Abstract
We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.
Highlights
Photovoltaics (PV) contributes substantially to the power supply in many developed countries
By analysing real outdoor measurements from electroluminescence imaging, we demonstrate, firstly, that the spatial correlations and local clusters arise in such PV data and, secondly, that the normality assumptions imposed by classical linear mixed models are violated (Section 7), providing empirical justification for our approach
The proposed approach allows for stratification, various forms of correlations, such as spatial correlations, correlations due to random effects or serial correlations, and non-normal measurement errors
Summary
Photovoltaics (PV) contributes substantially to the power supply in many developed countries. Various other site-specific factors may affect response variables related to quality and reliability issues, for example, the exposition to salt or snow, the type of the electrical connectors or the direct current (DC) to alternating current (AC) converter, called solar inverter Another issue is that quality measurements taken at PV modules may be affected by spatial correlations. We develop a methodology for sampling and statistical analysis, which allows for such correlations Those considerations, as well as the fact that collecting measurements from PV modules randomly spread over a relatively large area, generate much higher sampling costs than taking measurements from modules that are located side by side.
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