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.
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