area in your process with a high potential to add errors.
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