J. Marcus Jobe

Buehler confidence bounds for a reliability-maintainability measure

This article presents an upper confidence bound for a measure of reliability/maintainability of a series system in which component repair is assumed to restore the system to its original status. Under exponentiality of component-repair time and survival time distributions, the measure M is the ratio of expected system-repair time to expected system-survival time. Moreover, under this exponentiality assumption, the bound is uniformly minimum among all bounds of specified level that are nondecreasing functions of the maximum likelihood estimator of M. As a matter of practical interest, the measure M has been incorporated into Military Standard MIL-STD-470B and is an official statistic of the Air Force Reliability Maintainability Information System.

A Cluster-Based Outlier Detection Scheme for Multivariate Data

Detection power of the squared Mahalanobis distance statistic is significantly reduced when several outliers exist within a multivariate dataset of interest. To overcome this masking effect, we propose a computer-intensive cluster-based approach that incorporates a reweighted version of Rousseeuw’s minimum covariance determinant method with a multi-step cluster-based algorithm that initially filters out potential masking points. Compared to the most robust procedures, simulation studies show that our new method is better for outlier detection. Additional real data comparisons are given. Supplementary materials for this article are available online.

Elementary Statistical Methods and Measurement Error

How the sources of physical variation interact with a data collection plan determines what can be learned from the resulting dataset, and in particular, how measurement error is reflected in the dataset. The implications of this fact are rarely given much attention in most statistics courses. Even the most elementary statistical methods have their practical effectiveness limited by measurement variation; and understanding how measurement variation interacts with data collection and the methods is helpful in quantifying the nature of measurement error. We illustrate how simple one- and two-sample statistical methods can be effectively used in introducing important concepts of metrology and the implications of those concepts when drawing conclusions from data.

Including quality costs in the lot‐sizing decision

In the past, traditional lot‐sizing decisions were based on total cost functions that did not explicitly consider quality costs such as inspection of incoming materials and damage costs incurred when faulty material slipped through inspection. Rather, the cost of maintaining quality for a batch was incorporated into the fixed ordering costs of the batch. Provides an adaptation of the traditional lot‐sizing model that does explicitly consider quality costs. Derives an expression for the optimal lot‐size under such conditions. Bayesian methods are provided to estimate this expression. Includes examples to illustrate the use of this approach. Demonstrates that the traditional approach inappropriately inflates estimates of the economically optimal lot size.

Quality of the log transformation for an incorrectly assumed error structure

A log transformation is often applied to nonlinear models with an assumed multiplicative error structure. Then the parameters are estimated using ordinary least squares (o. l. s. ) and back transformed predictions made. This paper examines the bias involved with this procedure when the actual error structure is additive and not multiplicative, A correction factor is introduced to help reduce the bias when the back transformed o. l. s. approach is used. We strongly suggest, however, that one should use nonlinear least squares when the analyst believes he is working with an additive error structure.

Statistics and Measurement

Good measurement is fundamental to quality assurance. That which cannot be measured cannot be guaranteed to a customer. If Brinell hardness 220 is needed for certain castings and one has no means of reliably measuring hardness, there is no way to provide the castings. So successful companies devote substantial resources to the development and maintenance of good measurement systems. In this chapter, we consider some basic concepts of measurement and discuss a variety of statistical tools aimed at quantifying and improving the effectiveness of measurement.

A Statistical Approach for Additional Infill Development

Ultimate recovery data are frequently modeled as being lognormal without consideration of other possible distributions. A typical approach is to use lognormal probability paper and a mean value (Swansons mean) is calculated as well as chance factors. Engineers have identified a competing probability model for lifetime data called the Weibull distribution. In this paper, we consider the Weibull distribution as a potential alternative probability model for ultimate recovery data. Optimal methodologies of estimating the mean ultimate recovery for both the lognormal and the Weibull distributions are presented. Statisticians refer to this optimal approach as maximum likelihood methodology. Further, probability plots and hypothesis testing methods are presented that help reveal whether one should use the Weibull model or the lognormal model for available ultimate recovery data. Finally, a simulation approach is proposed to predict the average ultimate recovery value for “n” additional wells. An example with real data concludes the paper.

Process Characterization and Capability Analysis

The previous chapter dealt with tools for monitoring processes and detecting physical instabilities. The goal of using these is finding the source(s) of any process upsets and removing them, creating a process that is consistent/repeatable/ predictable in its pattern of variation. When that has been accomplished, it then makes sense to summarize that pattern of variation graphically and/or in terms of numerical summary measures. These descriptions of consistent process behavior can then become the bases for engineering and business decisions about if, when, and how the process should be used. This chapter discusses methods for characterizing the pattern of variation exhibited by a reasonably predictable system. Section 4.1 begins by presenting some more methods of statistical graphics (beyond those in Sect. 1.5) useful in process characterization. Then Sect. 4.2 discusses some “Process Capability Indices” and confidence intervals for them. Next, prediction and tolerance intervals for measurements generated by a stable process are presented in Sect. 4.3. Finally, Sect. 4.4 considers the problem of predicting the variation in output for a system simple enough to be described by an explicit equation, in terms of the variability of system inputs.

Experimental Design and Analysis for Process Improvement Part 1: Basics

The first four chapters of this book provide tools for bringing a process to physical stability and then characterizing its behavior. The question of what to do if the resulting picture of the process is not to one’s liking remains. This chapter and the next present tools for addressing this issue. That is, Chaps. 5 and 6 concern statistical methods that support intelligent process experimentation and can provide guidance in improvement efforts.

Experimental Design and Analysis for Process Improvement Part 2: Advanced Topics

The basic tools of experimental design and analysis provided in Chap. 5 form a foundation for effective multifactor experimentation. This chapter builds on that and provides some of the superstructure of statistical methods for process-improvement experiments.