A Nonparametric Phase I Control Chart for Individual Observations Based on Empirical Likelihood Ratio

One common challenge in nonmanufacturing control chart applications is that many of the nonmanufacturing quality characteristics are not normally distributed. In these applications, normal transformation of the observations is certainly feasible; however, it will be done at the expense of the interpretability of the analysis that is particularly important to control chart users in nonmanufacturing industries. Most of the existing nonparametric control charts are designed for Phase II monitoring. Little has been done in developing nonparametric Phase I control charts especially for individual observations that are prevalent in nonmanufacturing applications. In this work, we propose a new nonparametric Phase I control chart for monitoring the location parameter whose construction is essentially based on the empirical likelihood ratio test. The performance of the proposed chart, in terms of the signal probability, compares favorably with the recently developed charts for individual observations. A nonmanufacturing example is included in which the proposed chart and the other competing charts are applied and compared.