A generalization of anderson's modified sequential probability ratio test

A generalization of Anderson's sequential probability ratio test procedure is proposed in which the continuation region is bounded by a pair of converging lines up to a certain stage of the experiment and later by another pair of converging lines until the procedure is truncated at a predetermined stage of the experiment. The OC and the ASN functions have been derived. For certain parameter values the proposed procedure attains lower average sample numbers than that attainable by any other known procedure.     

A synthetic control chart for monitoring the small shifts in a process mean based on an attribute inspection

Abstract

In this paper, a synthetic control chart is proposed by integrating the salient features of the np_x chart and the CRL chart. The synthetic chart achieves higher detection effectiveness on both small and large mean shifts while retaining the operational simplicity of the attribute charts owing to only using attribute inspection. Both statistical and economic design of the synthetic chart are considered and numerical tests have indicated that the synthetic chart has a higher power for detecting mean shifts than the np_x chart, MON chart and CUSUM chart. In addition, sensitivity analyses are also performed under both the statistical and economic design model.     

A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

CUSUM charts for monitoring the mean of a multivariate Gaussian process

In this paper control charts for the mean of a multivariate Gaussian process are considered. Using the generalized likelihood ratio approach and the sequential probability ratio test under an additional constraint on the magnitude of the change various types of CUSUM control charts are derived. It is analyzed under which conditions these schemes are directionally invariant. These charts are compared with several other control schemes proposed in literature. The performance of the charts is studied based on the maximum average delay.     

A new synthetic control chart for monitoring process mean using auxiliary information

ABSTRACT

Quality control charts have been widely recognized as a potentially powerful statistical process monitoring tool in statistical process control because of their superior ability in detecting shifts in the process parameters. Recently, auxiliary-information-based control charts have been proposed and shown to have excellent speed in detecting process shifts than those based without it. In this paper, we design a new synthetic control chart that is based on a statistic that utilizes information from both the study and auxiliary variables. The proposed synthetic chart encompasses the classical synthetic chart. The construction, optimal design, run length profiles, and the performance evaluation of the new chart are discussed in detail. It turns out that the proposed synthetic chart performs uniformly better than the classical synthetic chart when detecting different kinds of shifts in the process mean under both zero-state and steady-state run length performances. Moreover, with reasonable assumptions, the proposed chart also surpasses the exponentially weighted moving average control chart. An application with a simulated data set is also presented to explain the implementation of the proposed control chart.     

Likelihood ratio test-based chart for monitoring the process variability

This article proposes a new chart with the generalized likelihood ratio (GLR) test statistics for monitoring the process variance of a normally distributed process. The new chart can be easily designed and constructed and the computation results show that it provides quite a satisfactory performance, including the detection of the decrease in the variance and the individual observation at the sampling point which are very important in many practical applications. Average run length (ARL) comparisons between other procedures and the new chart are presented. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the ARL are described. The application of our proposed method is illustrated by a real data example from chemical process control.     

A two- sample partially sequential probability ratio test

A two-sample partially sequential probability ratio test (PSPRT) is considered for the two-sample location problem with one sample fixed and the other sequential. Observations are assumed to come from two normal poptilatlons with equal and known variances. Asymptotically in the fixed-sample size the PSPRT is a truncated Wald one sample sequential probability test. Brownian motion approximations for boundary-crossing probabilities and expected sequential sample size are obtained. These calculations are compared to values obtained by Monte Carlo simulation.     

A single-featured EWMA-X control chart for detecting shifts in process mean and standard deviation

The combined EWMA-X chart is a commonly used tool for monitoring both large and small process shifts. However, this chart requires calculating and monitoring two statistics along with two sets of control limits. Thus, this study develops a single-featured EWMA-X (called SFEWMA-X) control chart which has the ability to simultaneously monitor both large and small process shifts using only one set of statistic and control limits. The proposed SFEWMA-X chart is further extended to monitoring the shifts in process standard deviation. A set of simulated data are used to demonstrate the proposed chart's superior performance in terms of average run length compared with that of the traditional charts. The experimental examples also show that the SFEWMA-X chart is neater and easier to visually interpret than the original EWMA-X chart.     

An EWMA chart for monitoring process mean

In the statistical process control literature, there exists several improved quality control charts based on cost-effective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-effective RSS scheme has been recently introduced for efficiently estimating the population mean, namely varied L RSS (VLRSS). In this article, we propose a new exponentially weighted moving average (EWMA) control chart for monitoring the process mean using VLRSS, named the EWMA-VLRSS chart, under both perfect and imperfect rankings. The EWMA-VLRSS chart encompasses the existing EWMA charts based on RSS and MRSS (named the EWMA-RSS and EWMA-MRSS charts). We use extensive Monte Carlo simulations to compute the run length characteristics of the EWMA-VLRSS chart. The proposed chart is then compared with the existing EWMA charts. It is found that, with either perfect or imperfect rankings, the EWMA-VLRSS chart is more sensitive than the EWMA-RSS and EWMA-MRSS charts in detecting small to large shifts in the process mean. A real dataset is also used to explain the working of the EWMA-VLRSS chart.     

A generalized likelihood ratio test for monitoring profile data

Profile data emerges when the quality of a product or process is characterized by a functional relationship among (input and output) variables. In this paper, we focus on the case where each profile has one response variable Y, one explanatory variable x, and the functional relationship between these two variables can be rather arbitrary. The basic concept can be applied to a much wider case, however. We propose a general method based on the Generalized Likelihood Ratio Test (GLRT) for monitoring of profile data. The proposed method uses nonparametric regression to estimate the on-line profiles and thus does not require any functional form for the profiles. Both Shewhart-type and EWMA-type control charts are considered. The average run length (ARL) performance of the proposed method is studied. It is shown that the proposed GLRT-based control chart can efficiently detect both location and dispersion shifts of the on-line profiles from the baseline profile. An upper control limit (UCL) corresponding to a desired in-control ARL value is constructed.     

A new nonparametric synthetic EWMA control chart for monitoring process mean

The exponentially weighted moving average (EWMA) control charts are widely used in chemical and process industries because of their excellent speed in catching small to moderate shifts in the process target. In usual practice, many data come from a process where the monitoring statistic is non-normally distributed or it follows an unknown probability distribution. This necessitates the use of distribution-free/nonparametric control charts for monitoring the deviations from the process target. In this paper, we integrate the existing EWMA sign chart with the conforming run length chart to propose a new synthetic EWMA (SynEWMA) sign chart for monitoring the process mean. The SynEWMA sign chart encompasses the synthetic sign and EWMA sign charts. Monte Carlo simulations are used to compute the run length profiles of the SynEWMA sign chart. Based on a comprehensive comparison, it turns out that the SynEWMA sign chart is able to perform substantially better than the existing EWMA sign chart. Both real and simulated data sets are used to explain the working and implementation of existing and proposed control charts.     

A new adaptive EWMA control chart using auxiliary information for monitoring the process mean

The adaptive memory-type control charts, including the adaptive exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, have gained considerable attention because of their excellent speed in providing overall good detection over a range of mean shift sizes. In this paper, we propose a new adaptive EWMA (AEWMA) chart using the auxiliary information for efficiently monitoring the infrequent changes in the process mean. The idea is to first estimate the unknown process mean shift using an auxiliary information based mean estimator, and then adaptively update the smoothing constant of the EWMA chart. Using extensive Monte Carlo simulations, the run length profiles of the AEWMA chart are computed and explored. The AEWMA chart is compared with the existing control charts, including the classical EWMA, CUSUM, synthetic EWMA and synthetic CUSUM charts, in terms of the run length characteristics. It turns out that the AEWMA chart performs uniformly better than these control charts when detecting a range of mean shift sizes. An illustrative example is also presented to demonstrate the working and implementation of the proposed and existing control charts.     

A sequential approximation to a permutation test

A sequential method for approximating a general permutation test (SAPT) is proposed and evaluated. Permutations are randomly generated from some set G, and a sequential probability ratio test (SPRT) is used to determine whether an observed test statistic falls sufficiently far in the tail of the permutation distribution to warrant rejecting some hypothesis. An estimate and bounds on the power function of the SPRT are used to find bounds on the effective significance level of the SAPT. Guidelines are developed for choosing parameters in order to obtain a desired significance level and minimize the number of permutations needed to reach a decision. A theoretical estimate of the average number of permutations under the null hypothesis is given along with simulation results demonstrating the power and average number of permutations for various alternatives. The sequential approximation retains the generality of the permutation test,- while avoiding the computational complexities that arise in attempting to computer the full permutation distribution exactly     

Improved CUSUM charts for monitoring process mean

In this paper, we propose new cumulative sum (CUSUM) and Shewhart-CUSUM (SCUSUM) control charts for monitoring the process mean using ranked-set sampling (RSS) and ordered RSS (ORSS) schemes. The proposed CUSUM charts include the Crosier's CUSUM (CCUSUM) and Shewhart-CCUSUM (SCCUSUM) charts using RSS, and the CUSUM, CCUSUM, SCUSUM and SCCUSUM charts using ORSS. Moreover, fast initial response features are also attached with these CUSUM charts to improve their sensitivities for an initial out-of-control situation. Monte Carlo simulations are used to compute the run length characteristics of the proposed CUSUM charts. Upon comparing the run length performances of the CUSUM charts, it turns out that the proposed CUSUM charts are more sensitive than their existing counterparts. A real dataset is used to explain the implementation of the proposed CUSUM charts.     

An adaptive exponentially weighted moving average control chart for monitoring process variances

The exponentially weighted moving average (EWMA) control chart is efficient in detecting small changes in process parameters but less efficient when the changes are relatively large, due to what is known as the inertia problem. To diminish the inertia, an adaptive EWMA (AEWMA) chart has been proposed for monitoring process locations to improve over the traditional EWMA charts. The basic idea of the AEWMA scheme is to dynamically weight the past observations according to a suitable function of the current prediction error. This article extends the idea of the AEWMA chart for monitoring process locations to the case of monitoring process dispersion. A Markov chain model is established to analyze and design the suggested chart. It is shown that the AEWMA dispersion chart performs better than the EWMA and other dispersion charts in terms of its ability to perform relatively well at both small and large changes in process dispersion.     

A group sequential test for the inverse Gaussian mean

The present paper deals with the development of a group sequential test when response variable has an inverse Gaussian distribution with known scale parameter.     

A binomial CUSUM chart for detecting large shifts in fraction nonconforming

This article studies a unique feature of the binomial CUSUM chart in which the difference (d _t ?d ₀) is replaced by (d _t ?d ₀)² in the formulation of the cumulative sum C _t (where d _t and d ₀ are the actual and in-control numbers of nonconforming units, respectively, in a sample). Performance studies are reported and the results reveal that this new feature is able to increase the detection effectiveness when fraction nonconforming p becomes three to four times as large as the in-control value p ₀. The design of the new binomial CUSUM chart is presented along with the calculation of the in-control and out-of-control Average Run Lengths (ARL₀ and ARL₁).     

A new non-parametric multivariate EWMA sign control chart for monitoring process dispersion

In this paper, a new non-parametric multivariate exponentially weighted moving average (NMEWMA) sign chart is proposed for monitoring the process dispersion. The run length characteristics of the NMEWMA sign chart are computed with the help of Markov chain and Monte Carlo simulations. Moreover, the NMEWMA sign chart is also used to detect changes in the process mean and dispersion simultaneously. An illustrative example is also used to explain the implementation of proposed control chart.