2.1

Specimen preparation

For this investigation, 200 caries-free human molars were collected and directly cleaned. Consequently, all teeth were stored in 0.5% chloramine T solution (Sigma–Aldrich, Seelze, Germany) at room temperature for a maximum of 7 days. Afterwards, they were stored in distilled water for a maximum of 180 days at 5 °C until the bond strength tests.

In order to achieve flat surfaces, the buccal surfaces of the teeth were leveled parallel to the tooth axis using a polishing machine (LaboPol-21, Struers, Bellerup, Denmark) with SIC paper P400 (ScanDia, Hagen, Germany). The teeth were then embedded in self-curing acrylic resin (ScandiQuick, ScanDia) and ground finished with carbide polishing paper (P500, ScanDia) until a sufficient bond area of 4 mm × 4 mm dentin surface was exposed.

The embedded teeth ( N = 200, n = 50 per cement) were then randomly divided into 4 cement groups (VAN, PAN, RXU, GCM). Prior to the application of the resin cement systems, the dentin test area was ground with the fine polishing paper P500 under water-cooling. While the self-adhesive cements did not require dentin conditioning, the corresponding adhesive systems of the conventional resin cements were applied to the dentin prior to cementation according to the manufacturer instructions. The specimen’s stepwise preparation is shown in Fig. 1 a–h . Subsequently, the resin cements were activated and placed in an acrylic cylinder (inner diameter: 2.9 mm) that was pressed onto the dentin surface by a holding device ( Fig. 1 a). In order to achieve homogeneous dispersion of the cement in the acrylic cylinder, a hexagonal steel screw with an outer diameter of 2.8 mm was inserted parallel to the long axis of the acrylic cylinder in its center ( Fig. 1 b). A load of 100 g was applied on the screw ( Fig. 1 c) and the excess cement was removed using microbrushes ( Fig. 1 d). This procedure allowed resin cement thickness in non-luted state of 0.5 mm in all specimens. VAN, RXU and GCM were dual-polymerized ( Fig. 1 e) and PAN was chemically polymerized.

Production process of the specimens. (A) Acrylic cylinder pressed on the dentin surface; (B) cement put in the acrylic cylinder; (C) steel screw put into the acrylic cylinder; (D) removed of excess cement; (E) cement luted; (F) finished specimen; (G) specimen in sample’s holder; (H) test design of shear bond strength.

2.2

Shear bond strength test

The prepared bond strength specimens ( Fig. 1 f) were analyzed in the Universal Testing Machine (1 mm/min; Zwick/Roell Z010, Zwick, Ulm, Germany). The specimens were positioned in the sample holder of the testing machine with the tooth surface parallel to the chisel-shaped loading piston loading with a width of 1 mm ( Fig. 1 g) and then loaded until fracture ( Fig. 1 h). The bond strength (MPa) was calculated using the following formula: force to failure (N)/bonding area (mm ² ).

2.3

Statistical methods

The cumulative distribution function for the three-parameter Weibull distribution is defined by:

where s is called scale or characteristic value, m indicates the shape or Weibull modulus and s ₀ denotes the threshold (location, minimum life, origin, guaranteed minimum life, shift). G ( x ) is usually interpreted as the probability of fracture for a test specimen and “ x ” is the shear bond strength of the specimen tested. If s ₀ is positive, it provides a guaranteed failure free period from 0 to s ₀ . A non-zero threshold parameter should not be used unless it is anchored in the physics of the failure process. Frequently the two-parameter Weibull is considered for small sample sizes. It is obtained by assuming that the threshold is equal to zero ( s ₀ = 0). In such a case the following probability density function:

is obtained. Frequently the Weibull statistic is computed based on the statistical approach .

Although the parameters of the underlying Weibull distribution are denoted by s and m their estimates obtained from the analysis of the data are identified by “hats” leading to ˆs
s ˆ
and ˆm
m ˆ
respectively. Note that at least five different parameterizations of the Weibull distribution have been proposed .

2.4

Least squares estimates (LS)

The application of the LS approach to the parameters of the Weibull distribution is justified by the following property of the Weibull cumulative distribution function G ( x ) for s ₀ = 0 with log denoting the logarithm with basis e :

In order to compute LS, in each sample group, ˆGi
G ˆ i
has to be the estimated for each observation . After ordering the data from the smallest to the largest value the i th position is considered to be a representative population percentage near to which the i th ordered observation falls. After taking the logarithm of the bond strength ( X -axis) it is plotted against log(−log(1−ˆGi))
log ( − log ( 1 − G ˆ i ) )
on the Y -axis and the linear regression fit of the scattered points is computed by means of LS with the sum of squares of the vertical distances being minimized. In other words log(−log(1−ˆGi))
log ( − log ( 1 − G ˆ i ) )
is regressed onto log( x ). Due to the equation stated above, the estimate of the modulus ˆm
m ˆ
of the assumed underlying Weibull distribution is the slope of the linear regression. In order to obtain a value of ˆGi
G ˆ i
McCabe and Carrick suggested that the specimens within one test group should be ranked by calling the weakest specimen as “rank 1” and the strongest as “rank n ”. The probability of failure ˆGi
G ˆ i
for each specimen from a group containing n specimens is given by

where R _i is the ranking number of the specimen. This way of computing ˆGi
G ˆ i
is frequently called mean rank and can be also found in MINITAB and SPSS under differing names, specifically, Herd–Johnson and Van der Waerden respectively.

Many alternative methods for estimating ˆGi
G ˆ i
in practical applications were suggested . In MINITAB software, several options such as median rank, modified Kaplan–Meier, and Kaplan–Meier (Hazen) are provided for ˆGi
G ˆ i
estimation. Conversely, in SPSS Rankit, Tukey and Blom choices are used. Abernethy recommends median rank:

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