Jay Schaffer

Number of Replications Required in Control Chart Monte Carlo Simulation Studies

Monte Carlo simulations have been used extensively in studying the performance of control charts. Researchers have used various numbers of replications in their studies, but almost none of them provided justifications for the number of replications used. Currently, there are no empirically based recommendations regarding the required number of replications to ensure accurate results. This research examined six recently published studies to develop recommendations for the minimum number of replications necessary to reproduce the reported results within a specified degree of accuracy. The results of this study indicated that using 10,000 replications was unnecessarily large and a smaller number of replications could be used to reproduce the target ARLs within the 2% error bands satisfying the modified Mundfroms criteria. In many cases, only 5,000 replications or fewer were required. In general, the number of replications required to reproduce the target ARL decreased as the shift size increased. In addition, the results of this study provide general recommendations for the required number of replications to use in future SPC simulation studies.

A Double Multivariate Exponentially Weighted Moving Average (dMEWMA) Control Chart for a Process Location Monitoring

A new control scheme, dMEWMA, for detecting shifts in the mean vector of multivariately normally distributed quality characteristics is presented. It is shown that the ARL performance of dMEWMA depends on the mean and variance-covariance matricies only through the non-centrality parameter value. Through Monte Carlo simulations, the performance of dMEWMA for detecting various shifts is compared to the competing control schemes, MEWMA and Hotellings χ2. It is concluded that dMEWMA outperforms MEWMA and Hotellings χ2 control schemes for small and larger shifts. In comparison to MEWMA control schemes, dMEWMA schemes are optimal for larger values of the smoothing parameter λ and perform much better for very small shifts in the process mean. Finally, an example to illustrate the construction of the dMEWMA control scheme is introduced.

Doping in Two Elite Athletics Competitions Assessed by Randomized-Response Surveys

BackgroundDoping in sports compromises fair play and endangers health. To deter doping among elite athletes, the World Anti-Doping Agency (WADA) oversees testing of several hundred thousand athletic blood and urine samples annually, of which 1–2% test positive. Measures using the Athlete Biological Passport suggest a higher mean prevalence of about 14% positive tests. Biological testing, however, likely fails to detect many cutting-edge doping techniques, and thus the true prevalence of doping remains unknown.MethodsWe surveyed 2167 athletes at two sporting events: the 13th International Association of Athletics Federations Word Championships in Athletics (WCA) in Daegu, South Korea in August 2011 and the 12th Quadrennial Pan-Arab Games (PAG) in Doha, Qatar in December 2011. To estimate the prevalence of doping, we utilized a “randomized response technique,” which guarantees anonymity for individuals when answering a sensitive question. We also administered a control question at PAG assessing past-year use of supplements.ResultsThe estimated prevalence of past-year doping was 43.6% (95% confidence interval 39.4–47.9) at WCA and 57.1% (52.4–61.8) at PAG. The estimated prevalence of past-year supplement use at PAG was 70.1% (65.6–74.7%). Sensitivity analyses, assessing the robustness of these estimates under numerous hypothetical scenarios of intentional or unintentional noncompliance by respondents, suggested that we were unlikely to have overestimated the true prevalence of doping.ConclusionsDoping appears remarkably widespread among elite athletes, and remains largely unchecked despite current biological testing. The survey technique presented here will allow future investigators to generate continued reference estimates of the prevalence of doping.