Non‐normal Capability Indices for the Weibull and Lognormal Distributions

Because the normal process capability indices (PCIs) C_p, C_pu, C_pl, and C_pk represent the times that the process standard deviation is within the specification limits; then, based on and by using the direct relations among the parameters of the Weibull, Gumbel (minimum extreme value type I) and lognormal distributions, the Weibull and lognormal PCIs are derived in this paper. On the other hand, because the proposed PCIs P_p, P_pu, P_pl, and P_pk were derived as a function of the mean and standard deviation of the analyzed process, they have the same practical meaning with those of the normal distribution. Results show that the proposed PCIs could be used as the standard C_p, C_pu, C_pl, and C_pk if a short‐term variance is analyzed. An application to a set of simulated data is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

A Method of Estimating the Process Capability Index from the First Four Moments of Non‐normal Data

A method is presented to estimate the process capability index (PCI) for a set of non‐normal data from its first four moments. It is assumed that these four moments, i.e. mean, standard deviation, skewness, and kurtosis, are suitable to approximately characterize the data distribution properties. The probability density function of non‐normal data is expressed in Chebyshev–Hermite polynomials up to tenth order from the first four moments. An effective range, defined as the value for which a pre‐determined percentage of data falls within the range, is solved numerically from the derived cumulative distribution function. The PCI with a specified limit is hence obtained from the effective range. Compared with some other existing methods, the present method gives a more accurate PCI estimation and shows less sensitivity to sample size. A simple algebraic equation for the effective range, derived from the least‐square fitting to the numerically solved results, is also proposed for PCI estimation. Copyright © 2004 John Wiley & Sons, Ltd.     

Performance of Multivariate Process Capability Indices Under Normal and Non‐Normal Distributions

In the context of process capability analysis, the results of most processes are dominated by two or even more quality characteristics, so that the assessment of process capability requires that all of them are considered simultaneously. In recent years, many researchers have developed different alternatives of multivariate capability indices using different approaches of construction. In this paper, four of them are compared through the study of their ability to correctly distinguish capable processes from incapable processes under a diversity of simulated scenarios, defining suitable minimum desirable values that allow to decide whether the process meets or does not meet specifications. In this sense, properties analyzed can be seen as sensitivity and specificity, assuming that a measure is sensitive if it can detect the lack of capability when it actually exists and specific if it correctly identifies capable processes. Two indices based on ratios of regions and two based on the principal component analysis have been selected for the study. The scenarios take into account several joint distributions for the quality variables, normal and non‐normal, several numbers of variables, and different levels of correlation between them, covering a wide range of possible situations. The results showed that one of the indices has better properties across most scenarios, leading to right conclusions about the state of capability of processes and making it a recommendable option for its use in real‐world practice. Copyright © 2015 John Wiley & Sons, Ltd.     

Some Modifications of the Classical Pre‐control Technique

Pre‐control is a simple technique for the initial evaluations of the capability of a process. It can be seen as a tool to get the set‐up approval or fulfilment of the specifications of a production process. As the resultant information of pre‐control should be used to adjust the process, it can be understood as a form of feedback controller. It has sometimes been considered as an alternative to statistical control charts for monitoring processes, although these tools differ in a number of ways. In this work, we propose some new alternatives to the classical pre‐control, particularly in its initial phase that aim to qualify the process, that is, to certify that it is capable. We present a comparative analysis of the power of the different alternatives. Copyright © 2003 John Wiley & Sons, Ltd.     

On the Performance of Phase‐I Bivariate Dispersion Charts to Non‐Normality

A phase‐I study is generally used when population parameters are unknown. The performance of any phase‐II chart depends on the preciseness of the control limits obtained from the phase‐I analysis. The performance of phase‐I bivariate dispersion charts has mainly been investigated for bivariate normal distribution. However, this assumption is seldom fulfilled in reality. The current work develops and studies the performance of phase‐I |S| and |G| charts for monitoring the process dispersion of bivariate non‐normal distributions. The necessary control charting constants are determined for the bivariate non‐normal distributions at nominal false alarm probability (FAP₀). The performance of these charts is evaluated and compared in a situation when samples are generated by bivariate logistic, bivariate Laplace, bivariate exponential, or bivariate t₅ distribution. The analysis shows that the proper consideration to underlying bivariate distribution in the construction of phase‐I bivariate dispersion charts is very important to give a real picture of in or out of control process status. Copyright © 2016 John Wiley & Sons, Ltd.     

Computing process capability indices for non‐normal data: a review and comparative study

When the distribution of a process characteristic is non‐normal, C_p and C_pk calculated using conventional methods often lead to erroneous interpretation of the process's capability. Though various methods have been proposed for computing surrogate process capability indices (PCIs) under non‐normality, there is a lack of literature that covers a comprehensive evaluation and comparison of these methods. In particular, under mild and severe departures from normality, do these surrogate PCIs adequately capture process capability, and which is the best method(s) in reflecting the true capability under each of these circumstances? In this paper we review seven methods that are chosen for performance comparison in their ability to handle non‐normality in PCIs. For illustration purposes the comparison is done through simulating Weibull and lognormal data, and the results are presented using box plots. Simulation results show that the performance of a method is dependent on its capability to capture the tail behaviour of the underlying distributions. Finally we give a practitioner's guide that suggests applicable methods for each defined range of skewness and kurtosis under mild and severe departures from normality. Copyright © 1999 John Wiley & Sons, Ltd.     

Autocorrelated SPC for Non‐Normal Situations

The importance of statistical process control (SPC) techniques in quality improvement is well recognized in industry. However, most conventional SPC techniques have been developed under the assumption of independent, identically and normally distributed observations. With advances in sensing and data capturing technologies, large volumes of data are being routinely collected from individual units in manufacturing industries. These data are often autocorrelated and skewed. Conventional SPC techniques can lead to false alarms or other types of poor performance monitoring of such data. There is a great need for process control techniques for variation reduction in these environments. Much recent research has focused on the development of appropriate SPC techniques for autocorrelated data, but few studies have considered the impact of non‐normality on these techniques. This paper investigates the effect of skewness on conventional autocorrelated SPC techniques, and provides an effective approach based on a scaled weighted variance approach to improve SPC performance in such an environment. Copyright © 2005 John Wiley & Sons, Ltd.     

On Efficient Skewness Correction Charts Under Contamination and Non‐normality

Shewhart control charts are very popular in a variety of disciplines such as industry, agriculture and medical science. The design structure of the usual Shewhart charts depends on normality and one point decision rule. This makes the scope of these charts quite limited and not very efficient for small shifts. This study comes up with an intermediate solution by implementing runs rules schemes and adjusting the limits' coefficients for non‐normality using the idea of skewness correction. We have covered some commonly used location and dispersion charts, namely , R and S charts. We have investigated the performance of the proposals in terms of false alarm rate and signalling probability. We have observed that the proposals serve the dual purpose in terms of robustness and efficiency. The study also provides an application example using numerical dataset. Copyright © 2015 John Wiley & Sons, Ltd.     

EWMA Dispersion Control Charts for Normal and Non‐normal Processes

Process monitoring through control charts is a quite popular practice in statistical process control. This study is planned for monitoring the process dispersion parameter using exponentially weighted moving average (EWMA) control chart scheme. Most of the EWMA dispersion charts that have been proposed are based on the assumption that the parent distribution of the quality characteristic is normal, which is not always the case. In this study, we develop new EWMA charts based on a wide range of dispersion estimates for processes following normal and non‐normal parent distributions. The performance of all the charts is evaluated and compared using run length characteristics (such as the average run length). Extra quadratic loss, relative average run length, and performance comparison index measures are also used to examine the overall effectiveness of the EWMA dispersion charts.Copyright © 2014 John Wiley & Sons, Ltd.     

Non‐ionic Dendronized Multiamphiphilic Polymers as Nanocarriers for Biomedical Applications

A new class of non‐ionic dendronized multiamphiphilic polymers is prepared from a biodegradable (AB)_n‐type diblock polymer synthesized from 2‐azido‐1,3‐propanediol (azido glycerol) and polyethylene glycol (PEG)‐600 diethylester using Novozym‐435 (Candida antarctica lipase) as a biocatalyst, following a well‐established biocatalytic route. These polymers are functionalized with dendritic polyglycerols (G1 and G2) and octadecyl chains in different functionalization levels via click chemistry to generate dendronized multiamphiphilic polymers. Surface tension measurements and dynamic light scattering studies reveal that all of the multiamphiphilic polymers spontaneously self‐assemble in aqueous solution. Cryogenic transmission electron microscopy further proves the formation of multiamphiphiles towards monodisperse spherical micelles of about 7–9 nm in diameter. The evidence from UV–vis and fluorescence spectroscopy suggests the effective solubilization of hydrophobic guests like pyrene and 1‐anilinonaphthalene‐8‐sulfonic acid within the hydrophobic core of the micelles. These results demonstrate the potential of these dendronized multiamphiphilic polymers for the development of prospective drug delivery systems for the solubilization of poorly water soluble drugs.     

Non‐destructive Examination of Loads in Regular and Self‐locking Spiralock® Threads through Energy‐resolved Neutron Imaging

Energy‐resolved neutron transmission imaging is utilised for in situ comparisons of strain distributions in fastened assemblies with regular and self‐locking Spiralock® female threads. The strain maps measured within torqued steel bolts indicate that for a Spiralock® thread, the load is distributed over a larger section of the fastener, making this type of thread more suitable for fastening of assemblies subject to transverse vibrations.     

Non‐linear analysis of structures using high performance hybrid elements

In this work, we describe the formulation and implementation for stress‐based hybrid elements for conducting non‐linear analysis of elastic structures. The motivation behind developing these elements is that they should be as simple to use as standard displacement‐based isoparametric brick elements, but at the same time, be relatively immune to the shortcoming that these elements suffer from, namely, ‘locking’ problems which occur when they are used to model plate/shell geometries, almost incompressible materials or when the elements are distorted, and so on. The formulation is based on a two‐field mixed variational principle. Numerical examples are presented to demonstrate the excellent performance of the proposed elements on a variety of challenging problems involving very large deformations, buckling, mesh distortions, almost incompressible materials, etc. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating the Change Point of the Process Fraction Non‐conforming with a Monotonic Change Disturbance in SPC

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we propose a maximum‐likelihood estimator for the change point of the process fraction non‐conforming without requiring knowledge of the exact change type a priori. Instead, we assume the type of change present belongs to a family of monotonic changes. We compare the proposed change‐point estimator to the maximum‐likelihood estimator for the process change point derived under a simple step change assumption. We do this for a number of monotonic change types and following a signal from a binomial cumulative sum (CUSUM) control chart. We conclude that it is better to use the proposed change point estimator when the type of change present is only known to be monotonic. The results show that the proposed estimator provides process engineers with an accurate and useful estimate of the time of the process change regardless of the type of monotonic change that may be present. Copyright © 2006 John Wiley & Sons, Ltd.     

A Comparison of MCUSUM‐based and MEWMA‐based Spatiotemporal Surveillance Under Non‐homogeneous Populations

Motivated by the application in health‐care surveillance under non‐homogeneous populations, this paper compares the performance of multivariate exponentially weighted moving average (MEWMA)‐based methods with that of multivariate cumulative sum (MCUSUM)‐based methods for spatiotemporal chronic disease surveillance. We perform the comprehensive simulation studies of the MEWMA‐based methods for the selection of weight parameters. Under temporally or spatially non‐homogeneous population trends, we compare the MEWMA methods with the MCUSUM methods, which are specific forms of the spatiotemporal scan statistics if the baseline rate is known. The performance of the MCUSUM methods has extreme variations depending on whether the change occurs on a small population or a large population. When the change occurs in the time period or within the spatial region with a small population, the weighted likelihood ratio‐based MCUSUM has better detection speed, but worse identification of detection clusters than the likelihood ratio‐based MCUSUM. On the other hand, when the change occurs in the time period or within the region with a large population, the weighted likelihood ratio‐based MCUSUM has worse detection speed, but better identification than the likelihood ratio‐based MCUSUM. Unlike the MCUSUM methods, the MEWMA‐based methods show relatively stable and robust performance in terms of detection speed, and they show better identification than the MCUSUM‐based methods under most cases. Copyright © 2014 John Wiley & Sons, Ltd.     

A t‐chart for Monitoring Multi‐variety and Small Batch Production Run

Statistical process control is an important tool to monitor and control a process. It is used to ensure that the manufacturing process operates in the in‐control state. Multi‐variety and small batch production runs are common in manufacturing environments like flexible manufacturing systems and Just‐in‐Time systems, which are characterized by a wide variety of mixed products with small volume for each kind of production. It is difficult to apply traditional control charts efficiently and effectively in such environments. The method that control charts are plotted for each individual part is not proper, since the successive state of the manufacturing process cannot be reflected. In this paper, a proper t‐chart is proposed for implementation in multi‐variety and small batch production runs to monitor the process mean, and its statistical properties are evaluated. The run length distribution of the proposed t‐chart has been obtained by modelling the multi‐variety process. The ARL performance for various shifts, number of product types, and subgroup sizes has also been obtained. The results show that the t‐chart can be successfully implemented to monitor a multi‐variety production run. Finally, illustrative examples show that the proposed t‐chart is effective in multi‐variety and small batch manufacturing environment. Copyright © 2013 John Wiley & Sons, Ltd.     

Measuring PPM Non‐conformities for Processes with Asymmetric Tolerances

Process yield has been the most basic and common criterion used in the manufacturing industry for evaluating process capability. The C_pk index has been used widely in the manufacturing industry. In this note, we considered a generalization of C_pk index which handles processes involving a target T with asymmetric tolerances. Particularly, we established a formula for measuring the PPM non‐conformities for given ratios of the two‐side tolerances. We proved the validity of the established formula and tabulated the upper bounds on PPM non‐conformities for various given C_pk index values and ratios of the two‐side tolerances. Copyright © 2012 John Wiley & Sons, Ltd.     

Using independent component analysis to monitor 2‐D geometric specifications

Functional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2‐dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non‐normality of the error term is present. The performance of this method is evaluated and compared with a regression‐ and PCA‐based approach through simulation of the average run length criterion. The results reveal that the proposed ICA‐based approach is robust against non‐normality in the in‐control analysis, and its out‐of‐control performance is on par with that of the PCA‐based method in case of normal and near‐normal error terms.     

The development of a target‐focused process capability index with multiple characteristics

Within an industrial manufacturing environment, Process Capability Indices (PCIs) enable engineers to assess the process performance and ultimately improve the product quality. Despite the fact that most industrial products manufactured today possess multiple quality characteristics, the vast majority of the literature within this area primarily focuses on univariate measures to assess process capability. One particular univariate index, C_pm, is widely used to account for deviations between the location of the process mean and the target value of a process. While some researchers have sought to develop multivariate analogues of C_pm, modeling the loss in quality associated with multiple quality characteristics continues to remain a challenge. This paper proposes a multivariate PCI that more appropriately estimates quality loss, while offering greater flexibility in conforming to various industrial applications, and maintaining a more realistic approach to assessing process capability. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessing the Proportion of Conformance of a Process from a Bayesian Perspective

A Bayesian technique for assessing the posterior probability that the proportion of conformance of a normally distributed process exceeds a particular value is suggested. Both exact and approximate formulae for the assessment of this probability are derived. Copyright © 2013 John Wiley & Sons, Ltd.