No description available.

No description available.

No description available.

This study uses Monte Carlo simulation to examine the performance of a variable frequency sampling cumulative sum control chart scheme for controlling the mean of a normal process. The study compares the performance of the method with that of a standard fixed interval sampling cumulative sum control chart scheme. The results indicate that the variable frequency sampling cumulative sum control chart scheme is superior to the standard cumulative sum control chart scheme in detecting a small to moderate shift in the process mean.

Control charts are designed to monitor population parameters. Selection of a control chart sampling plan involves determination of the frequency of samples, size of each sample, and critical values to determine when the system is sending an out-of-control signal. Since the main use of control charts is in industry, a widely accepted measure of a good sampling plan is one that minimizes the total cost of operating the system per unit time. Methods for selection of control chart sampling plans for economically optimal X charts are well established. These plans focus on single stage sampling at each sampling period. However, some populations naturally call for two stage sampling. Here, the cost of operating a system per unit time is redefined in terms of two stage sampling plans, and computer search techniques are developed to determine the control chart parameters. First the sample sizes and critical values are fixed, and Newton's method is used to determine the optimal time between samples. Then, a Hooke - Jeeves search is used to simultaneously determine the optimal critical value, sample sizes and time between samples. Adjustment to the latter is required whenever any of the other three parameters change. Alternative methods are also discussed. Information from a single sample is usually used to control shifts in both the process mean and variance. With two stage sampling, this means two additional control charts are used, one for each variance component. The computer algorithm developed for selection of parameters for X charts is adapted by expanding the Hooke Jeeves search region to a six dimensional space, now over three critical values, sample sizes for both stages of sampling, and the time between samples. These methods are applied to a real data set that requires two stage sampling. A representative analysis of the sensitivity of the optimal sampling scheme to the input parameters completes the paper. / Graduation date: 1990

No description available.

Control charts based on cumulative gauging scores rely on gauge scoring systems used for transforming actual observations into integer gauging scores. In some cases, the gauging scores are easy to obtain by using a mechanical device such as in the go-no-go inspection process. Thus, accurate measurements of selected quality characteristics are not necessary. Also, different control purposes can be achieved p by using different scoring systems. Cumulative gauging score charts based on two pairs of gauges are proposed to control the process mean or the standard deviation by either gauging one or several observations. Both random walk and cusum type cumulative gauging score charts are used. For controlling the process mean and standard deviation at the same time, a cusum type and a two-dimensional random walk type procedure are proposed. A gauging scheme can be applied to multivariate quality control by gauging either x² or T² statistics. A simple multivariate control chart which is based on the multivariate sign score vector is also proposed. The exact run length distribution of these cumulative gauging score charts can be obtained by formulating the procedures as Markov chain processes. For some procedures, the average run length (ARL) can be obtained in a closed form expression by solving a system of difference equations with appropriate boundary conditions. Comparisons based on the ARL show that the cumulative gauging score charts can detect small shifts in the quality characteristic more quickly than the Shewhart type X-chart. The efficiency of the cusum type gauging score chart is close to the regular CUSUM chart. The random walk type gauging score chart is more robust than the Shewhart and CUSUM charts to observations which have heavy a tailed distribution or which are serially correlated. For multivariate quality control. A procedure based on gauging the x² statistic has better performance than the x² chart. Also, a new multivariate control chart procedure which is more robust to the misspecification of the correlation than the x² chart is proposed. / Ph. D.

In statistical process control, it is usually assumed that observations on the process output at different times are lID. However, for many processes the observations are correlated and control charts for monitoring these processes have recently received much attention. For monitoring the process level, this study evaluates the properties of control charts, such as the EWMA chart and the CUSUM chart, based on the residuals from the forecast values of an ARMA model. It is assumed that the process mean is a ftrst order autoregressive (AR(l)) model and the observations are the mean plus a random error. Properties of these charts are evaluated using a Markov chain approach or an integral equation approach. The performance of control charts based on the residuals is compared to the performance of control charts based on the original observations. A combined chart using forecasts and residuals as the control statistics as well as a combined chart using the EWMA of observations and the EWMA of residuals as the control statistics are also studied by simulation. It is found that no universally "good" chart exists among all the charts investigated in this study. In addition, for monitoring the process variance, two kinds of EWMA chart based on residuals are studied and compared. / Ph. D.

In recent years, variable sampling interval (VSI) control charts have been intensively investigated. In contrast to traditional fixed sampling interval (FSI) control charts, VSI charts vary the sampling interval as a function of the data. VSI charts detect many process changes faster than their FSI counterparts. A disadvantage, however, of VSI charts as recently formulated is that the advance prediction of sampling times is impossible for more than the next sample. A control chart is proposed which applies a sequential probability ratio test (SPRT) at fixed sampling intervals, the SPRT chart, to monitor the mean of a process with a normal distribution. A natural modification of the SPRT chart, the SPRT chart with sampling at fired times (SFT), is also proposed in which samples are always taken at pre-specified, equally spaced fixed times, with additional samples taken between these times as indicated by the data. A third control chart is introduced as a generalization of the VSI cumulative sum (CUSUM) chart that uses two sampling intervals, called the universal CUSUM (UC) chart, in order to address the need for a general framework for the study of control charts that are equivalent to a sequence of SPRT’s. The UC chart can also be viewed as a generalization of the SPRT chart. The integral equation approach is adapted for the evaluation of properties of both the unmodified and modified with SFT versions of the SPRT chart, such as average time to signal (ATS), steady state ATS (SSATS), and average number of observations to signal (ANOS). After comparisons are performed within the general framework of the UC chart, the unmodified SPRT chart is found to be more efficient than both the FSI and VSI X charts and the FSI CUSUM chart, though very similar in efficiency to the VSI CUSUM chart. The modified SPRT chart with SFT is found to be more efficient than all five of the other control charts, including its unmodified version and the VSI CUSUM chart. General guidelines are provided for the design of both versions of the SPRT chart. / Ph. D.

The standard Shewhart control chart for monitoring process stability is generalized by selecting a point in time at which the distance between the control limits is reduced. Three cost models are developed to describe the total cost per unit time of monitoring the mean of a process using both the standard and the generalized Shewhart control chart. The cost models are developed under the assumption that the quality characteristic of interest is normally distributed with known and constant variance. In the development of the first model, the negative exponential distribution is employed to model the time to process shift. Then, the uniform distribution and the Weibull distribution are used for the same purpose in the second and the third model, respectively. The motivation for this effort is to increase chart sensitivity to small but anticipated shifts in the process average. Cost models are constructed to allow the optimal choice of change over time and the best values for the initial and adjusted control limit values. The cost models are analyzed to determine the optimal control chart parameters including those associated with both the standard and the generalized control chart. The models are also used to provide a comparison with conventional implementation of the control chart. It is shown that the proposed cost models are efficient and economical. Figures and tables are provided to aid in the design of models for both the standard and the generalized Shewhart control chart. / Ph. D.