Applications of the Sojourn - Time Problem to Reliability
The sojourn-time problem of Takáes can be applied to reliability theory. This note reviews Takács' results and applies them to redundant systems, cumulative damage, and a system under non-homogeneous operating conditions.
A Method for Predicting System Downtime
A system whose components, upon failure, are repaired or replaced is considered. Only two system states, the ``operating'' state and the ``failed'' state, are distinguished. The system is by defined a reliability network and by the failure rate and repair rate of each component. The time to failure and the time to repair of the components are assumed to be exponentially distributed. A criterion of system worth is the random variable ``downtime,'' denoted by D(t), which is defined as the time the system is down during the time interval (0, t). The following questions are answered: 1) What is the distribution function of D(t)? 2) What are the mean and the variance of D(t)? 3) What is the asymptotic behavior of D(t) for large values of t? 4) How can one make approximate probability statements about D(t)? It is shown that the beta distribution is a suitable approximation for the conditional distribution of D(t)/t, given that at least one failure has occurred, and that for t greater than 20 mean failure times the distribution of D(t) is practically normal.
Parboiled rice effluent: A wastewater niche for microalgae and cyanobacteria with growth coupled to comprehensive remediation and phosphorus biofertilization
Abstract The potential of microalgae and cyanobacteria for bioremediation of wastewater by nutrient uptake combined with simultaneous biomass production is a well recognized perception of today's world. The present study illustrates the treatment of a highly polluted wastewater generated during parboiling of paddy in rice mill industries, widely operational in developing countries where rice is the staple food crop, with the help of microalgal and cyanobacterial isolates capable of growing at high rates in parboiled rice mill effluent (RME). This endeavor leads to comprehensive bioremediation of the said effluent and subsequent use of the harvested biomass as slow release phosphorus biofertilizers and the treated effluent for crop irrigation. The RME-acclimatized algal consortium demonstrated highest growth in terms of fresh weight and greatest remediation efficiency at the end of 36 days' treatment of RME, with 93.9% phosphorus and 100% ammonia-nitrogen removal, 98.7%, 91.6% and 93.5% reduction in biological oxygen demand, chemical oxygen demand and total dissolved solid, respectively, and an increment of 186 ± 0.3 mg L − 1 dissolved oxygen, bringing down the pollutants level well below the discharge limits suggested by Central Pollution Control Board, India. Additionally, microalgae in the consortium aggregated in clumps spontaneously in presence of the filaments of Phormidium sp. facilitating easy harvest. The RME-acclimatized algal consortium demonstrated highest accumulation of polyphosphate (poly-P) (0.76 ± 0.01% of dry weight) as well as highest release of phosphorus in non-sterile soil emphasizing the essential role of soil phosphorus solubilizing organisms to leach soluble phosphorus from the insoluble poly-P present in the biomass. The rice seedlings watered with treated RME also showed improved growth effect on shoot height and leaf width. The study results establish the suitability of RME as an excellent growth media for microalgae and cyanobacteria.