Reliability experiments provide important information regarding the life of a product, including how various factors affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling, which represents a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches, leading to a design involving blocks. This article proposes a method using Weibull regression for analyzing reliability experiments with random blocks and subsampling. An illustration of the method is provided.

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BackgroundA scaled logit model has previously been proposed to quantify the relationship between an immunological assay and protection from disease, and has been applied in a number of settings. The probability of disease was modelled as a function of the probability of exposure, which was assumed to be fixed, and of protection, which was assumed to increase smoothly with the value of the assay.MethodsSome extensions are here investigated. Alternative functions to represent the protection curve are explored, applications to case-cohort designs are evaluated, and approaches to variance estimation compared. The steepness of the protection curve must sometimes be bounded to achieve convergence and methods for doing so are outlined. Criteria for evaluating the fit of models are proposed and approaches to assessing the utility of results suggested. Models are evaluated by application to sixteen datasets from vaccine clinical trials.ResultsAlternative protection curve functions improved model evaluation criteria for every dataset. Standard errors based on the observed information were found to be unreliable; bootstrap estimates of precision were to be preferred. In most instances, case-cohort designs resulted in little loss of precision. Some results achieved suggested measures for utility.ConclusionsThe original scaled logit model can be improved upon. Evaluation criteria permit well-fitting models and useful results to be identified. The proposed methods provide a comprehensive set of tools for quantifying the relationship between immunological assays and protection from disease.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-015-0096-9) contains supplementary material, which is available to authorized users.