Renewal Rate of Filament Lamps: Theory and Experiment
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Renewal Rate of Filament Lamps: Theory and Experiment V. J. Menon Æ D. C. Agrawal
Submitted: 21 February 2007 / in revised form: 9 September 2007 / Published online: 2 November 2007 ASM International 2007
Abstract We calculate the renewal rate of fused lamps in an organization having large installation of filament lamps. This is achieved by using the standard mortality curve over the specified fractions of the half-life and setting up an algebraic relation for the renewed fraction at successive stages. The procedure for data analysis is described in detail for an actual experiment performed by us. Keywords Tungsten Filament lamps Large installation Failure Mortality curve Renewal rate Theory Experiment
Introduction In a clearly written paper, Leff [1] vividly described various operating features of incandescent filament lamps and also emphasized the fact that their failure is historydependent. This statement was corroborated further by us [2] by showing numerically that the half-life, average life, and most probable life are almost the same for a given type of bulb. Also, experimental mortality curves for commercial bulbs are reported in an engineering handbook [3], whose heuristic form was proposed by Leff and derived rigorously by us [4] using the laws of mathematical statistics. While continuing our research in this area, the following question occurred to us: ‘‘If an organization has a V. J. Menon Department of Physics, Banaras Hindu University, Varanasi 221 005, India D. C. Agrawal (&) Department of Farm Engineering, Banaras Hindu University, Varanasi 221 005, India e-mail: [email protected]
large installation of fresh lamps kept under continuous operation, then what is the mean renewal rate of fused bulbs after a periodic (or repeated) elapse of a chosen interval of time hereafter called the slab length?’’ We feel that a clear answer to this question is important because of three reasons: (i) A theoretical answer to the said question will give good training to physicists and engineers in the use of the parameterized lamp mortality curve [4]. (ii) Any organization (e.g., Blackpool, Lancashire) would like to have the aforementioned information because if the fused bulbs are periodically replaced by new ones then the installation will have all the requisite space illuminated. (iii) A knowledge of the numerical values as well as pictorial graphs of the renewal rate at various stages can be used by an organization to strike a balance between the replacement cost and quality of illuminance needed. The aim of the present paper is to address this problem algebraically, numerically, and experimentally. Theory Preliminaries It is known that many factors inherent in lamp material/ manufacture make it impossible to have each individual bulb operate for exactly the life for which it was designed. Rather, as the evaporation of tungsten atoms proceeds and the hot filament gets thinner the lamp can fail in a statistical manner in accordance with th
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