Simple Linear Profiles Research Articles

Process Capability Index for Simple Linear Profile in the Presence of Within- and Between-Profile Autocorrelation

In many situations, the quality of a process or product can be characterized by a functional relationship or profile. It is well-known that the independence assumptions of the error terms within or between profiles are not always valid and could be violated due to within or between profile autocorrelation. Since most of the process capability indices (PCIs) have been developed for simple linear profiles (SLPs) without considering autocorrelation, this paper provides some novel methods to analyze the capability of SLP under each of the two different autocorrelation effects separately, as well as the case where both autocorrelation effects are present. We assume that the first-order autoregressive AR(1) model explains the within- and between-profile autocorrelation in error terms. To evaluate the process capability, a new functional index called is introduced for SLP with independent errors, and then it is modified to include the three possible cases of within, between, and simultaneous autocorrelation. The simulation results demonstrate that the proposed schemes outperform existing schemes regarding bias and mean square error (MSE) criteria. Moreover, bootstrap confidence intervals for the proposed index are obtained. Finally, an illustrative example in the chemical industry is used to demonstrate the applicability of the proposed method.

A hybrid approach for estimating monotonic change points in the parameters of simple linear profiles in multistage processes

In this paper, a hybrid method is proposed for estimating monotonic change points in multistage processes where, at each stage, the quality of the process is represented by simple linear profile models. In the case of monotonic changes, the change type is not known a priori, and the only assumption is that the changes are non-decreasing or non-increasing in nature. In the proposed method, a support vector machine (SVM) algorithm is first developed to identify the parameters experiencing a change in each process stage. Then, the second SVM algorithm is applied to identify the type of change occurring in the related parameters. Finally, considering the identified parameters and change types, the maximum likelihood estimator (MLE) is proposed to estimate the change points of the process under different scenarios, including single and multiple change points, upward and downward step changes, increasing and decreasing linear trends, shift in both parameters of the profiles, shift in different stages of the process, and weak and strong autocorrelation coefficients. The performance of the proposed method is evaluated through extensive simulation experiments. The results indicate that the proposed method recognizes the patterns and estimates the monotonic change points accurately.

Process Capability Analysis for Simple Linear Profiles in Multistage Processes

When a process is statistically under control, one may be interested in assessing the process performance based on the specification limits provided by the customer. This evaluation is referred to as process capability analysis. Manufacturing operations are often involved with multistage processes, in which the output of a stage is the input of its subsequent stage. This property is known as the cascade property. Existing methods in capability analysis studies are not applicable when a process or product is represented by profiles. This study presents a method to conduct process capability analysis in a multistage process when quality of a product or process is characterized by a simple linear profile. The performance of the proposed method for a two-stage process is evaluated by numerical simulation using an example from the literature. The results indicate that the proposed method eliminates the effect of the cascade property for different shift sizes and autocorrelations.

Group runs control chart approach for monitoring simple linear profiles

Group runs control chart approach for monitoring simple linear profiles

Group runs control chart approach for monitoring simple linear profiles

Group runs control chart approach for monitoring simple linear profiles

Phase-II monitoring of AR(1) auto-correlated simple linear profiles in multi-stage processes (case study: tyre production industry)

Phase-II monitoring of AR(1) auto-correlated simple linear profiles in multi-stage processes (case study: tyre production industry)

Integration of production–maintenance planning and monitoring simple linear profiles via Hotelling's T2 control chart and particle swarm optimization

This paper introduces an integrated model that merges three key concepts: quality control through linear profile monitoring using Hotelling's T2 control chart, production cost evaluation, and maintenance policies. The objective function of the integrated model is to minimize total costs. This study is the first to jointly consider production and maintenance costs in the framework of profile monitoring using Hotelling’s T2 control chart for linear profiles without compromising on the versatility of simple linear profiles as a modeling tool, particularly in calibration applications. Appropriate assumptions are made for the proposed integrated model and the particle swarm optimization algorithm is implemented to determine decision variables. To evaluate the effectiveness of the integrated model, a numerical example and a comprehensive comparative analysis are conducted. Moreover, a sensitivity analysis to study the effects of various input parameters on the optimal solutions is performed. The findings suggest that adopting the integrated model with specific decision variables results in lower expected total costs when compared to the joint model and fixed parameter schemes.

Profile monitoring using synthetic T2 control chart

In this paper, we propose synthetic T2 chart for monitoring different parameters including Slope, Intercept and Error variance for simple and multiple linear regression profiles in Phase II. The construction and optimal design of the proposed synthetic T2 chart are discussed in detail. The steady-state performance of the proposed chart is evaluated by the Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) and is compared with the existing charts in the literature for monitoring simple and multiple linear profiles. It turns out that the proposed synthetic T2 chart performs uniformly better than the traditional T2 chart in detecting different kinds of shifts in the parameters of the simple and multiple linear profiles under steady-state run length performance. An example with a real data set is also presented to explain the implementation of the proposed chart.

New methods for phase II monitoring of multivariate simple linear profiles

In some statistical process control applications, the quality of a process or product is characterized by a function that relates a response variable to one or more explanatory variables, referred to as a “profile”. In some cases, multivariate simple linear profiles are required for effective quality modeling. In these profiles, there is a set of correlated response variables, regressed on an explanatory variable. There have been only a limited number of studies on multivariate simple linear profiles monitoring. In this paper, three new methods are proposed based on multivariate homogeneously weighted moving average (MHWMA) control chart to improve monitoring of multivariate simple linear profiles. The performance of the proposed methods is evaluated by simulated ARL metric. A comprehensive comparison is also conducted between the performance of the proposed methods and the existing ones. The results indicated that the proposed methods functioned very well under the various conditions considered. In addition, the practical application of the proposed control charts is also demonstrated using two real case studies.

Performance evaluation of DEWMA3 in phase-II for capturing changes in simple linear profiles based on run rule mechanism

In Statistical Process Control, many techniques exist for monitoring the stability of a process over time. In this work, we study the relationship of the response variable with explanatory variables in the form of linear profiles for detecting changes in slope and intercept of the linear quality profiles. We used the transformation of explanatory variables approach used for make the regression estimates independent of each other to have zero average. A comparative study of three phase-II methods using DEWMA statistics in monitoring and capturing undesirable deviations in the slope, intercept, and variability is also studied by applying different proposed run rules schemes i.e., R1/1, R2/3, R3/3. Monte Carlo simulations were carried out on R-Software for finding the results of proposed schemes by taking various levels of shifts for intercept, slope, and standard deviation in identifying the false alarm rate of a process. The simulation results based on the average run length criterion show that the proposed run rule schemes improve the detection ability of the control structure. Among all the proposed schemes R2/3 is found to be the best one because of its quick detection ability of false alarm rate. The proposed scheme also shows superiority in comparison to other schemes. The simulation results are further justified with a real data application.

Exploring the internal rotation of the extremely low-mass He-core white dwarf GD 278 with TESS asteroseismology

Context. The advent of high-quality space-based photometry, brought about by missions such as Kepler/K2 and TESS, makes it possible to unveil the fundamental parameters and properties of the interiors of white dwarf stars, particularly extremely low-mass white dwarfs, using the tools of asteroseismology. Aims. We present an exploration of the internal rotation of GD 278, the first known pulsating extremely low-mass white dwarf to show rotational splittings within its periodogram. Methods. We assessed the theoretical frequency splittings expected for different rotation profiles and compared them to the observed frequency splittings of GD 278. To this aim, we employed an asteroseismological model representative of the pulsations of this star, obtained by using the LPCODE stellar evolution code and the LP-PUL non-radial pulsation code. We also derived a rotation profile that results from detailed evolutionary calculations carried out with the MESA stellar evolution code and used it to infer the expected theoretical frequency splittings. Results. We find that the best-fitting solution when assuming linear profiles for the rotation of GD 278 leads to angular velocity values at the surface and center that are only slightly differential, and still compatible with rigid rotation. Additionally, the values of the angular velocity at the surface and the center for the simple linear rotation profiles and for the rotation profile derived from evolutionary calculations are in very good agreement. Also, the resulting theoretical frequency splittings are compatible with the observed frequency splittings, in general, for both cases. Conclusions. The results obtained from the different approaches followed in this work to derive the internal rotation of GD 278 agree. The fact that they were obtained by employing two independent stellar evolution codes gives our results robustness. Our results suggest only a marginally differential behavior for the internal rotation in GD 278 and, considering the uncertainties involved, this is very compatible with the rigid case, as has been observed previously for white dwarfs and pre-white dwarfs. The rotation periods derived for this star are also in line with the values determined asteroseismologically for white dwarfs and pre-white dwarfs in general.

Combination of Sequential Sampling Technique with GLR Control Charts for Monitoring Linear Profiles Based on the Random Explanatory Variables

Control charts play a beneficial role in the manufacturing process by reduction of non-compatible products and improving the final quality. In line with these aims, several adaptive methods in which samples can be taken with variable sampling rates and intervals have been proposed in the area of statistical process control (SPC). In some SPC applications, it is important to monitor a relationship between the response and independent variables—this is called profile monitoring. This article proposes adaptive generalized likelihood ratio (GLR) control charts based on variable sampling interval (VSI) and sequential sampling (SS) techniques for monitoring simple linear profiles. Because in some real-life problems, it may be possible that the user cannot control the values of explanatory variables; thus, in this paper, we focus on such a scenario. The performance of the proposed method is compared under three different situations, i.e., the fixed sampling rate (FSR), VSI, and SS, based on average time to signal (ATS) criteria for phase II analysis. Since the SS approach uses a novel sampling procedure based on the statistic magnitude, it has a superior performance over other competing charts. Several simulation studies indicate the superiority as the SS approach yields lower ATS values when there are single-step changes in the intercept, slope, standard deviation of the error term, and explanatory variables. In addition, some other related sensitivity analysis indicates that other aspects of the proposed methods, such as computational time, comparison with other control charts, and consideration of fixed explanatory variables. Furthermore, the results are supported by a real-life illustrative example from the adhesive manufacturing industry.

Improved Control Charts for Phase II Monitoring of Simple Linear Profiles Using Auxiliary Information

In some manufacturing or non-manufacturing systems, the process outcome is better characterized by a relationship between a main variable and some associated supporting variables. The monitoring of this functional relationship over time is termed as profile monitoring. This study aims to improve Phase II monitoring of simple linear profiles by using auxiliary information which is correlated with the main variable. To accomplish that, using a mean estimator, two auxiliary information-based (AIB) control charts namely AIB-MEWMA and AIB-DMEWMA charts are proposed for detecting different shifts in model parameters. Using two numerical examples based on simulation studies, the sensitivity of the proposed control charts is evaluated and compared with the existing MEWMA and DMEWMA charts in terms of the average run length (ARL) metric. The results of simulations reveal that the proposed charts perform better than the existing MEWMA and DMEWMA charts. The applicability of the proposed control charting methods is demonstrated using a real-life data example from the cylinder production process.

Monitoring simple linear profiles in the presence of within‐ and between‐profile autocorrelation

AbstractThe current study investigates the effect of within‐profile and between‐profile autocorrelations on the performance of four monitoring methods of simple linear profiles in Phase II. To this end, a general correlation model between error terms is considered such that the correlation structure of within‐profiles errors and the error terms between consecutive profiles follow an autoregressive (AR) times series model of order one. Extensive simulations have been done to assess the effect of both autocorrelation types and the profile size on the estimations of the model parameters as well as the performance of control charts. The performance of the monitoring schemes is investigated and compared with respect to the average run length (ARL) metric. The simulation study results show that the autocorrelation within and between profiles has a negative impact on the monitoring technique's performance. It reduces the control chart's ability to detect process shifts compared to no or weak autocorrelation cases. Moreover, the performance of all the methods is improved by increasing the profile size. An illustrative example is also provided to demonstrate the use of the proposed methods for monitoring the stability of profiles in the chemical industry.

A new incapability index for simple linear profile with asymmetric tolerances

Simple linear profiles (SLPs) are modeled by linear functional relationship between a response variable and an explanatory variable. A number of process capability indices (PCIs) for SLPs with symmetric tolerances have been proposed. However, PCIs for SLPs with asymmetric tolerances have received little attention. This article proposes a new functional incapability index for dealing with asymmetric tolerances. To demonstrate the improved performance of the new index, numerical examples and simulation studies are used to compare it to existing functional PCIs. Bootstrap confidence intervals for the proposed index are also obtained. Two examples illustrate the applicability of the proposed index.

A review and critique of auxiliary information-based process monitoring methods

ABSTRACT We review the rapidly growing literature on auxiliary information-based (AIB) process monitoring methods. Under this approach, there is an assumption that the auxiliary variable, which is correlated with the quality variable of interest, has a known mean, or some other parameter, which cannot change over time. We demonstrate that violations of this assumption can have serious adverse effects both when the process is stable and when there has been a process shift. Some process shifts in the quality variable of interest can become undetectable. We also show that the basic AIB approach is a special case of simple linear regression profile monitoring. The AIB charting techniques require strong assumptions. Based on our results, we warn against the uncritical use of the AIB approach in quality control applications.

Dynamic batch sentencing mechanisms for yield-based product acceptance determination with the simple linear profiles

Acceptance sampling plan has been extensively used in batch sentencing to provide the manufacturer and the customer a general benchmark to meet their predetermined needs on the batch quality. This paper develops a flexible sampling procedure, based on the SpkA index, for simple linear profiles by switching inspection rules. The plan parameters of the two suggested types of quick switching sampling (QSS) systems, satisfying the desirable quality levels and constraining the manufacturer’s and the customer’s risks, are derived by solving an optimization model. The comparisons between the suggested systems and the existing sampling plans are discussed, in terms of the discriminatory power and the average sample number to show the better performance of the suggested systems. Finally, the suggested QSS systems are applied in the electronics industry.

MEWMA based control charts with runs rules for monitoring multivariate simple linear regression profiles in Phase II

In this article, three control charts including MEWMA, MEWMA/ and DMEWMA equipped with proposed runs rules schemes, are developed to improve the performance of existing control charts in monitoring multivariate simple linear profiles. Using five criteria of average run length, percentile of the run length, standard deviation of run length, relative mean index and relative standard deviation index the behavior of the suggested control schemes has been assessed. The results of our study demonstrate that the suggested schemes have a better performance compared to current charts for detecting shifts. Ultimately, using an actual calibration application case in the automotive industry, the suggested control charts applicability is depicted.

Monitoring Simple Linear Profiles in the Presence of Within- and Between-Profile Autocorrelation

Monitoring Simple Linear Profiles in the Presence of Within- and Between-Profile Autocorrelation

Phase-II Monitoring of AR(1) Auto-correlated Simple Linear Profiles in Multistage Processes (Case Study: Tire Production Industry)

Phase-II Monitoring of AR(1) Auto-correlated Simple Linear Profiles in Multistage Processes (Case Study: Tire Production Industry)