When improving the quality of goods and services, almost any statistics software will capture the “low-hanging fruit”. Attaining continuous improvement is more difficult. It is then that software designed for textbook problems needs to be replaced with other tools.
OutliersEveryone who analyzes data has been faced with the problem of determining whether or not an apparent abnormality should be left in the data set or removed. The implications of wrongly making either decision can be serious. While no statistical technique can answer that question with certainty, the STATGRAPHICS Centurion Outlier Identification procedure provides important tools to deal with outliers:
(1) Grubbs’, Dixon’s, and Tukey’s tests examine the most extreme values to determine whether they come from the same population as the rest.
(2) Winsorized statistics adjust the sample mean and standard deviation for the possible presence of outliers.
(3) Nonparametric statistical procedures resist outliers by basing their analysis on ranks or minimizing absolute rather than squared deviations.
Design of Experiments for AttributesDesigned experiments are an important tool for achieving Six Sigma quality. While much attention is paid to developing a good design, the selection of suitable analytic tools often relies on an assumption of normality, even when such as assumption is clearly violated.
For attribute data in the form of counts or proportions, STATGRAPHICS Centurion provides several important procedures:
• Logistic and probit analysis for proportions.
• Poisson and negative binomial regression for counts.
STATGRAPHICS Centurion provides built-in transformations such as the arc sine square root to normalize proportions.
Non-Normal DataSince all data do not follow a Gaussian distribution, STATGRAPHICS Centurion will automatically fit up to 45 probability distributions and rank them according to goodness-of-fit.
Process Capability Analyses and Control Charts will adapt to any distribution, adjusting indices and control limits.
AutocorrelationWith today’s automated data collection systems, samples are often collected at closely spaced increments of time. Any sort of process dynamics introduces correlations into successive measurements, which causes havoc with standard control charts that assume independence between successive samples.
A good remedy is to use an ARIMA control chart based on a parametric time series model. ARIMA models capture the dynamics of a process by expressing the current observation as a function of previous observations and random shocks to the system. Uncoupling the dynamics of the process allows one to separate current observations from those in the past.
ConclusionWhen dealing with real-world data, analysts must be prepared to handle violations of standard assumptions. STATGRAPHICS Centurion provides an extensive toolbox designed to handle the types of data often encountered in practice. In addition, since many practitioners are not professional statisticians, tools such as the StatWizard™ and StatAdvisor™ are available to assist in selecting and interpreting the statistical techniques. When combined with STATGRAPHICS’ trademark graphics and accurate, reliable algorithms, proper application of Six Sigma statistical methods has never been easier.