There always exist nonzero inspection errors whether inspectors are humans or automatic inspection machines. Inspection errors can be categorized by two types, type I error and type II error, and they can be regarded as either a constant or a random variable. Under the assumption that two types of random inspection errors are distributed with the “uniform” distribution on a half-open interval starting from zero, it was proved that inspectors overestimate any given fraction defective with the probability more than 50%, if and only if the given fraction defective is smaller than a critical value, which depends upon only the ratio of a type II error over a type I error. In addition, it was also proved that the probability of overestimation approaches one hundred percent as a given fraction defective approaches zero. If these critical phenomena hold true for any error distribution, then it might have great economic impact on commercial inspection plans due to the unfair overestimation and the recent trend of decreasing fraction defectives in industry. In this paper, we deal with the same overestimation problem, but assume a “symmetrical triangular” distribution expecting better results since our triangular distribution is closer to a normal distribution than the uniform distribution. It turns out that the overestimation phenomenon still holds true even for the triangular error distribution.

This study investigated the effect of high concentration of free ammonia on microalgal growth and substrate removal by applying real wastewater nitrogen ratio. To test of this, the conditions of free ammonia 1, 3, 6, 9, 12, 15 mg-N/L are compared. After 3 days of incubation, algal growth of Chlorella vulgaris and carbon removal rate are respectively lower in the reactors of FA 12, 15 mg-N/L compared to the others. This indicates that the high concentration of free ammonia, in this case, above 12 mg-N/L, has negative effect on algal growth and metabolic activity. Also, high concentration of free ammonia causes the proton imbalance, ammonium accumulation in algae and has toxicity for these reasons. So, we have to consider free ammonia in applying the microalgae to wastewater treatment system by the way of diluting wastewater or controlling pH and temperature.

This study investigated the effect of NH4 + concentrations on microalgae growth by appling mixotrophic microalgae chlorella vulgaris in order to treat anaerobic digested food waste leachate. The growth rate and final microalgae growth were an order as 400 > 100 > 800 > 1300 mg-N/L. As results, The growth rate and final growth of microalgae were highest at ammonia concentration of 400 mg-N/L, On the other hand microalgae growth was inhibited when ammonia concentrations were over 800 mg-N/L. high concentrations of nitrogen over 800 mg-N/L interrupt the growth of microalgae. All of nitrogen and phosphorus were removed by microalgae at the ammonia concentration of 100~400 mg-N/L. In addition, when ammonia concentration was over 800 mg-N/L, the removal of nitrogen and phosphorus was limited mainly due to the microalgae growth limit. It was possible to treat anaerobic digested food waste leachate with mixotrophic microalgae when the ammonia concentration was controlled below 400 mg-N/L.