Applied Radiation and Isotopes 102 (2015) 93–97
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
A step towards accreditation: A robustness test of etching process F. Leonardi a,n, M. Veschetti a, S. Tonnarini a, F. Cardellini b, R. Trevisi a a b
INAIL (Italian National Workers Compensation Authority)- Research Sector – Department of Occupational Hygiene 00040 Monteporzio Catone, Rome, Italy INMRI-ENEA (National Institute of Ionizing Radiation Metrology)- Casaccia, 00133 Rome, Italy
H I G H L I G H T S
The evaluation of the robustness of the SSNTD etching process (KOH solution 6.0 N, 75 °C, 270 min) have considered several factors. The results evidenced that the etching process can be considered robust. The only critical factor is the etching solution's temperature. A strict control about stability of temperature during the etching process is needed.
art ic l e i nf o
a b s t r a c t
Article history: Received 22 July 2014 Received in revised form 6 May 2015 Accepted 6 May 2015 Available online 7 May 2015
In the present study the robustness of the etching process used by our laboratory was assessed. The strategy followed was based on the procedure suggested by Youden. Critical factors for the process were estimated using both Lenth's method and Dong's algorithm. The robustness test evidences that particular attention needs to be paid to the control of the etching solution's temperature. & 2015 Elsevier Ltd. All rights reserved.
Keywords: SSNTD Robustness Etching process Radon Method validation
1. Introduction In the framework of the general requirements for the competence of testing and calibration laboratories, the ISO/IEC standard (2005) requires the validation of all non-standard methods. For integrated radon measurements, experimental methods using NRPB/SSI type dosimeters and CR39 plastics (Intercast Europe, Italy) as detectors (SSNTD) can be applied: experimental details about the laboratory-developed method followed in the present work are described elsewhere (Mishra et al., 2005; Orlando et al., 2002). The validation of a laboratory-developed method is performed to ensure that an analytical methodology is accurate, specific, reproducible and robust over the specified range that an analyte will be analyzed. Some aspects of the quality assurance program for the validation of the integrated radon measurements method were previously described (D’Alessandro et al., 2010). In this work the attention of the authors has been focused principally to the n
Corresponding author. E-mail address: [email protected] (F. Leonardi).
http://dx.doi.org/10.1016/j.apradiso.2015.05.002 0969-8043/& 2015 Elsevier Ltd. All rights reserved.
robustness evaluation of the etching process of plastic detectors with the aim to study which factors influencing the final result. The robustness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate variations in method parameters and provides an indication of its reliability during normal usage. Robustness can be described as the ability to reproduce the analytical method in different laboratories or under different circumstances without the occurrence of unexpected differences in the obtained result. As well known heavy charged particles, impacting the plastic material surface (SSNTD), cause an extensive ionization of the material that led to the creation of a damaged zone (latent track) along the particles ‘path (Nikezic and Yu, 2004). The etching process allows to visualize the latent tracks and afterward to count them by using optical systems. The performance of the etching process is strictly influenced by the chemical characteristics, the concentration and temperature of the etchant (Hermsdorf et al., 2007). In our method, in order to have easily
94
F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
readable tracks (due to radon and its progeny alpha emissions), the following chemical etching conditions are employed: 4.5 h as etching time in a 6.0 N KOH aqueous solution at 75 °C. The evaluation of the robustness of an etching process is necessary to examine the potential source of variability of quantitative aspect of the method through the variation of variables (inherent to the analytical procedure) called “factors”. In particular in this work, to study the main effects of an analytical factor, the “screening design” developed by Plackett and Burman (1946) together with the procedure suggested by Youden (1972) for the robustness evaluation of an experimental method are used.
2. Material and methods As previously mentioned, to study the main effects of an analytical factor, the “screening design” has been used. Screening designs are two-level saturated fractional factorial designs centered on the analytical conditions. Plackett and Burman (1946) developed such design for studying f factors in N ¼ fþ1 experiments. The strategy followed to carry out a robustness study is based on the procedure suggested by Youden (1972): a. identify those factors which can influence the response; b. for each of these factors define the nominal and extreme levels to be accounted for a routine work, encoding them as follow: nominal value ¼0, high value ¼(þ ) low value ¼( ); c. arrange the experimental plan according to the two-level Plackett and Burman design; d. perform the experiments in random order and evaluate each factor effect. In Table 1 together with the real factor to be examined some dummy factors were introduced (factor b4, b7). The dummy factor is an imaginary factor for which the change from one level to the other has no physical meaning. The dummy factor is necessary to fill in all the columns needed for a Plackett–Burman design with 8 experiments. To establish the robustness of the SSNTD etching method, 9 experiments were carried out, 8 for the Plackett–Burman design and 1 as a reference. For each experiment 10 SSNTDs, previously exposed to radon atmosphere, were etched. Indeed all radon passive dosimeters, used in the 9 experiments, were exposed to the same radon atmosphere (1219 760 kBqh/m3) in the reference chamber of the Italian National Institute of Metrology of Ionizing Radiation (INMRI-ENEA in the following). The conditions under which, the experiments were performed, are reported in Table 2: these conditions affect only the etching process of detectors and in particular the tracks’ structure. To determine the influence of the variation of each factor the Table 1 Analytical parameter and relative variations using for evaluating the robustness of the process. Factor
b1 b2 b3 b4 b5 b6 b7
Level
Solutions’ temperature (°C) Etching time (min) KOH concentration (N) Etching bath CH3COOH concentration (N) Time in CH3COOH (min) Number of autofocus
þ
0
77 272 6.2 A 1.1 12 6
73 268 5.8 B 0.9 8 4
75 270 6.0 B 1.0 10 5
Table 2 Plackett–Burman design for 7 factor (N ¼8). Exp no.
b1
b2
b3
b4
b5
b6
b7
1 2 3 4 5 6 7 8
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
average track density was determined. Detectors are read out with the Politrack track detector reader, developed at the Politecnico di Milano and supplied by Mi.Am srl (Italy). The reader is an optical microscope with two exchangeable magnifications, about 100 μm and 200 μm, coupled with a 1024 768 pixel CCD camera. The spatial resolution is 0.92 μm per pixel for 100 magnification and 0.57 μm per pixel in the other case. The image is grabbed via firewire by a PC where an image analysis software runs. The same software drives a motorized cartesian Table that moves the detector under the microscope objective (Caresana et al., 2010). The reading protocol of the laboratory requires that each detector is scanned 10 times. So for each experiment 100 track density values were available. On whole data set statistical analysis (e.g. t-test) were performed in order to calculate the average track density for each experiment. In Table 3 the average track density calculated for each experiment is reported. For experiment 0 that is conducted in reference conditions (see Table 1) it is possible to applicate the calibration factor normally used by the laboratory in order to determine the exposure. The exposure so computed is equal to 1198 7120 kBqh/m3, which is in very good agreement with the one declared by INMRI-ENEA.
3. Results and discussion 3.1. Calculation of effects For each factor the effect is calculated according to the equation:
EX =
∑Y ( + ) ∑Y ( − ) − N /2 N /2
(1)
where X represents analytical factor (from b1 to b7), EX is the effect of X on the response Y and ΣY( þ) and ΣY( ) are the sums of the responses, where X is at the extreme level (þ ) and ( ), respectively, and N is the number of the experiments of the design (8 in our case). For example for Eb1, ΣY(þ) is given by the sum of the track densities of experiment number 1,4,6,7 and ΣY( ) is given by the sum of the track densities of experiment number 2,3,5,8. The effects can also be normalized respect to the average nominal Table 3 Average density track's for each experiment. Exp no.
Track/cm2
0 1 2 3 4 5 6 7 8
3490 2269 3563 3511 2601 3334 2724 2074 3215
F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
95
Table 4 Effects from a seven-factor Plackett–Burman design. Factor
Effect (EX)
Normalized effect (|Ex|)
b1 b6 b3 b2 b4 b5 b7
988.607 288.212 211.031 202.555 51.757 34.738 1.262
0.2833 0.0826 0.0605 0.0580 0.0148 0.0100 0.0004
result (Y̅ ). Usually normalized effects, much more than the regular effect estimates, allow the user of the method to consider the influence of a factor as important, even without statistical interpretation. For each factor the normalized effect is calculated according to the equation:
EX =
EX Y¯
(2)
In Table 4 for each factor the effect (EX) and the normalized effect (|Ex|) are reported. 3.2. Interpretation of effects The graphical identification of relevant effects is performed by using the half-normal plot as proposed by Daniel (Nijhuis et al., 1999; Daniel, 1959). To create half-normal plot, the n effects are ranked in a sequence according to the increasing of the absolute effect size. In Table 5 the rankits are given for the 8 experiments in a Plackett–Burman design (Vander Heyden et al., 2001) and the halfnormal plot for the normalized effects is reported in Fig. 1. When there is no significant effect all points are expected to fall around a straight line, so the identification of a relevant effect in half-normal plot is done visually. To avoid the subjectivity due to a visual interpretation, a statistical approach was also employed. The statistical interpretation provides a numerical limit value (Ecrit) that can be added on the half-normal plot allowing to define what is significant and what is not. This limit value is usually derived from Student's t-test (Nijhuis et al., 1999, Youden and Steiner, 1975; Miller and Miller, 1993).
t=
|EX | ⇔ tcrit (SE)
(3)
where (SE) is the standard error of an effect. For the robustness evaluation of a method there are different ways to estimate the error of an effect and then its critical effect (Ecrit): from Eq. (3) the limit value (Ecrit) can be expressed as:
EX ⇔ Ecrit = tcrit ⋅(SE)
(4)
In the present work for the evaluation of SE and Ecrit two Table 5 Rankits to draw a half- normal plot for the N ¼ 8 screening design. (Effect 1 indicates the smallest effect). Effect
Rankit
1 2 3 4 5 6 7
0.09 0.27 0.46 0.66 0.9 1.21 1.71
Fig. 1. Half-normal plot for the normalized effects of Table 4, with the identification of the critical effects ME e SME.
different models have been applied: Lenth's (1989) model and Dong's (1993) algorithm. In both, the median of the absolute effects is used as a first estimation (s0) of the standard error (SE) associated to the factors:
S0 = 1.5median bi
(5)
where bi is the value of the effect i. Lenth's method Starting from s0 a pseudo standard error (PSE) is derived:
PSE = 1.5median bi
(6)
With |bi| o 2.5s0. PSE value is used to calculate a margin error (ME) and simultaneous margin error (SME).
ME = t(1 − α /2, df ) PSE SME = t ⎛⎜1 − α*/2, df ⎞⎟ PSE ⎝
⎠
(7)
(8)
Where df1 ¼m/3 and m is the number of factors b. α n is the Bonferroni adjusted significance level (Haaland and O’Connell, 1995). According to Lenth (1989) when 7 factors are considered with a confidence level of 97.5% (α ¼0.05), Eqs. ((7) and 8) become:
ME = 2.297·PSE SME = 4.867· PSE where PSE is computed according to Eq. (6). The ME is a statistically valid criterion for significant testing when only one effect is to be tested. When multiple effects are tested the chance for non-significant effects that exceed the ME increases (Nijhuis et al., 1999). To counterbalance these events a second limit (SME) is defined. Practically the use of only ME as a limit increases the chance for false positive led to consider (with 2.5% of probability) a factor as significant when really it is not. Instead, the use of the only SME largely increase the possibility to consider non-significant an effect which is significant (false negative). Since, according to some authors (Haaland and O’Connell, 1995) the Lenth's procedure results in an overly conservative test, due to the use of a reduction number of degrees of freedom (df¼ m/3) to derive critical values (see formulas (7) and (8)) so to calculate 1
df¼ degrees of freedom
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F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
critical values a further method was also used: the Dong's method. This method, illustrated in the following, used a number of degrees of freedom equal to m instead of m/3. Dong's method In Dong's method the PSE is substituted by the standard error s1 derived as:
s1 =
1 m
∑ bi2
(9)
For all bi o 2.5s0, where m is the number of the factor smaller than 2.5s0. In this case m ¼6.
ME = t(1 − α /2, df ) s1
(10)
SME = t ⎛⎜1 − α*/2, df ⎞⎟ s1 ⎝
⎠
(11)
where df¼m and α is the Bonferroni adjusted significance level (Haaland and O’Connell, 1995). Assuming α ¼0.05 and using for Student's t the tabulated values, Eqs. (10) and (11) can be written as: n
ME = 2.45⋅s1 SME = 3.98⋅s1 The combination of Dong's method with Lenth's PSE test can represent a good solution for the evaluation of data. In Table 6 and Fig. 1 the values of ME and SME calculated with both methods starting from factors given in Table 1, were reported. Looking at Fig. 1 it can be observed that only b1 exceeds ME and SME values evaluated upon both the Lenth's model and Dong's algorithm: this means that in the etching process the temperature of the etchant solution (b1) is the only relevant factor.
4. Influence of factors on the tracks structure Due to the mechanism of tracks formation, the importance of the temperature factor is expected. Indeed both bulk and track etch rates (Vb and Vt, respectively) increase exponentially with the temperature (Nikezic and Yu, 2004) and track development is governed by the ratio V ¼Vt/Vb. The track formation is not possible if V is smaller than or equal to 1. The temperature effect can be further confirmed by analyzing the radius of tracks. The major (D) and the minor (d) axes of the track opening are given by (Nikezic and Yu, 2004):
D = 2h
V2 − 1 V sin θ + 1
d = 2h
(12)
V sin θ − 1 V sin θ + 1
(13)
h = vb ⋅t
(14)
where h is the removed layer during the etching process, t is the etching time and θ is the angle between the direction of the incident particle and the surface of the detector. Looking at the data related to experiments nos. 4, 6 and 8, Table 6 ME and SME values calculated with Dong's and Lenth's methods starting from factor.
ME SME
Lenth
Dong
0.1255 0.2660
0.1190 0.1934
Fig. 2. Major axe size distributions for etched tracks of experiments nos. 4 and 6 (a) and nos. 4 and 8 (b).
where the etching temperature and the etchant concentration varied, the distribution of the major axe of tracks (D) has been compared as shown in Fig. 2. The major axe size distribution is well fitted by a Gaussian curve (using OriginPro 9.1 by OriginLab USA) and the maximum of the distribution (Xc) for each experiment is reported in Table 7. In Fig. 2a it is shown that the variation of the etchant concentration (exp. nos. 4 and 6) does not influence the major axe size frequency distribution. In fact the two curves show the same tracks dimensions distributions with a maximum value (Xc) around 24 μm. Conversely, the decreasing of the etching temperature (comparing experiment no. 8–4) led to the formation of tracks with a major axe around 15 μm (see Fig. 2b). It is quite evident that the temperature represents the most important factor on the track dimensions. Moreover analyzing the results obtained in the same experiments in terms of average track density (see Table 3), it can be observed that an increase of the etchant concentration do not influence neither the average track density (E 4%) neither the track structure (both curves have the same Xc). While a variation of the etching temperature determine effects as in terms of average track density (E 39%) as in terms of tracks morphology (as Xc). For a factor considered relevant (b1 in our case), it is possible to estimate in which interval the factor effect is not significant. The limit values of the interval can be assessed as (Vander Heyden et al., 2001):
X0 ±
X + − X − Ecrit 2 Ex
(15)
Assuming for Ecrit the value of ME and SME estimated by the Dong's method, and applying Eq. (15) to factor b1, the interval in which the temperature of the KOH solution have no significant effect is 74 °C o b1 o76 °C. Table 7 Maximum of particle major axes Gaussian distribution for selected experiments. Also some etching parameters were reported. Exp. no.
Xc (μm)
b1 (°C)
b2 (min)
b3 (N)
4 6 8
23.9871 23.9886 15.3714
77 77 73
268 268 268
5.8 6.2 5.8
F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
5. Conclusions In the present work, the validation of a laboratory-developed method was focused. In particular, the etching process of CR39 plastics detectors (SSNTD) exposed to radon and its progeny has been analyzed. A robustness evaluation was performed as an important step of the validation process. The robustness study of the SSNTD etching method (KOH solution 6.0 N, 75 °C, 270 min) considered several factors such as etching time, etchant temperature and concentration, and treatment in CH3COOH solution to stop the etching process. The robustness evaluation of an experimental method performed using Youden procedure has been well applied to study other analytical methods, (Ragonese et al., 2000, Karageorgou and Samanidou, 2014). The results evidenced that the etching method can be considered robust: the only critical factor is the etching solution's temperature. Only a variability of 71 °C with respect to the reference values is admitted, then a strict control about stability of temperature during the whole process is needed. The results achieved by the application of mathematical models have been further confirmed by the analysis of the distribution of the main axis of tracks, etched in different condition: in fact a small increase of the temperature led to an increase of the dimension of track axes, while small variations of the etchant concentration do not result in any significant effect.
References Caresana, M., Ferrarini, M., Garlati, L., Parravicini A, A., 2010. About ageing and fading of Cr-39 PADC track detectors used as air radon concentration measurement devices. Radiat. Meas. 45, 183–189. D’Alessandro, M., Leonardi, F., Tonnarini, S., Trevisi, R., Veschetti, M., 2010. Development of a framework of quality assurance practices for a radon passive dosemeter service. J. Radiol. Prot. 30 (2), 149–159. Daniel, C., 1959. Use of half-normal plot in interpreting factorial two-level
97
experiment. Technometrics 1, 311–341. Dong, F., 1993. On the identification of active contrasts in unreplicated fractional factorials. Stat. Sin. 3, 209–217. Haaland, Perry D., O’Connell, M.A., 1995. Inference for Effect-Saturated Fractional Factorials. Technometrics 37 (1), 82–93. http://dx.doi.org/10.1080/ 00401706.1995.10485890. Hermsdorf, D., Hunger, M., Starke, S., Weickert, F., 2007. Measurement of bulk etch rates for poly-allyl-diglycol carbonate (PADC) and cellulose nitrate in a broad range of concentration and temperature of NaOH etching solution. Radiat. Meas. 42 (1), 1–7. http://dx.doi.org/10.1016/j.radmeas.2006.06.009. ISO/IEC 17025, 2005. General requirements for the competence of testing and calibration laboratories. edited by International Standard. Karageorgou, E., Samanidou, V., 2014. Youden test application in robustness assays during method validation. J. Chromatogr. A 1353 (0), 131–139. http://dx.doi.org/ 10.1016/j.chroma.2014.01.050. Lenth, R.V., 1989. Quick and easy analysis of unreplicated factorials. Technometrics 31, 469–473. Miller, J.C., Miller, J.N., 1993. Statistic for Analytical Chemistry. New York. Mishra, R., Orlando, C., Tommasino, L., Tonnarini, S., Trevisi, R., 2005. A better understanding of the background of CR-39 detectors. Radiat. Meas. 40 (2–6), 325–328. Nijhuis, A., van der Knaap, H.C.M., de Jong, S., Vandeginste, B.G.M., 1999. Strategy for ruggedness tests in chromatographic method validation. Anal. Chim. Acta 391 (2), 187–202. http://dx.doi.org/10.1016/S0003-2670(99)00113-0. Nikezic, D., Yu, K.N., 2004. Formation and growth of tracks in nuclear track materials. Mater. Sci. Eng. R46, 51–123. Orlando, C., Orlando, P., Patrizii, L., Tommasino, L., Tonnarini, S., Trevisi, R., Viola, P., 2002. A passive radon dosemeter suitable for workplaces. Radiat. Prot. Dosim. 102, 163. Plackett, R.L., Burman, J.P., 1946. The design of optimum multifactorials experiments. Biometrika 33 (4), 305–325. Ragonese, R., Mulholland, M., Kalman, J., 2000. Full and fractionated experimental designs for robustness testing in the high-performance liquid chromatographic analysis of codeine phosphate, pseudoephedrine hydrochloride and chlorpheniramine maleate in a pharmaceutical preparation. J. Chromatogr. A 870 (1–2), 45–51. http://dx.doi.org/10.1016/S0021-9673(99)00972-3. Vander Heyden, Y., Nijhuis, A., Smeyers-Verbekea, J., Vandeginsteb, B.G.M., Massarta, D.L., 2001. Guidance for robustness/ruggedness tests in method validation. J. Pharm. Biomed. Anal. 24 (5–6), 723–753. http://dx.doi.org/10.1016/ S0731-7085(00)00529-X. Youden, W.J., Steiner, E.H., 1975. Statistical manual of the Association of Official Analytical Chemists. Association of Official Analytical Chemists (AOAC), Arlington VA, pp. 33–36. Youden, W.J., 1972. Statistical Technique for Collaborative Tests. Association of Official Analytical Chemists (AOAC), Washington.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
A step towards accreditation: A robustness test of etching process F. Leonardi a,n, M. Veschetti a, S. Tonnarini a, F. Cardellini b, R. Trevisi a a b
INAIL (Italian National Workers Compensation Authority)- Research Sector – Department of Occupational Hygiene 00040 Monteporzio Catone, Rome, Italy INMRI-ENEA (National Institute of Ionizing Radiation Metrology)- Casaccia, 00133 Rome, Italy
H I G H L I G H T S
The evaluation of the robustness of the SSNTD etching process (KOH solution 6.0 N, 75 °C, 270 min) have considered several factors. The results evidenced that the etching process can be considered robust. The only critical factor is the etching solution's temperature. A strict control about stability of temperature during the etching process is needed.
art ic l e i nf o
a b s t r a c t
Article history: Received 22 July 2014 Received in revised form 6 May 2015 Accepted 6 May 2015 Available online 7 May 2015
In the present study the robustness of the etching process used by our laboratory was assessed. The strategy followed was based on the procedure suggested by Youden. Critical factors for the process were estimated using both Lenth's method and Dong's algorithm. The robustness test evidences that particular attention needs to be paid to the control of the etching solution's temperature. & 2015 Elsevier Ltd. All rights reserved.
Keywords: SSNTD Robustness Etching process Radon Method validation
1. Introduction In the framework of the general requirements for the competence of testing and calibration laboratories, the ISO/IEC standard (2005) requires the validation of all non-standard methods. For integrated radon measurements, experimental methods using NRPB/SSI type dosimeters and CR39 plastics (Intercast Europe, Italy) as detectors (SSNTD) can be applied: experimental details about the laboratory-developed method followed in the present work are described elsewhere (Mishra et al., 2005; Orlando et al., 2002). The validation of a laboratory-developed method is performed to ensure that an analytical methodology is accurate, specific, reproducible and robust over the specified range that an analyte will be analyzed. Some aspects of the quality assurance program for the validation of the integrated radon measurements method were previously described (D’Alessandro et al., 2010). In this work the attention of the authors has been focused principally to the n
Corresponding author. E-mail address: [email protected] (F. Leonardi).
http://dx.doi.org/10.1016/j.apradiso.2015.05.002 0969-8043/& 2015 Elsevier Ltd. All rights reserved.
robustness evaluation of the etching process of plastic detectors with the aim to study which factors influencing the final result. The robustness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate variations in method parameters and provides an indication of its reliability during normal usage. Robustness can be described as the ability to reproduce the analytical method in different laboratories or under different circumstances without the occurrence of unexpected differences in the obtained result. As well known heavy charged particles, impacting the plastic material surface (SSNTD), cause an extensive ionization of the material that led to the creation of a damaged zone (latent track) along the particles ‘path (Nikezic and Yu, 2004). The etching process allows to visualize the latent tracks and afterward to count them by using optical systems. The performance of the etching process is strictly influenced by the chemical characteristics, the concentration and temperature of the etchant (Hermsdorf et al., 2007). In our method, in order to have easily
94
F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
readable tracks (due to radon and its progeny alpha emissions), the following chemical etching conditions are employed: 4.5 h as etching time in a 6.0 N KOH aqueous solution at 75 °C. The evaluation of the robustness of an etching process is necessary to examine the potential source of variability of quantitative aspect of the method through the variation of variables (inherent to the analytical procedure) called “factors”. In particular in this work, to study the main effects of an analytical factor, the “screening design” developed by Plackett and Burman (1946) together with the procedure suggested by Youden (1972) for the robustness evaluation of an experimental method are used.
2. Material and methods As previously mentioned, to study the main effects of an analytical factor, the “screening design” has been used. Screening designs are two-level saturated fractional factorial designs centered on the analytical conditions. Plackett and Burman (1946) developed such design for studying f factors in N ¼ fþ1 experiments. The strategy followed to carry out a robustness study is based on the procedure suggested by Youden (1972): a. identify those factors which can influence the response; b. for each of these factors define the nominal and extreme levels to be accounted for a routine work, encoding them as follow: nominal value ¼0, high value ¼(þ ) low value ¼( ); c. arrange the experimental plan according to the two-level Plackett and Burman design; d. perform the experiments in random order and evaluate each factor effect. In Table 1 together with the real factor to be examined some dummy factors were introduced (factor b4, b7). The dummy factor is an imaginary factor for which the change from one level to the other has no physical meaning. The dummy factor is necessary to fill in all the columns needed for a Plackett–Burman design with 8 experiments. To establish the robustness of the SSNTD etching method, 9 experiments were carried out, 8 for the Plackett–Burman design and 1 as a reference. For each experiment 10 SSNTDs, previously exposed to radon atmosphere, were etched. Indeed all radon passive dosimeters, used in the 9 experiments, were exposed to the same radon atmosphere (1219 760 kBqh/m3) in the reference chamber of the Italian National Institute of Metrology of Ionizing Radiation (INMRI-ENEA in the following). The conditions under which, the experiments were performed, are reported in Table 2: these conditions affect only the etching process of detectors and in particular the tracks’ structure. To determine the influence of the variation of each factor the Table 1 Analytical parameter and relative variations using for evaluating the robustness of the process. Factor
b1 b2 b3 b4 b5 b6 b7
Level
Solutions’ temperature (°C) Etching time (min) KOH concentration (N) Etching bath CH3COOH concentration (N) Time in CH3COOH (min) Number of autofocus
þ
0
77 272 6.2 A 1.1 12 6
73 268 5.8 B 0.9 8 4
75 270 6.0 B 1.0 10 5
Table 2 Plackett–Burman design for 7 factor (N ¼8). Exp no.
b1
b2
b3
b4
b5
b6
b7
1 2 3 4 5 6 7 8
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
þ þ þ þ
average track density was determined. Detectors are read out with the Politrack track detector reader, developed at the Politecnico di Milano and supplied by Mi.Am srl (Italy). The reader is an optical microscope with two exchangeable magnifications, about 100 μm and 200 μm, coupled with a 1024 768 pixel CCD camera. The spatial resolution is 0.92 μm per pixel for 100 magnification and 0.57 μm per pixel in the other case. The image is grabbed via firewire by a PC where an image analysis software runs. The same software drives a motorized cartesian Table that moves the detector under the microscope objective (Caresana et al., 2010). The reading protocol of the laboratory requires that each detector is scanned 10 times. So for each experiment 100 track density values were available. On whole data set statistical analysis (e.g. t-test) were performed in order to calculate the average track density for each experiment. In Table 3 the average track density calculated for each experiment is reported. For experiment 0 that is conducted in reference conditions (see Table 1) it is possible to applicate the calibration factor normally used by the laboratory in order to determine the exposure. The exposure so computed is equal to 1198 7120 kBqh/m3, which is in very good agreement with the one declared by INMRI-ENEA.
3. Results and discussion 3.1. Calculation of effects For each factor the effect is calculated according to the equation:
EX =
∑Y ( + ) ∑Y ( − ) − N /2 N /2
(1)
where X represents analytical factor (from b1 to b7), EX is the effect of X on the response Y and ΣY( þ) and ΣY( ) are the sums of the responses, where X is at the extreme level (þ ) and ( ), respectively, and N is the number of the experiments of the design (8 in our case). For example for Eb1, ΣY(þ) is given by the sum of the track densities of experiment number 1,4,6,7 and ΣY( ) is given by the sum of the track densities of experiment number 2,3,5,8. The effects can also be normalized respect to the average nominal Table 3 Average density track's for each experiment. Exp no.
Track/cm2
0 1 2 3 4 5 6 7 8
3490 2269 3563 3511 2601 3334 2724 2074 3215
F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
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Table 4 Effects from a seven-factor Plackett–Burman design. Factor
Effect (EX)
Normalized effect (|Ex|)
b1 b6 b3 b2 b4 b5 b7
988.607 288.212 211.031 202.555 51.757 34.738 1.262
0.2833 0.0826 0.0605 0.0580 0.0148 0.0100 0.0004
result (Y̅ ). Usually normalized effects, much more than the regular effect estimates, allow the user of the method to consider the influence of a factor as important, even without statistical interpretation. For each factor the normalized effect is calculated according to the equation:
EX =
EX Y¯
(2)
In Table 4 for each factor the effect (EX) and the normalized effect (|Ex|) are reported. 3.2. Interpretation of effects The graphical identification of relevant effects is performed by using the half-normal plot as proposed by Daniel (Nijhuis et al., 1999; Daniel, 1959). To create half-normal plot, the n effects are ranked in a sequence according to the increasing of the absolute effect size. In Table 5 the rankits are given for the 8 experiments in a Plackett–Burman design (Vander Heyden et al., 2001) and the halfnormal plot for the normalized effects is reported in Fig. 1. When there is no significant effect all points are expected to fall around a straight line, so the identification of a relevant effect in half-normal plot is done visually. To avoid the subjectivity due to a visual interpretation, a statistical approach was also employed. The statistical interpretation provides a numerical limit value (Ecrit) that can be added on the half-normal plot allowing to define what is significant and what is not. This limit value is usually derived from Student's t-test (Nijhuis et al., 1999, Youden and Steiner, 1975; Miller and Miller, 1993).
t=
|EX | ⇔ tcrit (SE)
(3)
where (SE) is the standard error of an effect. For the robustness evaluation of a method there are different ways to estimate the error of an effect and then its critical effect (Ecrit): from Eq. (3) the limit value (Ecrit) can be expressed as:
EX ⇔ Ecrit = tcrit ⋅(SE)
(4)
In the present work for the evaluation of SE and Ecrit two Table 5 Rankits to draw a half- normal plot for the N ¼ 8 screening design. (Effect 1 indicates the smallest effect). Effect
Rankit
1 2 3 4 5 6 7
0.09 0.27 0.46 0.66 0.9 1.21 1.71
Fig. 1. Half-normal plot for the normalized effects of Table 4, with the identification of the critical effects ME e SME.
different models have been applied: Lenth's (1989) model and Dong's (1993) algorithm. In both, the median of the absolute effects is used as a first estimation (s0) of the standard error (SE) associated to the factors:
S0 = 1.5median bi
(5)
where bi is the value of the effect i. Lenth's method Starting from s0 a pseudo standard error (PSE) is derived:
PSE = 1.5median bi
(6)
With |bi| o 2.5s0. PSE value is used to calculate a margin error (ME) and simultaneous margin error (SME).
ME = t(1 − α /2, df ) PSE SME = t ⎛⎜1 − α*/2, df ⎞⎟ PSE ⎝
⎠
(7)
(8)
Where df1 ¼m/3 and m is the number of factors b. α n is the Bonferroni adjusted significance level (Haaland and O’Connell, 1995). According to Lenth (1989) when 7 factors are considered with a confidence level of 97.5% (α ¼0.05), Eqs. ((7) and 8) become:
ME = 2.297·PSE SME = 4.867· PSE where PSE is computed according to Eq. (6). The ME is a statistically valid criterion for significant testing when only one effect is to be tested. When multiple effects are tested the chance for non-significant effects that exceed the ME increases (Nijhuis et al., 1999). To counterbalance these events a second limit (SME) is defined. Practically the use of only ME as a limit increases the chance for false positive led to consider (with 2.5% of probability) a factor as significant when really it is not. Instead, the use of the only SME largely increase the possibility to consider non-significant an effect which is significant (false negative). Since, according to some authors (Haaland and O’Connell, 1995) the Lenth's procedure results in an overly conservative test, due to the use of a reduction number of degrees of freedom (df¼ m/3) to derive critical values (see formulas (7) and (8)) so to calculate 1
df¼ degrees of freedom
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F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
critical values a further method was also used: the Dong's method. This method, illustrated in the following, used a number of degrees of freedom equal to m instead of m/3. Dong's method In Dong's method the PSE is substituted by the standard error s1 derived as:
s1 =
1 m
∑ bi2
(9)
For all bi o 2.5s0, where m is the number of the factor smaller than 2.5s0. In this case m ¼6.
ME = t(1 − α /2, df ) s1
(10)
SME = t ⎛⎜1 − α*/2, df ⎞⎟ s1 ⎝
⎠
(11)
where df¼m and α is the Bonferroni adjusted significance level (Haaland and O’Connell, 1995). Assuming α ¼0.05 and using for Student's t the tabulated values, Eqs. (10) and (11) can be written as: n
ME = 2.45⋅s1 SME = 3.98⋅s1 The combination of Dong's method with Lenth's PSE test can represent a good solution for the evaluation of data. In Table 6 and Fig. 1 the values of ME and SME calculated with both methods starting from factors given in Table 1, were reported. Looking at Fig. 1 it can be observed that only b1 exceeds ME and SME values evaluated upon both the Lenth's model and Dong's algorithm: this means that in the etching process the temperature of the etchant solution (b1) is the only relevant factor.
4. Influence of factors on the tracks structure Due to the mechanism of tracks formation, the importance of the temperature factor is expected. Indeed both bulk and track etch rates (Vb and Vt, respectively) increase exponentially with the temperature (Nikezic and Yu, 2004) and track development is governed by the ratio V ¼Vt/Vb. The track formation is not possible if V is smaller than or equal to 1. The temperature effect can be further confirmed by analyzing the radius of tracks. The major (D) and the minor (d) axes of the track opening are given by (Nikezic and Yu, 2004):
D = 2h
V2 − 1 V sin θ + 1
d = 2h
(12)
V sin θ − 1 V sin θ + 1
(13)
h = vb ⋅t
(14)
where h is the removed layer during the etching process, t is the etching time and θ is the angle between the direction of the incident particle and the surface of the detector. Looking at the data related to experiments nos. 4, 6 and 8, Table 6 ME and SME values calculated with Dong's and Lenth's methods starting from factor.
ME SME
Lenth
Dong
0.1255 0.2660
0.1190 0.1934
Fig. 2. Major axe size distributions for etched tracks of experiments nos. 4 and 6 (a) and nos. 4 and 8 (b).
where the etching temperature and the etchant concentration varied, the distribution of the major axe of tracks (D) has been compared as shown in Fig. 2. The major axe size distribution is well fitted by a Gaussian curve (using OriginPro 9.1 by OriginLab USA) and the maximum of the distribution (Xc) for each experiment is reported in Table 7. In Fig. 2a it is shown that the variation of the etchant concentration (exp. nos. 4 and 6) does not influence the major axe size frequency distribution. In fact the two curves show the same tracks dimensions distributions with a maximum value (Xc) around 24 μm. Conversely, the decreasing of the etching temperature (comparing experiment no. 8–4) led to the formation of tracks with a major axe around 15 μm (see Fig. 2b). It is quite evident that the temperature represents the most important factor on the track dimensions. Moreover analyzing the results obtained in the same experiments in terms of average track density (see Table 3), it can be observed that an increase of the etchant concentration do not influence neither the average track density (E 4%) neither the track structure (both curves have the same Xc). While a variation of the etching temperature determine effects as in terms of average track density (E 39%) as in terms of tracks morphology (as Xc). For a factor considered relevant (b1 in our case), it is possible to estimate in which interval the factor effect is not significant. The limit values of the interval can be assessed as (Vander Heyden et al., 2001):
X0 ±
X + − X − Ecrit 2 Ex
(15)
Assuming for Ecrit the value of ME and SME estimated by the Dong's method, and applying Eq. (15) to factor b1, the interval in which the temperature of the KOH solution have no significant effect is 74 °C o b1 o76 °C. Table 7 Maximum of particle major axes Gaussian distribution for selected experiments. Also some etching parameters were reported. Exp. no.
Xc (μm)
b1 (°C)
b2 (min)
b3 (N)
4 6 8
23.9871 23.9886 15.3714
77 77 73
268 268 268
5.8 6.2 5.8
F. Leonardi et al. / Applied Radiation and Isotopes 102 (2015) 93–97
5. Conclusions In the present work, the validation of a laboratory-developed method was focused. In particular, the etching process of CR39 plastics detectors (SSNTD) exposed to radon and its progeny has been analyzed. A robustness evaluation was performed as an important step of the validation process. The robustness study of the SSNTD etching method (KOH solution 6.0 N, 75 °C, 270 min) considered several factors such as etching time, etchant temperature and concentration, and treatment in CH3COOH solution to stop the etching process. The robustness evaluation of an experimental method performed using Youden procedure has been well applied to study other analytical methods, (Ragonese et al., 2000, Karageorgou and Samanidou, 2014). The results evidenced that the etching method can be considered robust: the only critical factor is the etching solution's temperature. Only a variability of 71 °C with respect to the reference values is admitted, then a strict control about stability of temperature during the whole process is needed. The results achieved by the application of mathematical models have been further confirmed by the analysis of the distribution of the main axis of tracks, etched in different condition: in fact a small increase of the temperature led to an increase of the dimension of track axes, while small variations of the etchant concentration do not result in any significant effect.
References Caresana, M., Ferrarini, M., Garlati, L., Parravicini A, A., 2010. About ageing and fading of Cr-39 PADC track detectors used as air radon concentration measurement devices. Radiat. Meas. 45, 183–189. D’Alessandro, M., Leonardi, F., Tonnarini, S., Trevisi, R., Veschetti, M., 2010. Development of a framework of quality assurance practices for a radon passive dosemeter service. J. Radiol. Prot. 30 (2), 149–159. Daniel, C., 1959. Use of half-normal plot in interpreting factorial two-level
97
experiment. Technometrics 1, 311–341. Dong, F., 1993. On the identification of active contrasts in unreplicated fractional factorials. Stat. Sin. 3, 209–217. Haaland, Perry D., O’Connell, M.A., 1995. Inference for Effect-Saturated Fractional Factorials. Technometrics 37 (1), 82–93. http://dx.doi.org/10.1080/ 00401706.1995.10485890. Hermsdorf, D., Hunger, M., Starke, S., Weickert, F., 2007. Measurement of bulk etch rates for poly-allyl-diglycol carbonate (PADC) and cellulose nitrate in a broad range of concentration and temperature of NaOH etching solution. Radiat. Meas. 42 (1), 1–7. http://dx.doi.org/10.1016/j.radmeas.2006.06.009. ISO/IEC 17025, 2005. General requirements for the competence of testing and calibration laboratories. edited by International Standard. Karageorgou, E., Samanidou, V., 2014. Youden test application in robustness assays during method validation. J. Chromatogr. A 1353 (0), 131–139. http://dx.doi.org/ 10.1016/j.chroma.2014.01.050. Lenth, R.V., 1989. Quick and easy analysis of unreplicated factorials. Technometrics 31, 469–473. Miller, J.C., Miller, J.N., 1993. Statistic for Analytical Chemistry. New York. Mishra, R., Orlando, C., Tommasino, L., Tonnarini, S., Trevisi, R., 2005. A better understanding of the background of CR-39 detectors. Radiat. Meas. 40 (2–6), 325–328. Nijhuis, A., van der Knaap, H.C.M., de Jong, S., Vandeginste, B.G.M., 1999. Strategy for ruggedness tests in chromatographic method validation. Anal. Chim. Acta 391 (2), 187–202. http://dx.doi.org/10.1016/S0003-2670(99)00113-0. Nikezic, D., Yu, K.N., 2004. Formation and growth of tracks in nuclear track materials. Mater. Sci. Eng. R46, 51–123. Orlando, C., Orlando, P., Patrizii, L., Tommasino, L., Tonnarini, S., Trevisi, R., Viola, P., 2002. A passive radon dosemeter suitable for workplaces. Radiat. Prot. Dosim. 102, 163. Plackett, R.L., Burman, J.P., 1946. The design of optimum multifactorials experiments. Biometrika 33 (4), 305–325. Ragonese, R., Mulholland, M., Kalman, J., 2000. Full and fractionated experimental designs for robustness testing in the high-performance liquid chromatographic analysis of codeine phosphate, pseudoephedrine hydrochloride and chlorpheniramine maleate in a pharmaceutical preparation. J. Chromatogr. A 870 (1–2), 45–51. http://dx.doi.org/10.1016/S0021-9673(99)00972-3. Vander Heyden, Y., Nijhuis, A., Smeyers-Verbekea, J., Vandeginsteb, B.G.M., Massarta, D.L., 2001. Guidance for robustness/ruggedness tests in method validation. J. Pharm. Biomed. Anal. 24 (5–6), 723–753. http://dx.doi.org/10.1016/ S0731-7085(00)00529-X. Youden, W.J., Steiner, E.H., 1975. Statistical manual of the Association of Official Analytical Chemists. Association of Official Analytical Chemists (AOAC), Arlington VA, pp. 33–36. Youden, W.J., 1972. Statistical Technique for Collaborative Tests. Association of Official Analytical Chemists (AOAC), Washington.
