Some statistical considerations regarding the testing of LIP cigarettes
Supported by Lyapunov's Central Limit Theorem the assumption that measured values are normally distributed is generally made without further consideration. However, for LIP cigarettes this assumption does not hold as is demonstrated in two examples.First, from theoretical considerations it can be shown that the position of the bands on LIP cigarettes is uniformly distributed. This could also be confirmed by performing a statistical test on the band position measured on 1000 cigarettes.By evaluating a flow model of an LIP cigarette the influence of the band position on the draw resistance and the degree of filter ventilation are calculated. The results show, that the band position causes variations of about 3% in draw resistance and degree of filter ventilation. The probability distributions of draw resistance and degree of filter ventilation are also calculated by simulation, based on the assumption that the band position is the only source of variation. A comparison with experimental data shows that depending on the cigarette design a statistically significant deviation from a normal distribution can be proved for the open draw resistance but not for the degree of filter ventilation.As a second example for non-normal probability distributions, arguments are given that the self-extinguishment of non-banded LIP cigarettes represents a Poisson process. As a consequence the residual length of an extinguished LIP cigarette is shown to be exponentially distributed and closed form expressions for mean and standard deviation of the residual length are derived. A comparison of previously published data with the theoretical results on the mean residual length and on its standard deviation for LIP cigarettes with different ASTM pass rates shows exceptionally good quantitative and qualitative agreement. This demonstrates that there is also a theoretical justification for using residual lengths as an additional indicator for the ignition strength of cigarettes.