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Reducing sample size by tightening test conditions
Author(s) -
Klauenberg Katy,
Kramer Rainer,
Kroner Corinna,
Rose Jürgen,
Elster Clemens
Publication year - 2018
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2256
Subject(s) - reliability (semiconductor) , reliability engineering , sample (material) , sampling (signal processing) , sample size determination , population , statistics , computer science , confidence interval , measure (data warehouse) , engineering , mathematics , data mining , telecommunications , power (physics) , chemistry , physics , demography , chromatography , quantum mechanics , detector , sociology
Abstract The inspection of measurement devices according to statistical sampling plans allows conclusions to be drawn about the reliability of a whole population of devices. However, confirming high reliability levels requires large sample sizes and is thus expensive or even infeasible. For example, a reliability of 99.5% can only be guaranteed with 90% confidence by inspecting each item in a population of 280 (see ISO 2859‐2). When reliability is judged by not exceeding a certain threshold, this research provides a convenient solution allowing considerably more efficient sampling plans. Under certain distributional assumptions, in particular, we have proved that if 100 q % of a population meets a tighter threshold Δ/ γ , then at least 100 p % of the population meets threshold Δ(with p > q , γ >1). The importance and effect of different distributional assumptions are demonstrated and relevant scenarios for the parameters ( p , q , γ ) presented. Verifying that a smaller portion of devices comply requires smaller sample sizes. Costs may thus decrease when more stringent specifications are verified. For example, up to 98% of utility meters in Germany are required to measure correctly at inspections, to ensure a reliability of 95% in the future. Instead of applying costly sampling plans to meters in use to demonstrate these high reliability levels, this research enables the sample size to be reduced, eg, by half.