An alternative proof of the IFRA property of some shock models

Let , where A (t)/t is nondecreasing in t, {P(k)^1/k} is nonincreasing. It is known that H(t) = 1 — H (t) is an increasing failure rate on the average (IFRA) distribution. A proof based on the IFRA closure theorem is given. H(t) is the distribution of life for systems undergoing shocks occurring according to a Poisson process where P (k) is the probability that the system survives k shocks. The proof given herein shows there is an underlying connection between such models and monotone systems of independent components that explains the IFRA life distribution occurring in both models.     

On the reliability,availability and bayes confidence intervals for multicomponent systems

The problem of computing reliability and availability and their associated confidence limits for multi-component systems has appeared often in the literature. This problem arises where some or all of the component reliabilities and availabilities are statistical estimates (random variables) from test and other data. The problem of computing confidence limits has generally been considered difficult and treated only on a case-by-case basis. This paper deals with Bayes confidence limits on reliability and availability for a more general class of systems than previously considered including, as special cases, series-parallel and standby systems applications. The posterior distributions obtained are exact in theory and their numerical evaluation is limited only by computing resources, data representation and round-off in calculations. This paper collects and generalizes previous results of the authors and others. The methods presented in this paper apply both to reliability and availability analysis. The conceptual development requires only that system reliability or availability be probabilities defined in terms acceptable for a particular application. The emphasis is on Bayes Analysis and the determination of the posterior distribution functions. Having these, the calculation of point estimates and confidence limits is routine. This paper includes several examples of estimating system reliability and confidence limits based on observed component test data. Also included is an example of the numerical procedure for computing Bayes confidence limits for the reliability of a system consisting of N failure independent components connected in series. Both an exact and a new approximate numerical procedure for computing point and interval estimates of reliability are presented. A comparison is made of the results obtained from the two procedures. It is shown that the approximation is entirely sufficient for most reliability engineering analysis.     

The role of internal storage capacity in fixed cycle production systems

The reliability of a serial production line is optimized with respect to the location of a single buffer. The problem was earlier defined and solved by Soyster and Toof for the special case of an even number of machines all having equal probability of failure. In this paper we generalize the results for any number of machines and remove the restriction of identical machine reliabilities. In addition, an analysis of multibuffer systems is presented with a closed form solution for the reliability when both the number of buffers and their capacity is limited. For the general multibuffer system we present an approach for determining system reliability.     

Analyzing availability using transfer function models and cross spectral analysis

If we look at the literature of reliability and life testing we do not see much on the use of the powerful methods of time series analysis. In this paper we show how the methods of multivariate time series analysis can be used in a novel way to investigate the interrelationships between a series of operating (running) times and a series of maintenance (down) times of a complex system. Specifically, we apply the techniques of cross spectral analysis to help us obtain a Box-Jenkins type transfer function model for the running times and the down times of a nuclear reactor. A knowledge of the interrelationships between the running times and the down times is useful for an evaluation of maintenance policies, for replacement policy decisions, and for evaluating the availability and the readiness of complex systems.     

An application of statistical techniques to estimate engineering man-hours on major aircraft programs

Data on 23 lots of various aircraft programs were gathered. Total engineering man-hours, and information on performance, weight, area, avionics systems, data, and schedule were subjected to least squares analysis. An equation is presented which indicates a relationship between total engineering manhours and a set of seven predictor variables. While the equation derived could only be used with confidence by the manufacturer whose data was analyzed, this article should be looked upon as demonstrating a method of data analysis which others may also find useful, not only for predicting engineering manhours in major aircraft programs, but also in other situations where there is an abundance of possible predictor variables, and the problem is to sort out a meaningful subset of these variables. In order to demonstrate the viability of the formula obtained, comparisons were made with various bid programs.     

Computational results for a stopping rule problem on averages

Suppose x₁, x₂, … are independently distributed random variables with Pr (x_i = 1) = Pr(x_i = ?1) = 1/2, and let s_n =

     

An extension of the (szwarc) truck assignment problem

In this journal in 1967. Szware presented an algorithm for the optimal routing of a common vehicle fleet between m sources and n sinks with p different types of commodities. The main premise of the formulation is that a truck may carry only one commodity at a time and must deliver the entire load to one demand area. This eliminates the problem of routing vehicles between sources or between sinks and limits the problem to the routing of loaded trucks between sources and sinks and empty trucks making the return trip. Szwarc considered only the transportation aspect of the problem (i. e., no intermediate points) and presented a very efficient algorithm for solution of the case he described. If the total supply is greater than the total demand, Szwarc shows that the problem is equivalent to a (mp + n) by (np + m) Hitchcock transportation problem. Digital computer codes for this algorithm require rapid access storage for a matrix of size (mp + n) by (np + m); therefore, computer storage required grows proportionally to p². This paper offers an extension of his work to a more general form: a transshipment network with capacity constraints on all arcs and facilities. The problem is shown to be solvable directly by Fulkerson's out-of-kilter algorithm. Digital computer codes for this formulation require rapid access storage proportional to p instead of p². Computational results indicate that, in addition to handling the extensions, the out-of-kilter algorithm is more efficient in the solution of the original problem when there is a mad, rate number of commodities and a computer of limited storage capacity.