Statistical process monitoring
Runs and scan statistics can detect sustained shifts, clustering, or unusual local concentrations in process observations while preserving exact finite-sample probabilities.
Longest RunScan StatisticNumber of RunsCompute exact probabilities for runs, patterns, scan statistics, matching events, and Cochran-type tests using finite Markov chain imbedding methods.
Longest-run and scan-statistic ideas are used for exact monitoring and change detection.
Scan statistics and run-based summaries can help detect clustered signals and copy-number variation regions.
Finite Markov chain imbedding converts a runs, patterns, or scan-statistic problem into transitions among a finite collection of states, allowing probabilities to be calculated recursively and exactly.
The FMCI Web App provides a browser-based interface for studying events in binary sequences under independent-trial and Markov-dependent models. It supports waiting times, pattern counts, scan statistics, longest runs, numbers of runs, matching probabilities, and Cochran-type testing.
The app is intended for students learning probability, researchers developing exact methods, and practitioners who need interpretable alternatives to simulation or large-sample approximations.
Each module guides the user from model specification to an exact probability, distribution, or testing result.
Specify the run, pattern, window, match, or test statistic of interest.
Use independent Bernoulli trials or a Markov-dependent sequence where supported.
Track only the sequence information needed to determine progress toward the event.
Propagate state probabilities to obtain the requested distribution or tail probability.
Choose a module below to get started. Each tool includes detailed instructions and examples.
Distribution calculations for the number of success runs, failure runs, or total runs.
Learn moreProbability calculations for matching patterns between two sequences.
Learn moreExact p-value, type I error, and type II error calculations for Cochran-type testing.
Learn moreFMCI is especially valuable when the order and local structure of observations matter and an exact finite-sample probability is preferred over an approximation.
Runs and scan statistics can detect sustained shifts, clustering, or unusual local concentrations in process observations while preserving exact finite-sample probabilities.
Longest RunScan StatisticNumber of RunsBinary or categorized genomic measurements can be studied for unusually long segments, clustered signals, recurring patterns, or regions associated with copy-number variation (CNV).
Scan StatisticLongest RunNumber of PatternsRuns represent consecutive successes or failures, making FMCI useful for reliability systems, alarm sequences, streaks, and threshold rules based on repeated events.
Longest RunNumber of RunsWaiting TimeExact matching probabilities help quantify agreement, coincidence, or aligned similarities between two binary sequences under specified dependence assumptions.
Matching ProbabilityFinite-state calculations can deliver exact p-values and error probabilities when asymptotic approximations may be unreliable, including Cochran-type procedures.
Cochran's TestThe app does not open: the hosting address may be unavailable or the MATLAB Web App Server may be offline. Contact the maintainer using the email address shown here.
An input is rejected: verify the module guide, parameter ranges, dimensions of transition matrices, and the relationship among sequence length, run length, and window size.
The result is unexpected: confirm whether the selected model is independent or Markov-dependent and whether the requested result is a point, cumulative, or tail probability.