Measurement was carried out by positioning the ionization chamber at the reference point in a water phantom. The National Reference and clinical ionization chambers were set up according to Figure 2 , in a water phantom, at a distance of 100 m from the source, at a depth of 5 cm² and then exposed to gamma beam. The chamber orientation was aligned at a mark on the stem towards the source for both the reference and user ionization chamber, as guided by [5] protocol. Before measurement, leakage current of the reference standard dosimeter was obtained before exposure.

The measurement was then carried out under defined reference conditions as outlined in IAEA protocol [12] . The equipment used for measurement are ionization chamber, electrometer, water phantom, barometer, thermometer, cobalt 60 source and calibration system. Ionization chambers was preferred for measurement because of its high accuracy and traceability to primary standards.

Measurement was performed in terms of absorbed dose to water in a water phantom [5] and using the ionization chamber as shown in Figure 3 . The water phantom was positioned on the central axis beam aligned to Cobalt calibration source. The measurement technique was carried out by substitution method, where the reference point of each chamber was placed successively at the same measurement point [1] . Constant environmental conditions was maintained throughout the measurement period for both clinical and SSDL ionization chambers.

Data for measurement was obtained from electrometer exposed to a Co-60 beam in water phantom, in form of charge. The air kerma rate for the reference instrument was determined by:

$K_a=N_k^{ref}{M}_{corr}^{ref}{k}_{Q,Q_0}$(1)

Calibration factor of the instrument used for radiotherapy derived by:

$N_k^{User}=\frac{k_a\cdot k_{source}}{M_{corr}^{user}}$(2)

where:

$N_k^{ref}$ is the air kerma calibration coefficient of the refence instrument, in a reference quality $Q_0$.

$N_k^{user}$ is the air kerma calibration coefficient of the user instrument in the calibration quality Q.

$K_a$ is the air kerma rate determined with the reference instrument.

$K_{source}$ is the correction for the effect of a change in source positioning.

$K_{Q,Q_0}$ is the correction effect for difference between qualities of the beams for KNH and SSDL.

The objective of measurement uncertainty is to express the statistical dispersion of values attributed to radiation measurand. Uncertainty of measurement is expressed as relative standard uncertainty and evaluation classified into type A and type B [6] . Type A are those that arise from random effect, while type B are those that arises from systematic effect. The method for evaluation of type A standard uncertainties is by statistical analysis of a series of observations, whereas evaluation of type B standard uncertainties is through non-statistical techniques [5] . Type B is based on scientific judgement using scientific information available including manufacturer manual, calibration certificate, previous records among others.

The best estimate of absorbed dose to water quantity is given by arithmetic mean $\stackrel{\dot{}}{x}$ in a series of measurement n with observed values $x_i$

$\stackrel{\dot{}}{x}=\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{x}_i}$(3)

where

$\stackrel{\dot{}}{x}$ is the arithmetic mean.

$x_i$ is the observed values.

n series of measurement.

Standard deviation $s\left(x_i\right)$ is given by:

$s\left(x_i\right)=\sqrt{\frac{1}{n-1}{\displaystyle {\sum }_{i=1}^n{\left(x_i-\stackrel{\dot{}}{x}\right)}^2}}$(4)

where

n is the number of measured values.

$s^2\left(x_i\right)$ is the sample variance.

The standard deviation of the mean value $s\left({\stackrel{\dot{}}{x}}_i\right)$ is given by:

$s\left({\stackrel{\dot{}}{x}}_i\right)=\frac{s\left(x_i\right)}{\sqrt{n}}$(5)

The standard uncertainty of type A, denoted $u_A$, is identified with the standard deviation of the mean value:

$u_A=s\left(\stackrel{\dot{}}{x}\right)$(6)

For type B standard uncertainty $u_B$ for rectangular probability is given by

$u_B=\frac{M}{\sqrt{3}}$(7)

where M is the given limits obtained from the literature.

The combined standard uncertainty quantity $u_c$ for type A and type B is given by:

$u_c=\sqrt{u_A^2+u_B^2}$(8)

where

$u_A$ combined uncertainty for type A.

$u_B$ combined uncertainty for type B.

$u_c$ overall combined uncertainty.

The expanded uncertainty, U is given by:

$U=k\cdot u_c\left(y\right)$(9)

where k is the coverage factor and is obtained from a student-t distribution table based on the required level of confidence.

Uncertainty budget provides itemized table of components that contribute to the uncertainty of the measurement results [6] . Uncertainty budget present information that identifies, quantifies, and characterizes each of the independent variable contributors in a structured manner, so as to allow validation of results [5] .

Influence quantities are regarded as parameters that are not subject to measurement but affect the measurement of ionization chamber readings. The influence quantities identified were air pressure, ageing, zero drift, beam quality, dose rate and field size [1] . The corresponding effects and their impact on the results were considered in the final analysis of results [13] .

Several sources of contributors to dose determination of uncertainties were considered from different physical quantities, procedures, and environment conditions. Evaluation was carried out for the uncertainties due to the calibration of the user ionization chamber $N_{D,w}$ at the SSDL [14] . This was followed by analysis of uncertainties measurement due to ⁶⁰Co beam and uncertainties associated with the measurements at the reference point in a water phantom and $k_Q$ values.

Table 1 shows how different uncertainty source and contributors that affect dosimetry measurement were identified and analyzed. Some of the contributors identified include calibration of standards, pressure, temperature, position of the chamber, stability of the chamber, electrometer of the chamber, resolution, and reproducibility. The best estimate of arithmetic mean was determined according to Equation (3), standard deviation according to Equation (4), combined standard uncertainty according to Equation (8) and expanded uncertainty according to Equation (9).

Uncertainty contribution u(y_i) is estimated by multiplying the standard uncertainty u(x_i) with the sensitivity coefficient. The resulting uncertainty contribution, standard deviation, is the same unit as the measurand and is scaled according to its influence on the measurand by

$u\left(y_i\right)=c_i\cdot u\left(x_i\right)$(10)

Using the central limit theorem to combine all the uncertainty contributors in order to have a single value representing the standard deviation of the measurement system:

$U_c\left(y\right)={\displaystyle {\sum }_{i=1}^{n}u{\left(y_i\right)}^2}$(11)

Using information from Table 1 ,

$\begin{array}{c}u{\left(y_i\right)}^{\text{2}}=0.00\text{4}+\left(\text{5}.\text{3E}-0\text{6}\right)+0.0\text{4}+0.0\text{7}+0.00\text{3}+\left(\text{5}.\text{3E}-0\text{6}\right)\\ +0.0\text{39}+0.0\text{133}+\left(\text{3}.\text{3E}-0\text{7}\right)+0.000\text{3}\\ =0.17\end{array}$

$\begin{array}{c}u{\left(y_i\right)}^{\text{4}}=\left(1.8\text{E}-0\text{5}\right)+\left(\text{2}.\text{8E}-\text{11}\right)+0.00\text{2}+0.000\text{2}+0.00\text{4}+\left(\text{6}.\text{2E}-0\text{6}\right)\\ +\left(\text{2}.\text{8E}-\text{11}\right)+0.00\text{2}+0.000\text{2}+\left(1.1\text{E}-\text{13}\right)+\left(\text{9}.\text{9E}-0\text{8}\right)\end{array}$

$u{\left(y_i\right)}^4=0.0073$

Combined uncertainty

$u_c\left(y\right)=\sqrt{u{\left(y_i\right)}^2}=\sqrt{0.17}=0.42$(12)

Effective degree of freedom calculated from Welch-Satterthwaite formula, in order to weighs the degree of freedom for each uncertainty by its uncertainty contribution:

$v_{eff}=\frac{{\left\{u_c\left(y\right)\right\}}^4}{\frac{u{\left(y_i\right)}^4}{V_i}}=6.1\times {10}^5$(13)

Taking Level of Confidence to be 95.45%, which translate to a coverage factor of K = 2,

$\text{Expanded Uncertainty}=u_c\left(y\right)\times 2.0=0.42\times 2=0.84\%$(14)

In this regard, the overall expanded uncertainty was found to be 0.8% associated with ND,W of 57 mGy/nC, with a coverage factor of 2 and at level of confidence of 95.45%. This illustrates that the dispersion of results of data obtained from the radiation measurement can be described approximately by a Gaussian or normal probability distribution, with 95.45% of the results falling within ±2 standard deviations of the average value. This is because uncertainty of measurement is for specific beam quality and ionization chamber. The investigation therefore outlined the importance of measurement of uncertainty in analyzing the quality of radiation radiotherapy beam thereby building on work done by Bulinski [9] .

Figure 4 illustrates that Type B had greater impact on the overall uncertainty contribution compared to Type A. In this case, 62% of the contribution was from Type B compared to 38% of Type B, using data obtained from Table 1 . This illustrates that external factor contribution of measurement had a more significant impact on the overall uncertainty contribution. Therefore, information obtained through measurement is limited and must be supplemented with information obtained from non-statistical means, which in this case include calibration certificates, manufacturer manuals, publications, historical data among others.

Figure 5 illustrates the magnitude of each identified contributor to the overall uncertainty. This follows analysis of different components that contribute to uncertainty of measurement including environmental conditions, stability of the chamber, ionization chamber under test (UUT), resolution, reproducibility of measurement, positioning of the chamber and electrometer. The largest contribution was from stability of the standard ionization chamber, followed by temperature contribution standard chamber (STD) and clinical chamber (UUT).

During analysis of uncertainty, not all the factors were available for consideration including information about the geometry of the chamber and software. Furthermore, the calibration factor was obtained from calibration certificate and is prone to change due to use in a different environment.