Joel A. Nachlas

X charts with variable sampling intervals

The usual practice in using a control chart to monitor a process is to take samples from the process with fixed sampling intervals. This article considers the properties of the chart when the sampling interval between each pair of samples is not fixed but rather depends on what is observed in the first sample. The idea is that the time interval until the next sample should be short if a sample shows some indication of a change in the process and long if there is no indication of a change. The proposed variable sampling interval (VSI) chart uses a short sampling interval if is close to but not actually outside the control limits and a long sampling interval if is close to target. If is actually outside the control limits, then the chart signals in the same way as the standard fixed sampling interval (FSI) chart. Properties such as the average time to signal and the average number of samples to signal are evaluated. Comparisons between the FSI and the VSI charts indicate that the VSI chart is substantially ...

Two-point constraint approximation in structural optimization

The use of constraint approximations is recognized as a primary means of achieving computational efficiency in structural optimization. Existing approximation methods are based upon the value of the constraint function and its derivatives at a single point. The present paper explores the use of approximations based upon the value of the constraint and its derivative at two points. Several candidate approximations are suggested and tested for randomly generated rational constraint functions* Several of the approximations prove to be superior to the single point approximations.

RELIABILITY ENGINEERING: Probabilistic Models and Maintenance Methods

Preface Introduction System Structures Status Functions System Structures and Status Functions Modules of Systems Multistate Components and Systems Exercises Reliability of System Structures Probability Elements Reliability of System Structures Modules Reliability Importance Reliability Allocation Conclusion Exercises Reliability Over Time Reliability Measures Life Distributions System Level Models Exercises Failure Processes Mechanical Failure Models Electronic Failure Models Other Failure Models Exercises Age Acceleration Age Acceleration for Electronic Devices Age Acceleration for Mechanical Devices Step Stress Strategies Exercises Nonparametric Statistical Methods Data Set Notation and Censoring Estimates Based on Order Statistics Estimates and Confidence Intervals Tolerance Bounds TTT Transforms Exercises Parametric Statistical Methods Graphical Models Method of Moments Method of Maximum Likelihood Special Topics Exercises Repairable Systems I-Renewal and Instantaneous Repair Renewal Processes Classification of Distributions and Bounds on Renewal Measures Residual Life Distribution Conclusion Exercises Repairable Systems II-Non-Renewal and Instantaneous Repair Minimal Repair Models Imperfect Repair Models Equivalent Age Models Conclusion Exercises Availability Analysis Availability Measures Example Computations System-Level Availability The Nonrenewal Cases Markov Models Exercises Preventive Maintenance Replacement Policies Nonrenewal Models Conclusion Acknowledgement Exercises Predictive Maintenance System Deterioration Inspection Scheduling More Complete Policy Analysis Conclusion Exercises Special Topics Warranties Reliability Growth Dependent Components Bivariate Reliability Acknowledgement Exercises Appendix A: Numerical Approximations Normal Distribution Function Gamma Function Psi Function Appendix B: Numerical Evaluation of Weibull Renewal Functions Appendix C: Laplace Transform for the Key Renewal Theorem Bibliography Index

A simulation approach to multivariate quality control

Abstract The use of Multivariate Quality Control techniques is usually avoided by practitioners because of the complexity involved in the design, implementation, and maintenance of the control system. In this paper a new approach to multivariate control problems is proposed, the Simulated Minimax control chart. The new control chart consists of placing upper and lower control limits on the maximum and the minimum of the p correlated variables standardized sample means such that the chart has a fixed probability of Type I error. The position of the control limits is determined by simulating the samples taken from a multivariate normal population. A comparison of the performance of the Simulated Minimax control chart and the Chi-squared control chart in terms of the average run length (ARL) is provided for two scenarios (n=5, p=2, ϱ=0 and n=5, p=2, ϱ=0.5) under different shifts in the mean. The results show that the Simulated Minimax control chart has excellent ARL properties as compared to the Chi-squared control chart. Thus, the Simulated Minimax control chart provides practitioners the advantage of interpreting the signals right from the chart, plus the simplicity of its use, and an excellent ARL performance.

Availability Analysis for the Quasi-Renewal Process

Historically, the behaviors of repairable systems were usually modeled under the assumption that repair implied system renewal. Availability functions were then constructed using renewal functions. Often, equipment is not renewed by repair, and for equipment that is not renewed, existing models fail to capture the key features of their behavior-ongoing degradation. More recently, nonrenewal models have been proposed to reflect the fact that equipment is usually not as good as new following maintenance. A wide variety of such models have been defined. They are usually called imperfect repair models. These models have the advantage that they are more realistic but they are also more complicated; therefore, analytical results for the models have been limited. In this paper, one of the nonrenewal models is analyzed, and an approach for obtaining a detailed measure of equipment performance, the point availability, is presented. The ultimate point availability function must be approximated numerically. Nevertheless, the analysis does lead to the time-dependent measure for a variety of possible distribution models. This paper contains two contributions to the study of repairable equipment performance. First, the models analyzed include both stochastic equipment deterioration and stochastically degrading repair performance over multiple operating intervals. Second, the analytical approach to obtaining the point availability function and its approximation is based on the combined analysis of operation-time- and downtime-based formulations of the system availability. This analytical approach to availability computation has not been used previously and is quite effective.

Evaluating and Implementing 3-Level Acceptance Sampling Plans

There are many situations in which product quality can be described by classifying a product using three or more discrete levels. For example, a food product may be classified as good, marginal, or bad depending on the concentration of harmful microorganisms in the product. In this paper, a generic framework is defined for establishing 3-level acceptance sampling plans. These plans utilize what we refer to as quality value functions. The Operating Characteristic function for these plans is constructed and used to develop an approximate parameter selection method based on the Central Limit Theorem. The results of testing this method using numerical examples are presented. The problem of quality value function selection is also addressed. A detailed example is presented, which includes the implementation of both the parameter and quality value function selection methods.

Microelectronic reliability predictions derived from component defect densities

A physics-of-failure approach to reliability prediction for integrated circuits is discussed. The analysis described is based upon the expectation that no integrated circuit can ever be free of imperfections and the assumption that both microscopic (point) defects and macroscopic flaws play influential roles in determining IC reliability. It is demonstrated that the microscopic defects can be directly implicated in gradual degradation over time via analyses related to those used in modeling a variety of solid-state phenomena.<<ETX>>

Evaluating and Implementing 3-Level Control Charts

In some situations, an appropriate quality measure uses three or more discrete levels (rather than an attributes or a variables measure) to classify a product characteristic. In previous work, we refer to such a classification scheme as a multi-level product quality measure, and present a general methodology for the evaluation and implementation of 3-level (conforming, marginal, nonconforming) acceptance sampling plans. In this paper, we apply this classification scheme and methodology for the purpose of evaluating and implementing 3-level control charts. The OC and ARL functions are formulated and integrated into an approximate parameter selection method. Because of the approximation, a manufacturer must overstate their ARL expectations in order to obtain reasonable control chart performance.

Estimation in Bernoulli Trials Under a Generalized Sampling Plan

The concept of generalized sampling plans is defined and is shown to encompass numerous sampling plans that are comprised of a sequence of independent Bernoulli trials. For such plans, the probability distribution of a sufficient statistic and a simple unbiased estimator for the success probability are obtained. The variance of the unbiased estimator and the average sample size are used as measures of performance to compare several inverse binomial sampling plans within the context of generalized sampling plans. The plans examined incorporate curtailment, extended sampling, or both. Evaluation of the performance of the plans provides insight into situations in which they may be used advantageously.

Availability of multifunctional systems

An availability model that captures the behavior of a multifunctional system is developed. The revised definitions and assumptions necessary to this construction are presented along with an appropriate notation. The defined model is compared to the traditional availability model that does not consider systems that can perform several missions using combinations of its multiple functions. An example that illustrates the improved accuracy of the proposed model is presented.