Calculation of uncertainty

1. What is a measurement?
A measurement tells us about a property of something. It might tell us how heavy an object is, or how hot, or
how long it is. A measurement gives a number to that property. Measurements are always made using an
instrument of some kind. Rulers, stopwatches, weighing scales, and thermometers are all measuring
instruments. The result of a measurement is normally in two parts: a number and a unit of measurement, e.g.
‘How long is it? ... 2 meters.’
What is not a measurement?
There are some processes that might seem to be measurements, but are not. For example, comparing two
pieces of wood to see which is longer is not really a measurement. Counting is not normally viewed as a
measurement. Often, a test is not a measurement: tests normally lead to a ‘yes/no’ answer or a ‘pass/fail’
result. (However, measurements may be part of the process leading up to a test result.)

2. Since there is always a margin of doubt about any measurement, we need to ask ‘How big is the margin?
(‫ش‬ِ‫’)هام‬ and ‘How bad is the doubt?’ Thus, two numbers are really needed in order to quantify Measurement.
One is the width of the margin, or interval. The other is a confidence level, and states how sure we are that
the ‘true value’ is within that margin.
For example: We might say that the length of a certain stick measures 20 centimeters plus or minus 1
centimeter, at the 95 percent confidence level. This result could be written: 20 cm ±1 cm, at a level of
confidence of 95%. The statement says that we are:
95 % percent sure that the stick is between 19 centimeters and 21 centimeters long.

3. Error versus Uncertainty
It is important not to confuse the terms ‘error’ and ‘uncertainty’.
Error is the difference between the measured value and the ‘true value’ of the thing being measured.
‫و‬ ‫المقاسة‬ ‫القيمة‬ ‫بين‬ ‫الفرق‬ ‫هو‬ ‫الخطأ‬
"
‫الحقيقية‬ ‫القيمة‬
"
‫قياسه‬ ‫يتم‬ ‫الذي‬ ‫للشيء‬
.
Uncertainty is a quantification of the doubt about the measurement result.
‫القياس‬ ‫نتيجة‬ ‫حول‬ ‫للشك‬ ‫كمي‬ ‫قياس‬ ‫هو‬ ‫اليقين‬ ‫عدم‬
.

5. What a standard deviation means?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small,
standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation
indicates data are more spread out.
‫للمتوسط‬ ‫بالنسبة‬ ‫البيانات‬ ‫تشتت‬ ‫لمدى‬ ‫مقياس‬ ‫هو‬
.
‫الب‬ ‫أن‬ ‫إلى‬ ‫الصغير‬ ‫أو‬ ‫المنخفض‬ ‫المعياري‬ ‫االنحراف‬ ‫يشير‬
‫يانات‬
‫ا‬ً‫انتشار‬ ‫أكثر‬ ‫البيانات‬ ‫أن‬ ‫إلى‬ ‫الكبير‬ ‫أو‬ ‫المرتفع‬ ‫المعياري‬ ‫االنحراف‬ ‫ويشير‬ ،‫المتوسط‬ ‫حول‬ ‫بإحكام‬ ‫متجمعة‬
.
σ ‫االنحراف‬
‫المعياري‬

8. in everyday life, calculating the speed and position of a moving object is relatively
straightforward. We can measure a car traveling at 60 miles per hour or a tortoise crawling at
0.5 miles per hour and simultaneously pinpoint where the objects are located. But in the
quantum world of particles, making these calculations is not possible due to a fundamental
mathematical relationship called the uncertainty principle.
Formulated by the German physicist and Nobel laureate Werner Heisenberg in 1927, the
uncertainty principle states that we cannot know both the position and speed of a particle,
such as a photon or electron, with perfect accuracy; the more we nail down the particle's
position, the less we know about its speed and vice versa.
‫ا‬ً‫ي‬‫نسب‬ ‫ا‬ً‫ط‬‫بسي‬ ‫ا‬ً‫أمر‬ ‫متحرك‬ ‫جسم‬ ‫وموضع‬ ‫سرعة‬ ‫حساب‬ ‫يعد‬ ،‫اليومية‬ ‫الحياة‬ ‫في‬
.
‫بسرعة‬ ‫تسير‬ ‫سيارة‬ ‫قياس‬ ‫يمكننا‬
60
‫الساعة‬ ‫في‬ ً‫ال‬‫مي‬
‫بسرعة‬ ‫تزحف‬ ‫سلحفاة‬ ‫أو‬
0.5
‫الوقت‬ ‫نفس‬ ‫في‬ ‫األشياء‬ ‫وجود‬ ‫مكان‬ ‫وتحديد‬ ‫الساعة‬ ‫في‬ ‫ميل‬
.
‫فإن‬ ،‫الكمومي‬ ‫الجسيمات‬ ‫عالم‬ ‫في‬ ‫لكن‬
‫اليقين‬ ‫عدم‬ ‫مبدأ‬ ‫تسمى‬ ‫أساسية‬ ‫رياضية‬ ‫عالقة‬ ‫بسبب‬ ‫ممكن‬ ‫غير‬ ‫الحسابات‬ ‫هذه‬ ‫إجراء‬
.
‫فيرنر‬ ‫نوبل‬ ‫جائزة‬ ‫على‬ ‫والحائز‬ ‫األلماني‬ ‫الفيزيائي‬ ‫صاغه‬ ‫الذي‬ ،‫اليقين‬ ‫عدم‬ ‫مبدأ‬ ‫ينص‬
‫هايزنبرغ‬
‫عام‬ ‫في‬
1927
‫ال‬ ‫أننا‬ ‫على‬ ،
،‫بسرعته‬ ‫معرفتنا‬ ‫ت‬ّ‫قل‬ ،‫الجسيم‬ ‫موقع‬ ‫حددنا‬ ‫كلما‬ ‫تامة؛‬ ‫بدقة‬ ،‫اإللكترون‬ ‫أو‬ ‫الفوتون‬ ‫مثل‬ ،‫الجسيم‬ ‫وسرعة‬ ‫موقع‬ ‫معرفة‬ ‫نستطيع‬
‫صحيح‬ ‫والعكس‬
.
Uncertainty = Best estimated value +- Amount of uncertainty

9. The science of measurement is commonly known as ‘metrology’. When something is
measured, the act of measurement causes a shift in the outcome. For instance, the accuracy of
the measurement will be limited by the equipment’s resolution. As a result, an instrument with
a resolution of 0.1 cannot measure an amount that is truly 0.665; it can only indicate 0.6 or 0.7.
As a result, measurement uncertainty exists. Simply holding a steel rule will cause it to heat up,
increasing its total length and creating tiny variations or “uncertainties.

10. DIFFERENT TYPES OF MEASUREMENT AND UNCERTAINTY IN ISO 17025?
Random : Random uncertainty occurs when different unexpected results are achieved after repeating an analysis.
Systematic : Systematic uncertainty is when the value achieved is more or less than the actual value.
Standard uncertainty : The uncertainty of the measurement’s outcome expressed as a standard deviation.
Combined standard uncertainty : The estimated standard deviation equivalent to the summation of the square root
of the total variance obtained by adding all the uncertainty components, commonly referred to as error
propagation.
Bias : The difference between the expected outcome of testing and the real value