The reliability analysis of balking and reneging in a repairable system with warm standbys

We study the reliability analysis of a repairable system with operating units, warm standby units and repairmen in which the balking and reneging of units are considered. It is assumed that failed units balk (refuse to join) with a constant probability ( ) and renege (leave the queue after joining) according to a negative exponential distribution with parameter . The failure times of the operating unit and of a standby unit are assumed to be exponentially distributed with parameters λ and α, respectively. The repair time distribution is also exponential. The repairable system is out of , in which . The reliability characteristics, such as the system reliability and the mean time to system failure (MTTF), in a repairable system are derived. Several cases are analysed graphically to study the effect of various parameters on the reliability and MTTF of the system. Copyright © 2002 John Wiley & Sons, Ltd.     

Distributional properties of estimated capability indices based on subsamples

Under the assumption of normality, the distribution of estimators of a class of capability indices, containing the indices , , and , is derived when the process parameters are estimated from subsamples. The process mean is estimated using the grand average and the process variance is estimated using the pooled variance from subsamples collected over time for an in‐control process. The derived theory is then applied to study the use of hypothesis testing to assess process capability. Numerical investigations are made to explore the effect of the size and number of subsamples on the efficiency of the hypothesis test for some indices in the studied class. The results for and indicate that, even when the total number of sampled observations remains constant, the power of the test decreases as the subsample size decreases. It is shown how the power of the test is dependent not only on the subsample size and the number of subsamples, but also on the relative location of the process mean from the target value. As part of this investigation, a simple form of the cumulative distribution function for the non‐central ‐distribution is also provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Eigenspannungen als Parameter des röntgenographischen Bruchkriteriums und der Lebensdauervoraussage

Residual stresses as parameters of X-ray criterion of fracture and of fatigue life prediction Fatigue testing is notorious for considerable scatter in specimen life even if special measures are taken to precisely control parameters of stress cycling. The reason for that must be ascribed to variation in material microstructure existing prior to fatigue loading. Structural condition of material may be determined by the following function: Extensive fatigue tests on α-Ti and (α + β)-Ti alloy at temperatures 77 K and 295 K showed that failure did not occur until function V reached its critical value at a plane characteristic of each lattice type (failure plane). The condition V = K may be therefore regarded an X-Ray criterion and, once determined numerically, a sort of material constant. The life N_B of fatigue tested specimen was found to be clearly depended on structural condition of virgin material exhibited natural variation of structural characteristics. The finite fatigue life was found to conform with the relationship The expression may be used for predicting life N_B if prior to fatigue loading the material condition function V value is made known for a characteristic lattice plane.     

A Comparative Study of Joint Monitoring Schemes for APC Processes

To monitor processes under automatic process control (APC), several joint monitoring schemes have recently been proposed, such as the U statistics, and , that originate from the uniformly most powerful test. It is known that the chart is sensitive to large shift detection whereas the chart is sensitive to small shift detection. To take advantage of both charts, this paper examines a combined use of the two U charts. A comparative study indicates that the combined procedure improves over a single U chart and performs better than other joint monitoring schemes, including Hotelling's chart for APC processes. Copyright © 2006 John Wiley & Sons, Ltd.     

An adaptive chart for monitoring the process mean and variance

Traditionally, an chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint and R charts with fixed or adaptive parameters, they are not reliable in identifying the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non‐central chi‐square statistic chart. This new chart is more effective than the adaptive and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright © 2006 John Wiley & Sons, Ltd.     

Determining the lifetime of CD‐RWs using efficient sampling on a production line

This work derives the intermittent batch size and sample size for product life testing on a production line. The sequential probability ratio test was adopted to determine the sample size, , and the expected number of samples (ENS). An inverse chi‐square approximation was used to determine the relationship between the degree of freedom, , and the estimated range of at various levels of confidence. Consequently, ENS and were used to determine the intermittent batch size, . Finally, rewritable compact disks (CD‐RWs) underwent testing to demonstrate the feasibility and effectiveness of the proposed efficient sampling approach. Copyright © 2003 John Wiley & Sons, Ltd.     

Capability measures for processes with multiple characteristics

Process capability indices, such as , , and , have been widely used in the manufacturing industry providing numerical measures on process precision, process accuracy, and process performance. Capability measures for processes with a single characteristic have been investigated extensively. However, capability measures for processes with multiple characteristics are comparatively neglected. In this paper, we consider a generalization of the yield index proposed by Boyles, for processes with multiple characteristics. We establish a relationship between the generalization and the process yield. We also develop a control chart based on the proposed generalization, which displays all the characteristic measures in one single chart. Using the chart, the engineers can effectively monitor and control the performance of all process characteristics simultaneously. Copyright © 2003 John Wiley & Sons, Ltd.     

Change of fatigue parameters with temperature

A fatigue crack growth rate (FCGR) equation, had been proposed which predicts the observed R-ratio effects correctly. Conceptually, this equation accounts for spectrum loading effects via the parameter “K”. The work presented deals with the temperature effect on the fatigue parameters entering the above FCGR-equation. For materials which do not experience a microstructural or a fracture mode transition within the temperature range of interest, the effect of temperature on the fatigue parameters “C” and “ΔK^T” can be interpolated or extrapolated from relatively few experimental data. Extrapolation of these fatigue parameters for Inconel X-750 measured between 300° K and 900° K allowed a very accurate prediction of the FCGR at 4° K. At higher temperatures the end of fatigue controlled crack growth is clearly indicated by a rapid increase of the fatigue parameter “C”. There, the fatigue parameter “C” increases withing a temperature span of 100° K by a factor of 10². This kind of information is of utmost importance for materials application at elevated temperatures as in nuclear systems.     

The variable sampling interval X̄ chart with estimated parameters

The VSI chart has been investigated by many researchers under the assumption of known process parameters. However, in practice, these parameters are usually unknown and it is necessary to estimate them from the past data. In this paper, we evaluate and compare the performance of the VSI chart in terms of its average time to signal in the case where the process parameters are known and in the case where these parameters are estimated. We also provide new chart constants taking into account the number of phase I samples. Copyright © 2011 John Wiley & Sons, Ltd.     

Measuring process capability based on Cpmk with gauge measurement errors

Due to their effectiveness and simplicity of use, the process capability indices , , and have been popularly accepted in the manufacturing industry as management tools for evaluating and improving process quality. Combining the merits of those indices, a more advanced index, , is proposed that takes into account process variation, process centering, and the proximity to the target value, and has been shown to be a very useful index for manufacturing processes with two‐sided specification limits. Most research works related to assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when highly advanced measurement instruments are employed. Conclusions drawn regarding process capability are therefore unreliable and misleading. In this paper, we conduct a sensitivity investigation for the process capability index in the presence of gauge measurement errors. We consider the use of capability testing of as a method for obtaining lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that using the estimator with sample data contaminated by measurement errors severely underestimates the true capability, resulting in an imperceptibly smaller test power. To measure the true process capability, three methods for the adjusted confidence bounds are presented and their performances are compared using computer simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

On the distribution of the estimated process yield index Spk

This paper considers an asymptotic distribution for an estimate of the process yield index proposed by Boyles (1994). The asymptotic distribution of is useful in statistical inferences for . An illustrative example is given for hypothesis testing and for interval estimation on the yield index . Copyright © 2002 John Wiley & Sons, Ltd.     

A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance

This article compares the effectiveness and robustness of nine typical control charts for monitoring both process mean and variance, including the most effective optimal and adaptive sequential probability ratio test (SPRT) charts. The nine charts are categorized into three types (the type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and adaptive version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and adaptive charts are designed optimally in order to minimize an index average extra quadratic loss for the best overall performance. Moreover, the probability distributions of the mean shift δ_µ and standard deviation shift δ_σ are studied explicitly as the influential factors in a factorial experiment. The main findings obtained in this study include: (1) From an overall viewpoint, the SPRT‐type chart is more effective than the CUSUM‐type chart and type chart by 15 and 73%, respectively; (2) in general, the adaptive chart outperforms the optimal chart and basic chart by 16 and 97%, respectively; (3) the optimal CUSUM chart is the most effective fixed sample size and sampling interval chart and the optimal SPRT chart is the best choice among the adaptive charts; and (4) the optimal sample sizes of both the charts and the CUSUM charts are always equal to one. Furthermore, this article provides several design tables which contain the optimal parameter values and performance indices of 54 charts under different specifications. Copyright © 2011 John Wiley & Sons, Ltd.     

A variable metric algorithm for constrained minimization based on an augmented Lagrangian

This paper concerns the implementation of a recent idea, attributed to Hestenes and Powell, based on solving the equality constrained finite dimensional minimization problem via the unconstrained problem where ? is a non-linear functional, g is a non-linear mapping into R^p, K is a prescribed matrix of penalty constants and λ is the Lagrange multiplier. The computational algorithm is based on restoring active constraints to first order and adjusting x in the remaining necessary conditions by gradient projection. The minimization is performed by the variable metric rank-two BGFS update with linear search by cubic interpolation. Computational results using the algorithm include two problems of minimum fuel trajectory optimization—two impulse rendezvous with Comet Encke and three impulse constrained positioning of a geostationary satellite.     

Mechanische Druckbestimmungen mit Turbopumpen

Some simple and useful equations were obtained by experiments with a turbomolecular pump (TMP 340). After switching off the current of the motor the rotation frequenzy f decreases proportionally with the time t: f(t) = f₀ ? αt . The coefficient α depends on the gasflow Q and the roughing pressure p _vv . An other linear equation is obtained for the retarding factor Δf/Δt in dependance of the roughing pressure . With increasing molecular mass M the factor - m decreases exponentially by the ratio of tangential rotation speed u _t to the most probable molecular speed c _w . The equation shows the same parameters as the compression ratio of any turbomolecular pump. The parameter Γ is effected by the geometrical dimensions of the pump. These results are valid within the molecular mass range 2 ? M ? 130 . The energy consumption of the pump and other quantities can be calculated by the parameters – Δf/Δt and m.     

A sensitivity analysis of an integrated model for joint determination of economic design of $\overline{x}$‐control charts,economic production quantity and production run length for a deteriorating production system

This study presents an integrated model for the joint economic design of ‐control charts and maintenance schedules and, simultaneously, determines the economic production quantity and production run length for a deteriorating production system. The operating state of the production process is classified as either in control or out of control. In the latter state, the process produces some defective items. An ‐control chart is used to monitor the process mean. Both uniform and non‐uniform inspection schemes are adopted. Inspection and maintenance are performed simultaneously. Replacement cost is assumed to be very high. The process failure mechanism is assumed to follow a general probability distribution with an increasing failure rate. The concept of a truncated production cycle is introduced. The production cycle begins when a new component is installed and ends with a repair after the detection of a failure or after a specified number of inspection intervals, , whichever occurs first. The effects of preventive maintenance on quality control are discussed. Numerical examples are provided to evaluate the performance of the model. Sensitivity analyses are conducted to study the effects of various model parameters. Copyright © 2002 John Wiley & Sons, Ltd.     

Attribute Charts for Monitoring a Dependent Process

For some repetitive production processes, the quality measure taken on the output is an attribute variable. An attribute variable classifies each output item into one of a countable set of categories. One of the simplest and most commonly used attribute variables is the one which classifies an item as either ‘conforming’ or ‘non‐conforming’. A tool used with a considerable amount of success in industry for monitoring the quality of a production process is the quality control chart. Generally a control charting procedure uses a sequence, of the quality measures to make a decision about the quality of the process. How this sequence is used to make a decision defines the control chart. In order to design a control chart one must consider how the underlying sequence, is modeled. The sequence is often modeled as a sequence of independent and identically distributed random variables. For many industrial processes, this model is appropriate, but in others it may not be. In this paper, a sequence of random variables, is used to classify an item as conforming or non‐conforming under a stationary Markov chain model and under 100% sequential sampling. Two different control charting schemes are investigated. Both schemes plot a sequence of measures on the control chart, that count the number of conforming items before a non‐conforming item. The first scheme signals as out‐of‐control if a value of falls below a certain lower limit. The second scheme signals as out‐of‐control if two out of two values of fall below a certain lower limit. The efficiency of both of the control charts is evaluated by the average run length (ARL) of the chart and the power of the chart to detect a shift in the process. The two out of two scheme is shown to have high power and a large ARL given certain parameter values of the process. An example of the two out of two scheme is provided for the interested reader. Copyright © 2006 John Wiley & Sons, Ltd.     

Three-dimensional crack analysis using singular boundary elements

A multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The displacement and traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.     

On the reliability of the estimated incapability index

Greenwich and Jahr‐Schaffrath (1995) introduced the process incapability index , which provides an uncontaminated separation between information concerning the process precision and process accuracy . In this paper, we consider the three indices, and investigate the statistical properties of their natural estimators. For the three indices, we obtain their UMVUEs and MLEs, and compare the reliability of the two estimators based on the relative mean square errors. In addition, we construct 90%, 95%, and 99% upper confidence limits, and the maximum values of for which the process is capable 90%, 95%, and 99% of the time. The results obtained in this paper are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability. Copyright © 2001 John Wiley & Sons, Ltd.     

An Improved R (Range) Control Chart for Monitoring the Process Variance

An R chart is often used to monitor shifts in the process variability. However, the range, , statistics from a sampling distribution are highly skewed. Hence, the classical R chart based on the control limits will not give an in‐control average run length of approximately 370, or equivalently a type I error, . In this paper, an approach is shown to obtain the control limits of an improved R chart based on a desired type I error from the density function of the R_i statistics. Copyright © 2004 John Wiley & Sons, Ltd.     

Fabrication of metal/sheathed high-Tc superconducting composites by explosive compaction/cladding: numerical simulation

Explosive compaction/cladding, usually followed by forming, is a technique used extensively for fabricating multilayer sandwich components of the same or different materials. In this paper, we report on experimental and numerical investigations into the explosive compaction/cladding for fabricating superconducting Y–Ba–Cu–O ceramic/metal composite grooved discs. The manufacturing process is numerically simulated by using the explicit finite element code LS-DYNA3D. The final dimensions of the compact and the pressure, temperature and density distributions during the entire cladding compaction process are predicted. The proposed model is validated, as the numerical results obtained were in good agreement with the experimental results.