Based on the geometric analysis of the problem in hand, an algorithm was developed and implemented in C programming language. The purpose of this program was to readily and accurately compute the following maximum positioning errors, permissible by the different sleeve/drill/guide properties (Fig. 2):

1. Deviation of the implant axis in degrees,

2. Error at the neck in mm,

2. Error at the apex in mm,

4. Vertical error at the apex in mm.

These computations were based on the four parameters: (1) implant length, (2) sleeve length, (3) clearance and (4) offset (Fig. 1), and the results were tabulated in reference tables. The implant length and the offset were added together to form a new variable termed total length used exclusively on the calculations related to the error at the apex.

The variability of the parameters was constrained to reflect probable clinical conditions: (1) implant length between 8 and 18 mm, in 1 mm steps; (2) sleeve length between 4 and 7 mm, in 1 mm steps; (3) clearance between 50 and 410 μm, in 30 μm steps; and (4) offset values between 6 and 17 mm, in 1 mm steps. The minimum distance between the bottom of the metal sleeve (towards the bone) and the neck of the implant was set at the considered clinically appropriate distance of 2 mm.

Multiple regression was employed twice, with three independent variables each time to separate the effects of clearance, total length, sleeve length and offset on the values of the error at the apex and the error at the neck.

Microsoft® Excel 2016 32 bit was used for the statistical analysis. Significance level was set to p < 0.05.

All the values in the reference tables were rounded to one significant digit after the decimal point.