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Earthquake in recent years has increased tremendously. This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charting technique to determine if the frequency of earthquake in the world is unusual. The frequency of earthquake in the world is considered from the period 1973 to 2016. As our data is auto correlated we cannot use the regular control chart like Shewhart control chart to detect unusual earthquake frequency. An approach that has proved useful in dealing with auto correlated data is to directly model time series model such as Autoregressive Integrated Moving Average (ARIMA), and apply control charts to the residuals. The EWMA control chart and the CUSUM control chart have detected unusual frequencies of earthquake in the year 2012 and 2013 which are state of statistically out of control.

When designing control charts the in-control parameters are unknown, so the control limits have to be estimated using a Phase I reference sample. To evaluate the in-control performance of control charts in the monitoring phase (Phase II), two performance indicators are most commonly used: the average run length (ARL) or the false alarm rate (FAR). However, these quantities will vary across practitioners due to the use of different reference samples in Phase I. This variation is small only for very large amounts of Phase I data, even when the actual distribution of the data is known. In practice, we do not know the distribution of the data, and it has to be estimated, along with its parameters. This means that we have to deal with model error when parametric models are used and stochastic error because we have to estimate the parameters. With these issues in mind, choices have to be made in order to control the performance of control charts. In this paper, we discuss some results with respect to the in-control guaranteed conditional performance of control charts with estimated parameters for parametric and nonparametric methods. We focus on Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) control charts for monitoring the mean when parameters are estimated.

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In statistical process control applications, situations may arise in which several presumably identical processes or “streams” are desired to be simultaneously monitored. Such a monitoring scenario...

The Conway-Maxwell Poisson (COM-Poisson) distribution is a generalization of the Poisson distribution and encompasses the geometric, the Poisson and the Bernoulli distribution as special cases. Thi...

In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average run length and the standard deviation of the run length are given. Practical guidelines concerning the chart design are investigated. Extensive computations based on designs of experiments are conducted to illustrate the validity of the proposed method. Comparisons with the conventional control charting procedure are also provided. The analysis of the monthly number of drug crimes in the city of Pittsburgh is displayed to illustrate our current method of process monitoring.

The objective of this study was to derive explicit formulas for the average run length (ARL) of an autoregressive moving average with an exogenous variable (ARMAX(p,q,r)) process with exponential white noise on a cumulative sum (CUSUM) control chart. To check the accuracy of the ARL derivations, the efficiency of the proposed explicit formulas was compared with a numerical integral equation (NIE) method in terms of the absolute percentage error. There was excellent agreement between the two methods, but when comparing their computational times, the explicit formulas only required 1 second whereas the NIE method required 599.499–835.891 s. In addition, real-world application of the derived explicit formulas was illustrated using Hong Kong dollar exchange rates data with an exogenous variable (the US dollar) to evaluate the ARL of an ARMAX (p,q,r) process on a CUSUM control chart.

In these last few decades, control charts have received a growing interest because of the important role they play by improving the quality of the products and services in industrial and non-industrial environments. Most of the existing control charts are based on the assumption of certainty and accuracy. However, in real-life applications, such as weather forecasting and stock prices, operators are not always certain about the accuracy of an observed data. To efficiently monitor such processes, this paper proposes a new cumulative sum (CUSUM) X¯ chart under the assumption of uncertainty using the neutrosophic statistic (NS). The performance of the new chart is investigated in terms of the neutrosophic run length properties using the Monte Carlo simulations approach. The efficiency of the proposed neutrosophic CUSUM (NCUSUM) X¯ chart is also compared to the one of the classical CUSUM X¯ chart. It is observed that the NCUSUM X¯ chart has very interesting properties compared to the classical CUSUM X¯ chart. The application and implementation of the NCUSUM X¯ chart are provided using simulated, petroleum and meteorological data.

Maximum multivariate cumulative sum (Max-MCUSUM) is one of the single control charts that plot single statistic as a representation of mean vector and covariance matrix. The Max-MCUSUM statistic ha...

Tukey control chart (TCC) is a popular choice for robust monitoring of process parameters. With the advancement in technology, we develop refined techniques that incorporate multiple aspects in a single structure. This article is a similar effort to design an improved charting structure in the form of mixed Tukey EWMA-CUSUM chart (namely MEC-TCC). We have investigated the performance of the proposed chart using different run length properties. We have observed that the proposed MEC-TCC design serves the dual objectives, namely the efficient detection of shifts and robustness against non-normality. The comparative analysis has revealed that the proposed scheme is an effective competitor to the existing counterparts, including classical Shewhart, EWMA, CUSUM, Tukey and some other variants such as mixed EWMA-CUSUM, Tukey EWMA, Tukey CUSUM. Moreover, the proposed design presents some of the aforementioned charts as special cases. For real life considerations, we have implemented the proposed and exist...

This paper is a study on the multivariate CUSUM control charts using three di er-ent control statistics for monitoring covariance matrix. We get control limits and ARLsof the proposed multivariate CUSUM control charts using three di erent control statis-tics by using computer simulations. The performances of these proposed multivariateCUSUM control charts have been investigated by comparing ARLs. The purpose ofcontrol charts is to detect assignable causes of variation so that these causes can befound and eliminated from process, variability will be reduced and the process willbe improved. We show that the charts based on three di erent control statistics arevery e ective in detecting shifts, especially shifts in covariances when the variables arehighly correlated. When variables are highly correlated, our overall recommendationis to use the multivariate CUSUM control charts using trace for detecting changes incovariance matrix.Keywords: Average run length, covariance matrix, multivariate CUSUM control chart.

The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters&mdash, which are the reference value ( a ) and control limit ( h )&mdash, for designing a CUSUM chart with a minimum out-of-control ARL is presented. In addition, the explicit formulas for the CUSUM control chart were applied with the practical data of a stock price from the stock exchange of Thailand, and the resulting performance efficiency is compared with an exponentially weighted moving average (EWMA) control chart. This comparison showed that the CUSUM control chart efficiently detected a small shift size in the process, whereas the EWMA control chart was more efficient for moderate to large shift sizes.

The analysis of designs based on saturated orthogonal arrays poses a very difficult challenge since there are no degrees of freedom left to estimate the error variance. In this paper we propose a heuristic approach for the use of cumulative sum control chart for screening active effects in orthogonal-saturated experiments. A comparative simulation study establishes the powerfulness of the proposed method.

We define zero-state (worst-state) and steady-state average run length metrics and discuss their computation for the proposed charts.

通常工程の状態は当初管理状態にあり,それが何らかの要因により管理状態から逸脱し,管理外れ状態に移行するものと考えられる.現工程の状態を判定する場合,現工程から得られたサンプル・データと併せて,これ以前に得られていたサンプル・データを十分に活用して現工程の状態を判定することは有意義な方法であるといえる.ここに,連続するサンプリングにおけるサンプル・データを活用し,工程状態を解析する方法として,CUSUM管理図やEWMA管理図といった時系列管理図法が存在する.ただし,従来の時系列管理図の検出特性の評価においては,時系列管理図の適用にあたって,適用当初から工程が管理外れ状態であった場合の検出特性が取り上げられている.これに対して,既述のように初期状態において管理状態にあった工程が何らかの要因によりある時点から管理外れ状態に移行する状況が一般的であると考えられる.そこで本研究では,まず工程の品質特性の管理状態の分布からの乖離の程度をKullback-Leibler情報量に基づき定量化し,これを打点統計量としそ工程の状態判定を行う(x,s)同時管理図をもとに,CUSUM管理図およびEWMA管理図といったいくつかの時系列管理図を設計する.さらに,管理図の適用当初から管理外れ状態にある状況のもとでの検出特性を評価する従来の研究とは別に,管理状態のままでいくらかの時間を経過した後に管理外れ状態に移行する状況を想定し,このもとでの管理外れ状態に対する検出特性を評価することを考える.くわえて,管理外れ状態を検出するばかりでなく,工程の管理状態からの逸脱期を特定することは品質管理・工程管理において重要な課題である.このことに鑑み,工程を時系列的に解析する上述の管理図をもとに,情報量規準に関する概念を応用し,どの時点において管理状態からの逸脱が生じたのかを解析的に識別する方法を提案する.

[This abstract is based on the author's abstract.]Control charts used to monitor for permanent shifts in a process do not indicate the exact time when the shift occurs, making it difficult to detect the assignable cause. A method for determining the tim..

The performance of the CUSUM control chart used to monitor the performance of production processes is usually evaluated with the assumption that the process parameters are know. In practice, however, the parameters are seldom known and are often replace..

Competition between the homoneous companies cause the company have to keep production quality. To cover this problem, the company controls the production with statistical quality control using control chart. Shewhart control chart is used to normal distributed data. The production data is often non-normal distribution and occured small process shift. Grand median control chart is a control chart for non-normal distributed data, while cumulative sum (cusum) control chart is a sensitive control chart to detect small process shift. The purpose of this research is to compare grand median and cusum control charts on shuttlecock weight variable in CV Marjoko Kompas dan Domas by generating data as the actual distribution. The generated data is used to simulate multiplier of standard deviation on grand median and cusum control charts. Simulation is done to get average run lenght (ARL) 370. Grand median control chart detects ten points that out of control, while cusum control chart detects a point out of control. It can be concluded that grand median control chart is better than cusum control chart.

The design of a CUSUM control chart typically involves choosing the subgroup size and sampling interval to achieve specified control chart performance. One can maintain a specified sampling intensity by using small subgroups at frequent intervals or larger subgroups at infrequent intervals. We use the average time to signal to investigate the performance of a CUSUM chart under alternative selections of the subgroup size and sampling interval. Recommendation are provided for both initial-state and steady-state performance.

One-sided CUSUM control chart have been developed for detecting shifts in the shape parameter of a Pareto distribution. It was realised that the parameters of the CUSUM chart, the lead distance and the mask angle changes considerably for a slight shift in the shape parameter of the Pareto distribution. The ARL also changes considerably for a slight shift in the parameters of the distribution.

The aim of the present study was to automatically predict the onset of farrowing in crate-confined sows. (1) Background: Automatic tools are appropriate to support animal surveillance under practical farming conditions. (2) Methods: In three batches, sows in one farrowing compartment of the Futterkamp research farm were equipped with an ear sensor to sample acceleration. As a reference video, recordings of the sows were used. A classical CUSUM chart using different acceleration indices of various distribution characteristics with several scenarios were compared. (3) Results: The increase of activity mainly due to nest building behavior before the onset of farrowing could be detected with the sow individual CUSUM chart. The best performance required a statistical distribution characteristic that represented fluctuations in the signal (for example, 1st variation) combined with a transformation of this parameter by cumulating differences in the signal within certain time periods from one day to another. With this transformed signal, farrowing sows could reliably be detected. For 100% or 85% of the sows, an alarm was given within 48 or 12 h before the onset of farrowing. (4) Conclusions: Acceleration measurements in the ear of a sow are suitable for detecting the onset of farrowing in individually housed sows in commercial farrowing crates.

A cumulative sum control chart scheme is designed for the detection of the outbreak of an epidemic to demonstrate the use of CUSUM chart in the non-manufacturing sector. The designed schemes are then applied on data on diabetic disease to illustrate the detection of outbreak of epidemic and also a retrospective analysis is carried out and the local means are computed