Weighted erlang and lomax distributions: Their properties and applications to water quality inspection

Abstract

Two new families of weighted Erlang and Lomax probability distributions are developed. Various properties including the moments and the bias in the estimated mean of a weighted distribution are derived. As applications of these distributions, time truncated acceptance sampling plans are designed to obtain the minimum sample size and the acceptance number for un-weighted and weighted distributions, where various pre-assigned producer��s and consumer��s risks, various ratios of true mean to the specified mean life, and various test termination time multipliers are considered. A real data set is analyzed to illustrate the proposed time-truncated sampling plan. ? 2017 KIIE.