Related papers: Optimal Design of the Shiryaev-Roberts Chart: Give…
We consider the problem of quickest change-point detection where the observations form a first-order autoregressive (AR) process driven by temporally independent standard Gaussian noise. Subject to possible change are both the drift of the…
For the most popular sequential change detection rules such as CUSUM, EWMA, and the Shiryaev-Roberts test, we develop integral equations and a concise numerical method to compute a number of performance metrics, including average detection…
In recent years, self-starting methods have garnered increasing attention in Statistical Process Control and Monitoring (SPC/M), as they offer real-time disorder detection without the need for a calibration phase (Phase I). This study…
We show optimality, in a well-defined sense, using cumulative sum (CUSUM) charts for detecting changes in distributions. We consider a setting with multiple changes between two known distributions. This result advocates the use of…
We establish a simple connection between certain in-control characteristics of the CUSUM Run Length and their out-of-control counterparts. The connection is in the form of paired integral (renewal) equations. The derivation exploits Wald's…
The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-vs.-"false-positive"-risk…
In Statistical Process Control, control charts are often used to detect undesirable behavior of sequentially observed quality characteristics. Designing a control chart with desirably low False Alarm Rate (FAR) and detection delay ($ARL_1$)…
Many tasks are accomplished via random processes. The completion time of such a task can be profoundly affected by restart: the occasional resetting of the task's underlying random process. Consequently, determining when restart will impede…
The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler…
Rapidly detecting problems in the quality of care is of utmost importance for the well-being of patients. Without proper inspection schemes, such problems can go undetected for years. Cumulative sum (CUSUM) charts have proven to be useful…
We propose a numerical method to evaluate the performance of the emerging Generalized Shiryaev--Roberts (GSR) change-point detection procedure in a "minimax-ish" multi-cyclic setup where the procedure of choice is applied repetitively…
We consider the problem of efficient financial surveillance aimed at "on-the-go" detection of structural breaks (anomalies) in "live"-monitored financial time series. With the problem approached statistically, viz. as that of multi-cyclic…
Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at $R_0=0$ (the original Shiryaev-Roberts procedure), at $R_0=r$ for fixed $r>0$, and at…
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We…
In this paper, we not only propose an new optimal sequential test of sum of logarithmic likelihood ratio (SLR) but also present the CUSUM sequential test (control chart, stopping time) with the observation-adjusted control limits…
Restart is a general framework, of prime importance and wide applicability, for expediting first-passage times and completion times of general stochastic processes. Restart protocols can use either deterministic or stochastic timers.…
We develop Shiryaev-Roberts schemes based on signed sequential ranks to detect a persistent change in location of a continuous symmetric distribution with known median. The in-control properties of these schemes are distribution free, hence…
During the recent years there was an increased interest in studying the performance of different types of control charts, under various distributional models for continuous proportions, such as percentages and rates. In this work we…
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point is assumed unknown (nonrandom). The object of interest is…
Control charts, one of the main tools in Statistical Process Control (SPC), have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades. Measurement errors (M.E's) are…