Stochastic Processes

In quality control, a proper Phase I analysis is essential to the success of Phase II monitoring. A literature review reveals no distribution-free Phase I multivariate techniques in existence. This research develops a Phase I location control chart for multivariate elliptical processes. The resulting in-control reference sample can then be used to estimate the parameters for Phase II monitoring. Using Monte Carlo simulation, the proposed method is compared with the Hotelling's T² Phase I chart. Although Hotelling's T² chart is preferred when the data are multivariate normal, the proposed method is shown to perform significantly better under nonnormality. This article has supplementary material online.     

Designing Phase I Shewhart X¯charts: Extended tables and software

Control charts play an important role in Phase I studies, which are conducted to establish process control and generate reference data for parameter estimation and calculation of prospective (Phase II) control limits. Researchers have tabulated the necessary charting constants for the normal theory–based Phase I Shewhart $\overline{X}$ chart for the process mean to achieve a desired nominal false alarm probability given the number of Phase I subgroups, m, up to 15. However, in practice, when parameters are estimated, the currently recommended number of Phase I subgroups is much larger than covered by their tables. Recognizing the need and taking advantage of some recently available software and computing resources, an extension to these tables is provided for m = 3(1)10 , 15(5)30 , 50(25)300 and n = 3 , 5 , 7 , 10. In addition to the tables, an R program is provided to calculate the charting constant, on demand, for user‐given values of nominal false alarm probability, m, and n. An appendix shows the details of how the program should be used.     

Phase I control charts for independent Bernoulli data

Phase I Shewhart p, np and runs of conforming charts are investigated. The performance of these charts are assessed using the probability of a false alarm. As with other Phase I Shewhart charts, the probability of a false alarm increases as the number, m, of samples increases for a fixed sample size, n. For a fixed value of m, the probability of at least one signal decreases as the sample size n increases. The probability of a signal for a runs of conforming chart depends on the number of samples m. Like the p and np charts, as m increases the probability of a false alarm increases. Unlike the p and np charts, the false alarm rate for a runs of conforming chart does not depend on the in‐control value of p. Copyright © 2001 John Wiley & Sons, Ltd.     

Inorganic salts and extractability of fresh and frozen fish proteins

Changes in protein extractability (PE) were followed in minced cod meat and in meat washed with distilled water containing added NaCl, KCl, MgCl₂, CaCl₂, and phosphates. In minces stored for 24 h at 4°C and pH 5.5–7.2 the PE decreases with increasing acidity. The same is also true in samples containing 0.2 M of added NaCl 100 g⁻¹ or KCl 100 g⁻¹, while in the presence of MgCl₂ and CaCl₂ in the same concentration PE is very significantly lower than in the control and does not depend so much upon the acidity of the mince.In water extracted and frozen minces after two weeks at−20°C at pH 7.2 and 6.4 the PE is 25% and 50% lower, respectively, than before freezing. NaCl, KCl, MgCl₂, and CaCl₂ added to the washed meat in concentrations corresponding to μ = 0.15 decrease the PE after two weeks of frozen storage by about 7%, 20%, 16%, and 43%, respectively.At μ>0.25, KCl, phosphates, and KCl+CaCl₂ have, during two weeks, a protective effect on PE. In water extracted mince PE decreases after 1 d at −20°C by 15%, which corresponds to a drop in PE in unextracted samples at pH 6.9 only after five weeks. A mixture of salts added to the water extracted mince, corresponding in composition and μ to those in cod flesh, brings about, after prolonged frozen storage, a drop in PE much higher than that in extracted samples.     

Determination of material fracture toughness by a computational/experimental approach for rapid crack propagation in PE pipe

Based on an investigation of the Small Scale Steady State (S4) test, an integrated computational/ experimental approach has been developed in order to assess the fracture behaviour of polyethylene (PE) gas distribution pipe material during rapid crack propagation (RCP). This paper describes the use of the results obtained from the S4 test and program modified from PFRAC (Pipeline Fracture Analysis Code) to evaluate the fracture toughness of the material, G _d, which could not be directly obtained from the test, and to predict critical pressure, p _c, for RCP in a full scale PE pipe. The contact algorithms are developed to consider the opening pipe wall impact against a series of containment rings and the capabilities of PFRAC are also extended. Since G _d is evaluated, the investigations are made on it to the effect of temperature and wall thickness. In addition, procedures to evaluate the critical pressure for the S4 test pipe are also discussed.     

A comparative study of phase II robust multivariate control charts for individual observations

Use of Hotelling's T² charts with high breakdown robust estimates to monitor multivariate individual observations are the recent trend in the control chart methodology. Vargas (J. Qual. Tech. 2003; 35: 367‐376) introduced Hotelling's T² charts based on the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD) estimates to identify outliers in Phase I data. Studies carried out by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615‐629) indicated that the performance of these charts heavily depends on the sample size, amount of outliers and the dimensionality of the Phase I data. Chenouri et al. (J. Qual. Tech. 2009; 41: 259‐271) recently proposed robust Hotelling's T² control charts for monitoring Phase II data based on the reweighted MCD (RMCD) estimates of the mean vector and covariance matrix from Phase I. They showed that Phase II RMCD charts have better performance compared with Phase II standard Hotelling's T² charts based on outlier free Phase I data, where the outlier free Phase I data were obtained by applying MCD and MVE T² charts to historical data. Reweighted MVE (RMVE) and S‐estimators are two competitors of the RMCD estimators and it is a natural question whether the performance of Phase II Hotelling's T² charts with RMCD and RMVE estimates exhibits similar pattern observed by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615‐629) in the case of MCD and MVE‐based Phase I Hotelling's T² charts. In this paper, we conduct a comparative study to assess the performance of Hotelling's T² charts with RMCD, RMVE and S‐estimators using large number of Monte Carlo simulations by considering different data scenarios. Our results are generally in favor of the RMCD‐based charts irrespective of sample size, outliers and dimensionality of Phase I data. Copyright © 2010 John Wiley & Sons, Ltd.     

Process Control for the Vector Autoregressive Model

Multivariate monitoring techniques for serially correlated observations have been widely used in various applications. This study examines several issues that have arisen in relation to the statistical quality control for the vector autoregressive (VAR) model, using a Monte Carlo approach. Different versions of the Hotelling T² statistic and control limits to monitor the VAR‐type process for both Phase I and Phase II schemes can be specified for different sample sizes and configurations of the model. Our simulation study suggests that the Hotelling's T² statistic can be tested against the χ² critical values during Phase I, but should be tested against scaled F critical values during Phase II. An unbiased covariance estimate of residuals is also recommended during Phase II when sample size is typically small. By reanalyzing some real data examples, the authors offer new conclusions. Copyright © 2012 John Wiley & Sons, Ltd.     

A general approach for testing the process capability index

This paper presents a generalized approach to the problem of testing with the process capability index C?_p. It allows for testing at any α-level and any sample size. For small sample sizes n < 30, n odd, tables are included with αs incremented by 0.025, which are generated by a computer program. This program is written in BASIC and appears in an Appendix. For different α levels (say α = 0·1) the program can be used to generate the appropriate value to use in determining the critical values. For larger sample sizes an approximation method is supplied. Additionally, the method to derive an associated operating characteristic curve is examined.     

Gas permeability in the polystyrene films uniaxially drawn under CO2 plasticizing

 Gas permeability coefficients, Ps, of CO₂, O₂, and N₂ have been measured in four kinds of polystyrene (PS) films: an unconditioned film with no orientation (1), a high pressure CO₂-conditioned film with no orientation (2), an uniaxially hot-drawn film with some orientation (3), and a film uniaxially drawn under CO₂ plasticizing with some orientation (4). Wide angle X-ray diffraction (WAXD) scans for each sample have also been made. High-pressure CO₂-conditioning effect was confirmed from the result that P values for any permeation gas in sample 2 were larger than those in sample 1. Values of P for any gas in sample 3 were almost close to those in sample 1 and decreased slightly with Hermans orientation function, f. Gas permeability coefficients in sample 4 are larger than those in sample 3 over the whole range of f studied in this work and increased with f. These results were discussed from a viewpoint of inter-segmental distances for PS films. Received: 2 January 1997 / Accepted: 27 March 1997     

不同包装材料对酱肉挥发性风味物质的影响

目的 研究酱肉在PET/AL/PE铝箔包装、PET/PE透明包装条件下不同时间段的挥发性风味物质的变化。方法 采用顶空固相微萃取–气相色谱–质谱连用法(SPME–GC–MS)并结合相对气味活度值(ROAV)、主成分分析(PCA)对酱肉挥发性风味物质变化进行分析。结果 研究发现,酱肉中挥发性物质主要为酯类、醇类,其中苯甲酸乙酯、乙酸芳樟酯、癸酸乙酯、正己酸乙酯、(+)–柠檬烯、壬醛、正己醛、(–)–4–萜品醇、桉叶油醇、芳樟醇、乙基麦芽酚、茴香脑的ROVA值大于1,为关键风味物质。PCA分析得出,2–甲基丁酸乙酯、(E,E)–2,4–壬二烯醛、正己酸乙酯、2,5–辛二酮、(1R)–2,6,6–三甲基双环[3.1.1]庚–2–烯、3–甲硫基丙醛、异丁酸乙酯、茴香脑为特征性挥发性风味物质。另外,通过对在PET/AL/PE铝箔和PET/PE透明包装下,酱肉各类风味物质含量、主体香味物质和异味物质ROVA值、主成分分析的比较,说明不同包装材料对酱肉挥发性风味物质的成分、含量均有影响。结论 从长期检测的结果看出,PET/AL/PE铝箔包装比PET/PE透明包装可显著地阻止脂肪氧化,较少生成异味物,可更好地保护酱肉的香味,为酱肉的贮藏保鲜提供了依据。     

Guaranteed in‐control performance of the EWMA chart for monitoring the mean

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in‐control average run‐length (ARL_IN). Recent research has highlighted the high variability in the in‐control performance of these charts. This has led to the recommendation of studying of the conditional in‐control average run‐length (CARL_IN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARL_IN distribution and the exceedance probability criterion (EPC). The CARL_IN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in‐order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and graphs of the adjusted constants are provided. An in‐control and out‐of‐control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in‐control and out‐of‐control performance tradeoff can be made to improve performance.     

Reliabilitv Growth During a Development Testing Progiam

The problem of estimating reliability of a system undergoing development testing is examined. It is assumed that the test program is conducted in K stages and that similar items are tested within each stage. In addition, it is assumed that the probability of an inherent failure, q ₀, remains constant throughout the test program while the probability of an assignable cause failure in the i-th stage, q_i , does not increase with i. The number of inherent failures, of assignable cause failures, and of successes is recorded in each stage. Maximum likelihood estimates of q ₀, q _i (i = 1, 2, …,K) and a conservative confidence bound for the reliability in the K-th stage are obtained. Numerical examples to illustrate the methods are given.     

Distributions in Statistics: Continuous Univariate Distributions-1 and 2

The density of a symmetric statistic T = g(X ₁, X ₂, …, X_n ), for a random sample from a mixed population with density f(x) = pf ₁(x) + pf ₂), is a binomial mixture of the densities of the statist.ics T_k = g(X_k1 , X_k2 , X_kn ), k = 0, 1, … n. where X_ki 's are independent with density f ₁(x) if i ≤ k and density f ₂(x) if i > k. It is shown how to find the distributions of some important symmetric statistics like sample mean, sample variance, and order statistics by using T_k 's. The results are applied to normal and exponential mixtures.     

Comparative study of size and distribution of lamellar thicknesses and long periods in polyethylene with a shish-kebab structure

This study contains a combined application of three different techniques for the study of injection moulded polyethylene (PE), showing an oriented shish-kebab structure: small angle X-ray scattering (SAXS), low frequency Raman spectroscopy (LAM) and transmission electron microscopy (TEM), A series of linear PEs and molecular weights in the range 51000–478000 has been investigated and two injection temperatures have been used (T _m=144 and 210 °C). SAXS patterns from the highly oriented regions show the presence of either one axial long period (L ₁) or two (L ₁ and L ₂) depending on molecular weight (¯M _w) and T _m. It is shown that L ₁ and L ₂ increase with ¯M _w up to a given critical molecular weight ¯M _c. Above ¯M _c, L ₁ and L ₂ remain constant. Raman results qualitatively confirm the existence of two separate distributions of straight-length chain segments for those samples having molecular weights above the critical value. Shorter segments are shown to be more abundant than the longer ones. In the lowest molecular weight sample, results from SAXS, TEM and Raman spectroscopy seem to be consistent with each other, although in some cases a tilted molecular arrangement within the lamellae has to be invoked. On the other hand, in case of the highest molecular weight sample, the length of the short straight-chain segments derived from Raman spectroscopy agrees well with the double periodicity obtained from SAXS. On the contrary, long periods measured from TEM only correspond to the shorter SAXS periodicity. This result is discussed by assuming the occurrence of crystalline bridges among adjacent lamellae.     

On the performance of coefficient of variation control charts in Phase I

Control charts are mainly carried out in 2 interconnected phases: Phase I (retrospective phase) and Phase II (monitoring phase). Phase I uses a stable historical sample to establish control limits that will be used later in Phase II. The preciseness of the control limits obtained from Phase I can greatly affect the performance of control charts in Phase II. Monitoring the coefficient of variation (CV) is an effective approach when the process mean or standard deviation is not constant. Until now, little work has been dedicated on investigating the performance of CV control charts in Phase I. Viewed under this perspective, this study investigates the performance of CV control charts in Phase I in terms of probability to signal. A real‐life example is also provided to illustrate the working of CV charts in Phase I.     

The predictive value of behavioural characteristics on the success of strategic alliances

An increasing number of companies are setting up strategic alliances with suppliers and customers. However, the majority of these alliances do not succeed. Our aim is to understand how different behavioural characteristics are associated with alliance success. We hypothesise that alliance attributes, communication behaviour, and alliance management are predictors of cost benefits and service benefits. Furthermore, we found that while alliance attributes are related with both cost and service benefits, communication behaviour and alliance management are only associated with service and cost benefits, respectively. We also see that alliance attributes explain most of the variance of supply chain success and are thus better predictors of alliance success than other behavioural characteristics. Furthermore, we provide insight into the way managers can build up supply chain performance by setting up strategic alliances.     

Delamination Controlled Ballistic Resistance of Polyethylene/Polyethylene Composite Materials

We have investigated ballistic response of polyethylene/polyethylene (PE/PE) composites to impact by Uzi bullets. For comparison, limited work was carried out on PE/aramid fiber hybrids and PE fiber/Polycarbonate plate laminates. The plates exhibited an average ballistic resistance, V ₅₀, of approximately 90 m/s per 1 kg/m² area density. In term of the protection level per thickness, the ballistic resistance was 76 m/s per 1 mm. Visual and microscopic examinations identified indentation and delamination as the prevailing failure mechanisms. The delamination, energy calculated on the basis of a simple delamination model considering the fracture surface energy of the matrix, was shown to fully balance the dissipated kinetic energy of the bullet, while the contribution of the fiber fracture process was negligible. This is taken as strong circumstantial evidence for the significant role of this failure process in the ballistic resistance of these composites.     

Process monitoring research with various estimator-based MEWMA control charts

Multivariate exponentially weighted moving average (MEWMA) control chart with five different estimators as population covariance matrix is rarely applied to monitor small fluctuations in the statistical process control. In this article, mathematical models of the five estimators (S₁, S₂, S₃, S₄, S₅) are established, with which the relevant MEWMA control charts are obtained, respectively. Thereafter, the process monitoring performance of the five control charts is simulated. And the simulation results show that the S₄ estimator-based MEWMA control chart is of the best performance both in step offset failure mode and ramp offset failure mode. Since the inline process monitoring of photovoltaic manufacturing is intended to be a problem of multivariate statistics process analysis, the feasibility and effectiveness of the proposed model are elaborated in the case study during the cell testing and sorting process control for the fabrication of multicrystalline silicon solar cells.     

Microstructural changes in polyethylene-polypropylene blends as revealed by microhardness

Microhardness is used to examine the microstructural changes of a series of polyethylene (PE) /polypropylene (PP) blends in a wide composition range. This study complements previous hardness results obtained on high-density/low-density polyethylene systems. The use of isotactic polypropylene, as a blend component allows investigation of a material in which the hardness of the amorphous phase, contrary to PE, differs from zero. The influence of treatments such as crystallization of the PP-phase in the presence of molten PE, within the blend, or annealing the PE phase, while leaving the PP component unmodified, are discussed with reference to the additivity hardness values of the single componentsH _PE andH _PP. It is shown that the coexistence of the PP and PE phases inhibits the crystallization capability of one phase and modifies the annealing behaviour of the other phase leading, as a result, to depressedH _PP andH _PE values. The observed deviations ofH _blend, throughout the composition range, from the additivity law of single components are quantitatively justified in the light of crystallinity changes of the PP phase and in terms of the population of modified lamellae of the PE component.