Reducing sample size by tightening test conditions

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 100q% of a population meets a tighter threshold Δ/γ, then at least 100p% 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.

A Contemplation on Electricity Meters In-Service Surveillance Assisted by Remote Error Monitoring

“…In [15], authors demonstrate how this type of sampling plan can be built by adapting binomial reliability models and still applying ISO standards. The future reliability prediction requires larger samples [15] or tightening of the test for conformance conditions [16]. Authors acknowledge the expectation of promising benefits from remote monitoring of meters in terms of gaining more information about real reliability models that are used in the sampling plan selection [16].…”

Hypothesis-based acceptance sampling for modules F and F1 of the European Measuring Instruments Directive

“…At present, the MID prescribes acceptance sampling by attribute, such that alternative approaches are beyond the scope here. However, more efficient sampling plans can be obtained, for example, by distribution-based attribute sampling [14,15], variable sampling [16], series of lots [10], sequential sampling, by using prior knowledge [17,18], applying rectifying inspection [6] or statistical process control [19,20].…”