The present paper studies the relative magnitudes of expected waiting times in extended machine-repair models, when processing times are of two Erlang types. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 864–870, 1999

This paper deals with the statistical design of control charts and describes a methodology to identify control schemes with action and warning limits that, for a fixed in-control average run length (ARL), minimize the ARL at a given out-of-control situation as measured by a shift in the process mean. This methodology allows the design of control charts with improved ARL performance for moderate shifts without degrading the in-control ARL as typically happens when run rules are applied to a conventional control chart. These optimal control schemes significantly reduce the out-of-control average run length compared with nonoptimal schemes.

This paper views ‘push’ and ‘pull’ production systems as mutually dual in a sense originally proposed by Finch and Foster. Four measures of production effectiveness are analysed for both systems in the light of this duality, using continuous-time Markov process modelling. Two of the four measures are found to be identical for the two systems, while the other two are found to be complementary in a sense explained in the body of the paper.

In this paper we study a certain counter-intuitive aspect of component importance in linear consecutive-k-out-of-n systems, when the components are independent with equal reliability p. It is shown that, in the case of the Birnbaum measure, the importance of the k-th component is greater than that of the (k + 1)-st when 2k + 1 less-than-or-equal-to n less-than-or-equal-to 3k + 1 for any p on [0,1] or when n > 3k + 1 for p and k such that (1 - p(k))k greater-than-or-equal-to 1 - p. The same pertains in the case of the Barlow-Proschan measure when 2k + 1 less-than-or-equal-to n less-than-or-equal-to 3k + 1 or when n is sufficiently large.

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.

Let theta be the location parameter of a location family, and let X be a single observation from a member of that family. Write T(X) right-pointing open triangle T'(X) when the statistic T(X) is closer in the Pitman sense to theta than is T'(X). This paper exhibits 1) for each of a large class of univariate location families, a set S of statistics T(X) with T(X) right-pointing open triangle X; 2) for each of the same class, a "Pitman-transitive" set S (i.e., such that, for T, T', T'' epsilon-S* T right-pointing open triangle T' and T' right-pointing open triangle T'' imply T right-pointing open triangle T'') in one-to-one correspondence with the closed unit interval, and 3) for the univariate Laplace location family with unit scale parameter, a "Pitman-intransitive" triplet (T,T',T'') of members of S.

Adopting a measure of dispersion proposed by Alamo [1964], and extending the analysis in Stangenhaus [1977] and Stangenhaus and David [1978b], an analogue of the classical Cramér-Rao lower bound for median-unbiased estimators is developed for absolutely continuous distributions with a single parameter, in which mean-unbiasedness, the Fisher information, and the variance are replaced by median-unbiasedness, the first absolute moment of the sample score, and the reciprocal of twice the median-unbiased estimator's density height evaluated at its median point. We exhibit location-parameter and scale-parameter families for which there exist median-unbiased estimators meeting the bound. We also give an analogue of the Chapman-Robbins inequality which is free from regularity conditions.

Many coals exhibit a certain degree of native hydrophobicity. The more hydrophobic coals (the higher-rank coals) are easily beneficiated by froth flotation or oil agglomeration, while the more hydrophilic coals (the lower-rank coals) are floated or agglomerated with difficulty. Coals of different ranks and often even of the same rank sometimes differ greatly in hydrophobicity as measured by contact angle or natural floatability. Although the degree of hydrophobicity of a coal is related to its rank and has been correlated with other surface properties of the coal , the known information is still not sufficient to allow a good estimation to be made of the hydrophobicity of a given coal and does not explain the variation of coal hydrophobicity as a function of rank. A statistical analysis of previously published data, as well as newly acquired data, shows that coal hydrophobicity correlates better with moisture content than with carbon content, and better with the moisture/carbon molar ratio than with the hydrogen/carbon or oxygen/carbon atomic ratios. These findings indicate that there is a strong association between hydrophobicity and coal moisture content.

A simple marked point process on the line (SMPPL) may be viewed as borrowing from semi-Markov processes the structure of a positive-valued waiting time process {Wn} modeling random delays between the state changes of a “mark process” {Jn}. Conditions are given ensuring that Cesaro limits with respect to time of state probabilities of a SMPPL are of a form analogous to limiting state probabilities of semi-Markov processes. These conditions include a condition restricting attention to "essentially finite" state spaces, in the sense of requiring a finite expected number of distinct visited states. Four examples are given, of which the first illustrates the extent to which a SMPPL satisfying our conditions may differ from a semi-Markov process. The remaining three examples are drawn from inventory theory, reliability and material science.

Many coals exhibit a certain degree of native hydrophobicity. The more hydrophobic coals (the higher rank coals) can be beneficiated by froth flotation or oil agglomeration, while the more hydrophilic coals (the lower rank coals) are difficult to float or agglomerate. Coals of different rank and sometimes even of the same rank differ greatly in hydrophobicity as measured by contact angle or natural floatability. Although the degree of hydrophobicity of a coal is related to its rank and the floatability of coal has been correlated with various indicators of hydrophobicity, the characterization of coal hydrophobicity is incomplete and its variation with rank has not been completely accounted for. A statistical analysis of previously published experimental data showed that coal hydrophobicity correlates better with coal moisture content than with carbon content.

Hammersley (1950) considered, among other matters, the asymptotic relative efficiency (ARE) of the rounded sample median M ε with respect to the rounded sample mean as estimate of a Normal population mean restricted to a uniform grid of mesh size 2ε. This article extends Hammersley's work to a certain class of two-sided extended increasing failure rate (TEIFR) distributions for which the (grid-valued) population mean and median coincide, their common value designated as μ. The ARE of M ε with respect to , as estimators of μ, is examined for our class via the theory of large deviations. The role of the TEIFR assumption is simply to ensure that the tails of the distribution of X i − μ fall off quickly enough to make comparison of asymptotic probabilities of large (beyond ε) deviations of the location-normalized sample median M − μ and mean relevant to the comparison of their asymptotic variances. Even within our somewhat narrow class, we find the ARE of M ε with respect to surprisingly sensitive to distribution shape, as well as to grid mesh size and the actual definition of ARE. Among our findings is that, in the symmetric TEIFR class, the ARE of M ε with respect to is continuous in ε at ε = 0 under a definition of ARE closely related to the commonly used limiting ratio of equivalent sample sizes, but it is not continuous at ε = 0 under Hammersley's definition of ARE. A related finding is that, within the TEIFR class, the asymptotic effective variance [in the sense of Bahadur (1960)] of the sample median M equals its asymptotic variance as usually defined. Another finding is that, in the case of the Laplace distribution, M ε is asymptotically more efficient than , as estimator of the grid-valued population center μ, when the grid is fine (ε small), but it is asymptotically less efficient when the grid is coarse (ε large). All of these findings stem from the comparison of large-deviation rates that are equally relevant to the comparisons of asymptotic error rates of certain tests using and M as test statistics, a matter mentioned briefly in the last section.

When the components of a bench-tested module contribute to its functioning in Boolean fashion, a Bayes approach allows extracting component failure rate information from module perform-ance data.

The network p-median (supply point location) problem has been generalized to the case where demand is continuously distributed. For p = 1 and uniformly distributed demand, and with the objective of minimizing distance, the interior points of an “edge” may be omitted from the search for an optimal supply point when that edge belongs to a “circuit.” Analogous conditions apply when demand is distributed in other than uniform fashion, and/or the objective is to minimize various forms of travel cost. In the case of p ≥ 2, with uniformly distributed demand and with the objective of minimizing distance, p-tuples of supply points, whose components are, respectively, interior points of p “mutually distant” edges, can be omitted from the search for p optimal supply points.

The new visibility of industrial statistics prompts us, in the process of attempting to put recent formulations in perspective, to reflect on some of the familiar themes. Two personal such reflections concern, respectively, Mood's Theorem andcontrol charts.

A notion of ‘uniform ε-independence’ (u.ε.i.) is proposed for a sequence {Xn} successively indexed by random indices {τk}. The u.∊.i. property yields results other than those in the previous random indexing literature. Complementing the u.∊.i. property by suitable ‘approximation’ one recovers these previous results.

The growing popular realization that American product quality and productivity are no longer without challenge for world leadership presents an opportunity for the American statistical community to make stronger contributions to sound industrial practice than it has in the past. Management consultants, such as Deming and Juran, are promoting philosophies that contain strong statistical components and are being heard by top U.S. executives. There are thus growing opportunities for industrial statisticians. Upon reviewing the content of typical graduate-level statistical quality control courses and books in the light of the present situation, we find them to be inadequate and in some cases to suffer from inappropriate emphases. In this article we discuss our perceptions of what is needed in the way of a new graduate-level course in statistics for quality and productivity (SQP). We further offer for discussion a syllabus for such a course (which is a modification of one used at Iowa State in the 1983 spring semester), some comments on how specific topics might be approached, and also a partially annotated list of references for material that we believe belongs in a modern SQP course. Key Words: Statistical quality controlGraduate educationIndustrial statistics

If P is a stochastic matrix corresponding to a stationary, irreducible, positive persistent Markov chain of period d>1, the powers Pn will not converge as n → ∞. However, the subsequences Pnd+k for k=0,1,...d-1, and hence Cesaro averages Σnk-1 Pk/n, will converge. In this paper we determine classes of nonstationary Markov chains for which the analogous subsequences and/or Cesaro averages converge and consider the rates of convergence. The results obtained are then applied to the analysis of expected average cost.