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Researchers can use many statistical tools to fit data, either simple or complex, based on the likelihood. However, more parameters usually provide a smooth resolution, due to the order of likelihood increases, however, the main issue is to use special tools to estimate parameters. For example, we are used the process capability indices (CL) for measuring the performance of a process with, lower specification limit L). The article adopts a method of CL when the unit’s lifetime has two parameters generalised half-logistic lifetime population. The real-world dataset is collected with respected to Type-I generalised hybrid censoring scheme. The scale parameter is specified under data transformation technology. The Bayes and maximum likelihood estimators are formulated using the conjugate form of the prior and examined using the squared error loss procedure. The developed estimators construct credible and confidence intervals for CL. Real world examples in this article illustrate the pattern of the estimate value of confidence interval for the parameter CL and the interval estimations of CL are assessed by a Monte Carlo simulation studies.

Researchers can use many statistical tools to fit data, either simple or complex, based on the likelihood. However, more parameters usually provide a smooth resolution, due to the order of likelihood increases, however, the main issue is to use special tools to estimate parameters. For example, we are used the process capability indices (C L) for measuring the performance of a process with, lower specification limit L). The article adopts a method of C L when the unit's lifetime has two parameters generalised half-logistic lifetime population. The real-world dataset is collected with respected to Type-I generalised hybrid censoring scheme. The scale parameter is specified under data transformation technology. The Bayes and maximum likelihood estimators are formulated using the conjugate form of the prior and examined using the squared error loss procedure. The developed estimators construct credible and confidence intervals for C L. Real world examples in this article illustrate the pattern of the estimate value of confidence interval for the parameter C L and the interval estimations of C L are assessed by a Monte Carlo simulation studies. [ABSTRACT FROM AUTHOR]

AbstractStability is an important criterion to be investigated at the early stage of any industrial process and stable processes are usually preferred over unstable ones. But a process can be unstable and nevertheless capable and, therefore, there is a clear need to monitor such situations to ensure an acceptable capability. In this study we introduce, in a first step, a new Shewhart-type control chart for normal processes based on the yield index Spk to monitor the capability of potentially unstable processes and then, in a second step, we extend it using an Exponentially Weighted Moving Average (EWMA) scheme. Moreover, the optimal values of the control parameters are obtained using a nonlinear optimization problem for which the out-of-control average run length is the objective function. The introduced charts’ sensitivity is examined for deterministic shift sizes. Numerical and graphical analyses are given to display the features of the proposed charts. A simulation study shows, how in such a situation, the introduced tool is successful to recognize changes in the process capability. [ABSTRACT FROM AUTHOR]

Multiple sampling plan (MSP) has been proved that the sample units required for inspection at each stage are usually smaller than the conventional single or double sampling. However, it is more complex to administer and difficult to derive the corresponding operating characteristic function since the judgment on the submitted lot under the MSP is not only dependent on the result of current sampling but also on previous sampling results. Thus, this paper attempts to provide a relaxed type of conventional MSP by assuming the sampling inspection at each stage is independent which is called variables stage-independent multiple sampling plan and integrated with the most widely-used process capability index Cpk. For the cost-efficient purpose, the plan parameters are solved under an optimisation model that minimises the average sample number by satisfying the required quality levels and tolerated risks. Finally, the applicability of the proposed plan is illustrated in a case study. [ABSTRACT FROM AUTHOR]

A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index is frequently utilized by a manufacturer to gauge the quality of a process. This index can be utilized by not only an internal process engineer to assess the quality of the process but also as a communication tool for an external sales department. When the manufacturing process deviates from the target value T, the process capability index CPMK can be quickly detected, which is conducive to the promotion of smart manufacturing. Therefore, this study applied the index CPMK as an evaluation tool for process quality. As noted by some studies, process capability indices have unknown parameters and therefore must be estimated from sample data. Additionally, numerous studies have addressed that it is essential for companies to establish a rapid response mechanism, as they wish to make decisions quickly when using a small sample size. Considering the small sample size, this study proposed a 100 (1 − α)% confidence interval for the process capability index CPMK based on suggestions from previous studies. Subsequently, this study built a fuzzy testing model on the 100 (1 − α)% confidence interval for the process capability index CPMK. This fuzzy testing model can help enterprises make decisions rapidly with a small sample size, meeting their expectation of having a rapid response mechanism. [ABSTRACT FROM AUTHOR]

Abstract Besides achieving high quality products, statistical techniques are applied in many fields associated with health such as medicine, biology and etc. Adhering to the quality performance of an item to the desired level is a very important issue in various fields. Process capability indices play a vital role in evaluating the performance of an item. In this paper, the larger-the-better process capability index for the three-parameter Omega model based on progressive type-II censoring sample is calculated. On the basis of progressive type-II censoring the statistical inference about process capability index is carried out through the maximum likelihood. Also, the confidence interval is proposed and the hypothesis test for estimating the lifetime performance of products. Gibbs within Metropolis–Hasting samplers procedure is used for performing Markov Chain Monte Carlo (MCMC) technique to achieve Bayes estimation for unknown parameters. Simulation study is calculated to show that Omega distribution's performance is more effective. At the end of this paper, there are two real-life applications, one of them is about high-performance liquid chromatography (HPLC) data of blood samples from organ transplant recipients. The other application is about real-life data of ball bearing data. These applications are used to illustrate the importance of Omega distribution in lifetime data analysis.

In today's manufacturing environment, the rate of defective products has been continuously decreasing; thus, variables sampling plans with process capability indices (PCIs) have been recommended to gather more information about a manufacturing process and reduce required sample sizes for inspection. In particular, skip-lot sampling plan (SkSP) is suitable for a series of lots having stable and excellent product quality. Moreover, the concept of repetitive group sampling (RGS), which can allow the use of less samples to maintain desired protection to producers and consumers, is especially appropriate where inspection or testing is costly or destructive. This study, by incorporating the advantages of PCIs, SkSP, and RGS, constructs a variables SkSP with RGS as the reference plan (called SkSP-RGS) based on one-sided PCIs for products with a unilateral specification limit. The proposed plan reduces the sample size while achieving a similar discriminatory power, compared with a conventional variables single sampling plan (SSP), a RGS plan (RGSP), and a SkSP of type 2 (SkSP-2). Tables of plan parameters are provided for frequently applied quality and risk requirements so that practitioners can easily apply the proposed plan. [ABSTRACT FROM AUTHOR]

Process capability analysis (PCA) is an important stage to check variability of process by using process capability indices (PCIs) that are very effective statistics to summarize process' performance. Traditional PCIs can produce some incorrect results and declare misinterpretation about process' quality if the process includes uncertainties. Additionally, definitions of process' parameters with exact values is not possible when there are uncertainty caused by measurement errors, sensitivities of measuring instruments or quality engineers' hesitancies. Although the fuzzy set theory (FST) has been successfully used in PCA, it is the first time to use of Pythagorean fuzzy sets (PFSs) to model uncertainties of process more than traditional fuzzy sets in PCA. Since the PFSs has two-dimensional configurations by defining membership and non-membership values, they also have a huge ability to model uncertainty that arises from the human's thinking and hesitancies, and has brought flexibility, sensitivity and reality for PCA. In this paper, specification limits (SLs), mean (μp), standard deviation (σ) and target value (T) main parameters of PCIs have been analyzed by using PFSs and Pythagorean fuzzy process capability indices (PFPCIs) for two well-known PCIs such as ( C ˜ pm) and ( C ˜ pmk) have been derived. The Pythagorean ( C ˜ pm) and ( C ˜ pmk) indices have also been applied and tested on some numerical examples based on real case applications from manufacturing industry. The obtained results show that PFPCIs provide wider knowledge about capability of process and to obtain more realistic results. As a result of considering all possibilities about the process, it has been concluded that the process is incapable. In light of this information, the results obtained using different fuzzy set extensions for (Cpm) and (Cpmk) indices can be compared. [ABSTRACT FROM AUTHOR]

The paper discusses the effect of autocorrelations on process capability indices (PCIs).Confidence intervals are constructed for PCIs when data are autocorrelated. Approximate lower confidence limits for various Cpk are computed for AR(1) model. Industrial examples are considered to illustrate the results. [ABSTRACT FROM AUTHOR]

Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (µ) and variance (σ²) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more broadly more flexibility. For this aim, the main parameters of PCIs have been defined and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as ...sp, ...spk, ...fp and ...fpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic, more sensitive, and more comprehensive results. [ABSTRACT FROM AUTHOR]

For the lifetime of products following a Burr XII distribution, the lifetime performance index was measured to assess the performance of the manufacturing process under type I interval censoring. The sampling design is investigated to reach the given level of significance and power level. When the inspection interval length is fixed, the required number of inspection intervals and sample size are determined to reach the minimum total cost. When the termination time of experiment is not fixed, the required number of inspection intervals, sample size and equal interval length are determined to reach the minimum total cost. The optimal sampling design for different situations is tabulated for the practical use of users. At last, one practical example is given for illustrative aim to show the use of the optimal sampling design to collect data and then conduct the testing procedure to see if the process is capable. [ABSTRACT FROM AUTHOR]

Due to worldwide awareness of the sustainable environment, research on green production and distribution has grown within academic and industrial communities. For an eco‐friendly environment, limiting hazardous substances (HSs) concentration in products quality assessment is one of the most crucial strategies to achieve the 4Rs of the products, namely, Reduction, Reuse, Recycle, and Recovery. Trustworthy inspection, evaluation, and validation methods to ensure multiprocess yield and risk of acquiring green product quality are desired for the industry. However, the existing methods use arbitrary inspection sizes, levels of capability, and ignore controls for both Types I and II risks. To overcome these drawbacks and pursue Six‐Sigma green capability suppliers, this study establishes a multiprocess performance chart, called the green product quality analysis chart (GPQAC), to inspect and analyze green product submissions. GPQAC implements variables sampling plans based on unilateral and bilateral process capability indices. The chart operates at given Six‐Sigma green and quality compliance and simultaneously controlled Type I and Type II risks. The required sample size and rejection and acceptance capability zones are determined from the multiprocess optimization taking into account the Bonferroni correction. This determination enables GPQAC to aggregate the overall status of a group of processes and assess the ability of the supplier processes to execute efficiently and economically relative to the customer specifications. We also establish web‐based GPQAC graphs using a cloud‐computing program for lot disposition. Finally, a real‐world case illustrates the utility of the GPQAC integrated variables sampling scheme in enhancing environmental sustainability. [ABSTRACT FROM AUTHOR]

Process Capability Indices (PCIs) are devices widely used in the industry to evaluate process quality. The commonly used process capability indices all contain accuracy indices and precision indices. As the accuracy index is closer to zero, the process accuracy is higher. The precision index mainly represents the extent of process variation. As the value is smaller, the process variation is smaller, that is, the precision is higher. In fact, process capability indices are the functions of accuracy indices and precision indices. Obviously, as long as accuracy indices and precision indices are controlled, the process capability indices can be controlled as well. Therefore, this study first derived accuracy and precision control charts to observe not only process accuracy but also process precision. Then, this study adopted in-control data to acquire a 100 (1 −  α)% confidence region of an accuracy index and a precision index, with which statistical tests were performed. Subsequently, according to the definition of the six sigma quality level, both indices were examined. Furthermore, based on the testing results, suggestions for process improvement were proposed, including correcting the direction of process deviation and deciding whether to reduce process variation. Finally, this study demonstrated the applicability of the proposed model using an empirical example. [ABSTRACT FROM AUTHOR]

One of the quality tools used to determine if a process is capable of meeting the desired technical specifications is the capability analysis, which constitutes one of the premises to guarantee the quality of products. For this reason, the present work aims to implement the process capability analysis in the gauge manufacturing. To carry out the evaluation, a complex or multipurpose caliber is taken as a sample, manufactured in a military company, intended for checking the channels of the new sniper rifle barrels, 25 measurements are made in different sections of its diameter. As a result, the values of the process capability indices were obtained and it was concluded that the gauge manufacturing process is unsuitable due to its incapability to produce gauges within the established specifications. [ABSTRACT FROM AUTHOR]

Process capability and performance indices (PCIs and PPIs) are used in industry to provide numerical measures for the capability and performance of several processes. The majority of the literature refers to PCIs and PPIs for continuous data. The aim of this paper is to compute the classical indices for discrete data following Poisson, binomial or negative binomial distribution using various transformation techniques. A simulation study under different situations of a process and comparisons with other existing PCIs for discrete data are also presented. The methodology of computing the indices is easy to use, and as a result, one can have an assessment of the process capability and performance without difficulty. Three examples are further provided to illustrate the application of the transformation techniques. [ABSTRACT FROM AUTHOR]

The improvement process of six-sigma DMAIC refers to the process that the industry performs to enhance process quality via the following five procedures: (1) define, (2) measure, (3) analyze, (4) improve, and (5) control. It is a common tool used in the industry to ameliorate and enhance process quality. In addition, the process capability index is a tool that the industry most frequently uses to measure process quality. Though many studies have discussed six-sigma methods, none of the specific theoretical models could be provided as a reference for the above five DMAIC improvement steps, making it difficult to control the effect. In order to solve this problem, this paper developed the multi-characteristic process capability analysis chart, MPCAC, using the process capability index and applied the method of statistical inference as a tool promoting define, measure, and analyze in the improvement process of six-sigma DMAIC. Additionally, the testing of the orthogonal table in the Taguchi method can efficiently assist process engineers in finding the optimum combination of machining parameters to improve or boost the process quality level of the quality characteristics by reducing the number and the cost of experiments. Therefore, this paper then adopted the testing of the orthogonal table in the Taguchi method as a tool for process improvement in the fourth step. Finally, according to the optimal combination of machining parameters improved in the fourth step, a standard operating procedure for transistor gaskets was established as a tool for process control in the fifth step. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) are effective quality tools for evaluating process performance in the manufacturing industry. Over a period of more than 15 years, sampling plans based on PCIs have been developed for lot sentencing. Sampling plans that involve repetitive sampling or multiple dependent (deferred) state sampling achieve significant sample size reductions relative to sampling plans that involve single sampling. In this study, we combine the concepts of repetitive and multiple dependent state sampling to propose a new variable sampling plan based on one-sided PCIs. The proposed sampling plan minimizes the average sample number while satisfying the principle of two points on the operating characteristic curve. To demonstrate the performance of the proposed sampling plan, a comparison with existing homogeneous sampling plans is performed. [ABSTRACT FROM AUTHOR]

Process capability index (PCI) is widely used to evaluate the process capability in various industries. In this article, generalized confidence intervals (GCIs) of two widely used percentile-based PCIs for the inverse Gaussian (IG) distribution are constructed. Meanwhile, the GCI of the difference between two IG processes' PCIs is also considered. In addition, the performance of the proposed GCI is evaluated and compared with that of the confidence intervals based on the traditional bootstrap method. The simulation results indicate that the GCI outperforms the bootstrap counterparts in terms of the coverage probabilities, and the actual coverage probabilities of the GCI are sufficiently close to the target value. Finally, two real examples are presented to illustrate the implementation of the proposed method. [ABSTRACT FROM AUTHOR]

The lifetime performance index was used for the evaluation on the process performance to promote the quality and productivity especially with products following a one-parameter exponential distribution. Based on the hypothesis testing procedure using the maximum likelihood estimator as testing statistic, the sampling design is determined under different situations. For given power of hypothesis testing, the minimum sample size is determined and tabulated to reach the given power. When the termination time is fixed and the number of inspection intervals is not fixed, the required number of inspection intervals and sample size with minimum total cost are determined and tabulated. When the termination time is not fixed, the required number of inspection intervals, sample size and equal interval length to reach the minimum total cost are determined and tabulated. At last, one numerical example is given to illustrate the use of this sampling design to collect data and then implement the testing procedure to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

Lifetime performance indices CL is usually used as the measurement for the larger-the-better type quality characteristics to assess the process performance of products. The lifetimes of products are assumed to have Rayleigh distribution in this study. This research presents another approach to the hypothesis testing procedure for the index without the transformation of Rayleigh distribution to the exponential distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample and its asymptotic distribution of this estimator is also developed to build a new hypothesis testing procedure under a pre-assigned lower specification limit. A simulation study is done and the results show that the power performance of this approach is better than the existing one. Finally, two practical examples are given to illustrate the use of two testing algorithmic procedures to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

Introduction When the production process is under statistical control, process capability indices are used to measure process capability. In the past, manufacturers used histograms, frequency charts, and quality control charts to compare process data with technical specifications. Today, the concept of efficiency ratio is called process capability index and was first proposed by Juran et al. (1974). He introduced the first and foremost process capability index, Cp. Then Kane (1986) introduced the Cpk capability index to address the limitations of Cp. The Cpm capability index is then formally stated by Chan et al. (1988), which complements the Cpk capability index. The Cpmk capability index is a combination of the Cpk and Cpm capability indices introduced by Pearn and Lin (2002). Most evaluations of process capability indices focus only on their points estimation, so it is possible to make unreliable comments about process capability. In other words, the use of these process capability indicators is an important part of statistical process control applications to achieve continuous quality improvements. These indicators are used to provide a small measure of manufacturing performance in industry or to measure the performance of a product. Many statisticians and quality engineers emphasize research on process capability indicators to suggest more effective methods for measuring process capability. The capability index is a measure based on process parameters and specification limit. So far, confidence intervals for the difference between process capability indices for the two processes have been obtained using pivotal quantity method and also using the bootstrap resampling simulation method. In situations such as selecting a supplier and assessing process improvement, it is of interest to compare capability indices for two different processes. Material and Methods In this paper, first, a generalized confidence interval for the Cpmk capability indices ratio of two different processes is presented and then this comparison is performed by performing an appropriate hypothesis test and providing an example. To compare the Cpmk index in the two processes, the confidence interval structures are not accurate and the confidence intervals are obtained only according to approximate methods. Due to the importance of using the Cpmk index, then the generalized confidence interval for Cpmk1 Cpmk2 is presented and using the confidence interval obtained for the ratio variable, the relevant hypothesis test is tested. The generalized confidence interval idea was first proposed by Weerahandi (1995). When there is no standard pivotal quantity or it is difficult to obtain it, the use of the generalized confidence interval method will be more valuable. In other words, the definition of a confidence interval is generalized when we are faced with problems such as constructing exact confidence regions for the difference between the mean of two normal distributions without assuming equality of variance. In addition, using simulating, the generalized confidence interval was compared with the bootstrap confidence interval. Bootstrap sampling was introduced in 1979 by Efron. In this paper, the standard bootstrap confidence interval and percentile bootstrap for the Cpmk1 Cpmk2 ratio is also calculated. Results The simulation results were performed using 5000 replications for the generalized confidence interval and 1000 times for the bootstrap confidence interval, and the coverage probability (CR) and mean distance length (AL) were also calculated. The SB-CI, PB-CI, G-CI are the standard bootstrap confidence interval, the percentile bootstrap confidence interval, and the generalized confidence interval, respectively. In this simulation, two different samples of the same size and the normal distribution were performed for three different samples of size (20, 40 and 60). The simulation results showed that the generalized confidence interval works better than the bootstrap confidence interval. Therefore, the confidence interval presented in this paper can be generalized to compare the capability indices of several processes or pairwise comparisons. In addition, the data in the used example in this paper, taken from Chen and Tong (2003), are from two suppliers who prepare aluminum foil for an electronics company in Taiwan. Aluminum foil as a key component determines the quality of batteries and voltage is one of the most important quality characteristics of aluminum foil. The generalized confidence interval of (1-α)*100% for the Cpmk ratio of the two processes when α = 0.05 was obtained as (1.741, 3.387), which indicates that process 1 is more efficient than process 2. Conclusion Generalized pivotal quantity and generalized confidence intervals are very useful tools for inferring industrial statistics problems. Process capability indices are important quantities that are used to determine the process efficiency of manufactured products. According to the results obtained for the Cpmk ratio in the two communities, it can be seen that the generalized confidence interval can be well used to compare the performance of the two processes. [ABSTRACT FROM AUTHOR]

The-Nominal-The-Best (N-type) loss function is established based on the Taylor expansion. Results become more accurate as more Taylor expansion items are retained. N-type loss function neglects terms with powers higher than two, which inevitably leads to a certain deviation between the calculated result and the true value. In this paper, Taylor expansion is retained to the third-order, and the quality loss function is extended to three items. The quality loss coefficients of each item are determined, and the asymmetric piecewise cubic quality loss function is established. The deviation between the cubic and quadratic functions is evaluated. The formula for calculating the hidden quality cost of a product is derived by choosing an appropriate density distribution function and using process capability. Two cases are utilised to analyse and discuss the quality loss and hidden quality cost of a product using the cubic quality loss and quadratic quality loss functions. This paper provides a more accurate approach for the study of product quality management. [ABSTRACT FROM AUTHOR]

The method of six-sigma and the index of process capability are both commonly used tools in the industrial community. Process engineers can follow five improvement steps of the six-sigma method, including "define", "measure", "analyze", "improve", and "control" (DMAIC), aiming to improve and enhance the process quality. However, none of these five improvement steps have a clear corresponding approach. This paper considered process capability indices not only a process quality evaluation tool widely used in the industrial community but also a process quality evaluation and analysis tool adopted by internal engineers. Therefore, this paper applied the method integrating process capability indices and statistical testing to develop execution models for the five improvement steps, DMAIC, of the six-sigma method. First, this paper, based on the concept of yield, not only deduced the relationship between the required value of the process capability index for the product and the process capability index value of the individual quality characteristic but also discussed the definition of the quality level of six-sigma as well as its relationship with the process capability index. Next, according to these results, five improvement execution models of the six-sigma method were developed and served as a reference for the process engineers in the industry to promote the performance of the six-sigma project. The proposed method in this paper applied various normal processes and combined the six-sigma method and process capability indices, both of which are tools commonly used in the industrial community. It also has taken into account the advantages of theoretical contribution and industrial acceptance. [ABSTRACT FROM AUTHOR]

In this paper, we shall discuss some statistical properties of the estimator of C p when sample observations are autocorrelated and affected by measurement errors. The presence of autocorrelation in production units is very common in many industries like chemical, food processing, pharmaceutical, paper, and mineral. At the same time some amount of measurement error is invariably present in the sample observations due to inaccurate measurement process. In this paper, we discuss the case of a first-order stationary autoregressive process where measurement error follows a Gaussian distribution. The comparison of the statistical properties of the estimator in this case with the error-free case is the subject matter of this paper. [ABSTRACT FROM AUTHOR]

Process Capability Indices (PCIs) are devices widely used in the industry to evaluate process quality. The commonly used process capability indices all contain accuracy indices and precision indices. As the accuracy index is closer to zero, the process accuracy is higher. The precision index mainly represents the extent of process variation. As the value is smaller, the process variation is smaller, that is, the precision is higher. In fact, process capability indices are the functions of accuracy indices and precision indices. Obviously, as long as accuracy indices and precision indices are controlled, the process capability indices can be controlled as well. Therefore, this study first derived accuracy and precision control charts to observe not only process accuracy but also process precision. Then, this study adopted in-control data to acquire a 100 (1 − α)% confidence region of an accuracy index and a precision index, with which statistical tests were performed. Subsequently, according to the definition of the six sigma quality level, both indices were examined. Furthermore, based on the testing results, suggestions for process improvement were proposed, including correcting the direction of process deviation and deciding whether to reduce process variation. Finally, this study demonstrated the applicability of the proposed model using an empirical example.

Acceptance sampling plan has been a practical tool in quality management, which provides both the producer and the consumer a general rule for sentencing lots. In recent years, a new strategy, chain sampling plan, considering disposition of historical lots for sentencing the current lot has been discussed. However, reviewing results of preceding lots only happens when the quality of current lot is on the undefined region,which may not be completely utilized. Therefore, in this study, we develop a variables modified-ChSP (VMChSP) for variable inspection based on the Taguchi capability index to improve above situation. Optimization model of the proposed plan is formulated to solve plan parameters by minimizing the required sample size. Plan parameters under various allowable risks and quality levels are also provided for practical purpose. Finally, further analysis and comparisons between the proposed plan and conventional plans are provided and discussed in this research. [ABSTRACT FROM AUTHOR]

The article aims to assess the improvement of the process capability by implementing the Six Sigma methodology in furniture enterprises with different levels of the quality management system (QMS) and ownership. The implementation of the Six Sigma methodology according to the DMAIC steps, also analysis, evaluation, and comparison of the implementation results were performed to improve the process performance. The implementation of the Six Sigma methodology was carried out in an international enterprise with foreign capital and a certified Quality Management System (QMS) and in a domestic enterprise with purely domestic capital without an established Quality Management System. The implementation results confirmed the positive development in the key indicators of critical processes, namely, in the reduction of DPMO, the increase of efficiency and the level of Sigma Process, and the values of process capability indices. The positive effects were more pronounced in the international enterprise compared to the domestic. The application of the Six Sigma methodology brings better results in manufacturing companies with international management skills and implemented certified QMS. These two aspects can be key success factors by managing and improving process capability. The practical contribution of the paper can be seen in the proposal of suitable methods and tools by implementing Six Sigma conception in furniture manufacturing regardless of the ownership or level of quality management systems.

Process capability indices (PCIs) are widely used as a measure of process potential and process performance. Unfortunately, the use of sample data to estimate PCIs means that any error in the sampling can introduce considerable uncertainty into the assessment of process capability. This necessitates the use of the lower confidence limit (LCL) in the estimation of minimum process capability. Furthermore, the complexity of sampling distributions of the PCIs greatly hinders interval estimation, such that only an approximate or asymptotic LCL can be achieved. This paper proposes a novel approach to deriving theLCL of indicesCpu,CplandCpkusing Boole’s inequality and DeMorgan’s theorem. This approach is based on subsample data collected from a stable process. Hypothesis testing is also used to determine whether the process is capable of satisfying the quality requirements of customers. We calculated the critical values of the PCIs for various significance levels, capability requirements and sample sizes. Finally, we present analysis of two cases to demonstrate the applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

The important and common applications of process capability indices (PCI’s) is the process capability ratio and the process capability index , and the use of these measures in practical applications is based on the assumption that the process is under statistical control and that the outputs of that process follow the normal distribution. In practice, however, there are many cases in which the outputs of the process are not follow normal distribution, in such cases, calculating PCI’s will lead to misleading results. In this paper, the non-normal production process capability was evaluated. The evaluation process was conducted using four methods: The first method involved the use of Box-Cox power transformation to normal distribution of data and then calculating indicators of the capability process by traditional methods. The second method is by using the weighted variance method, and the third method is by using the Clements’ method based on the percentiles calculation of data, and the fourth method is based on the use of the Darling-Anderson goodness of fit test to accommodate some of the probability distributions of the original data, this test shows that the log-normal distribution is the most appropriate distribution for the data The results showed that although the process is stable and under statistical control, it is not capable based on the value of the process capability index that did not exceed (65%), as the percentage defect units, which is outside the specifications, is large and located between (3.6%) and (13.4%). The results also showed that there is a convergence in the results of the PCI’s calculated by all methods, and that the Clements’ method is the best method as it gives the highest values ​​for the PCI’s. The research recommended studying and calculating other PCI’s like, , , and CMA(τ,v). One of the recommendations for future research and studies is to do a theoretical study to compare the mentioned methods and choose the best ones based on some statistical criteria.

The improvement process of six-sigma DMAIC refers to the process that the industry performs to enhance process quality via the following five procedures: (1) define, (2) measure, (3) analyze, (4) improve, and (5) control. It is a common tool used in the industry to ameliorate and enhance process quality. In addition, the process capability index is a tool that the industry most frequently uses to measure process quality. Though many studies have discussed six-sigma methods, none of the specific theoretical models could be provided as a reference for the above five DMAIC improvement steps, making it difficult to control the effect. In order to solve this problem, this paper developed the multi-characteristic process capability analysis chart, MPCAC, using the process capability index and applied the method of statistical inference as a tool promoting define, measure, and analyze in the improvement process of six-sigma DMAIC. Additionally, the testing of the orthogonal table in the Taguchi method can efficiently assist process engineers in finding the optimum combination of machining parameters to improve or boost the process quality level of the quality characteristics by reducing the number and the cost of experiments. Therefore, this paper then adopted the testing of the orthogonal table in the Taguchi method as a tool for process improvement in the fourth step. Finally, according to the optimal combination of machining parameters improved in the fourth step, a standard operating procedure for transistor gaskets was established as a tool for process control in the fifth step.

In healthcare monitoring, the quality of medical services and patient outcomes are significantly influenced by the unnatural variations emphasizing the importance of effective control and monitoring strategies. In such scenarios the quality is compromised when a shift in the medical process is not detected timely. In this study, we commenced a comprehensive analysis of the variability present in the patient's hematocrit levels. We introduced a novel approach using fuzzy control charts for individual measurements to detect shift within hematocrit levels effectively. For the initial forecasting of hematocrit level variability, we employed the exponential smoothing method by using R software. Following this, we proposed a set of fuzzy control charts intended for individual measurements, including the fuzzy moving average control chart, fuzzy weighted moving control chart, and fuzzy moving range control chart. These control charts are defined with fuzzy control rules, allowing them to analyze and interpret the small shifts in the process precisely. Also, to measure the process's capability for providing a deeper understanding of the processes, fuzzy process capability indices are introduced. A Monte Carlo simulation approach is employed to obtain the performance metrics. Finally, a case study sourced from Kaggle was conducted to evaluate the performance of the proposed fuzzy control charts for assessing hematocrit levels. • Innovative fuzzy control charts, including FMACC, FWMACC, and FMRCC, are proposed for individual measurements in health monitoring. • The proposed control charts use fuzzy control rules to detect small shifts in complex medical data. • Fuzzy Process Capability Indices are proposed for assessing process capability and improving the precision of healthcare decision-making. • The study aims to enhance patient care and treatment results by connecting healthcare practices with fuzzy control chart methods. • The research aims to improve patient care and treatment outcomes by enhancing data analysis and monitoring techniques. [ABSTRACT FROM AUTHOR]

In this study we propose a sequential test for hypothesis testing on the C pmk process capability index. Furthermore, we propose a sequential sampling plan for lot acceptance based on C pmk . We compare the statistical properties of the sequential procedures with the performance of the corresponding non-sequential methodologies by carrying out an extensive simulation study. The results show that the proposed sequential methods make it possible to reach decisions much more quickly, on average, than the fixed sample size procedures with the same discriminating power. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the paper is the construction of confidence intervals for the ratio of the values of process capability index Cpm for two processes. These confidence intervals can be used for comparing the capability of any pair of competitive processes. Design/methodology/approach: Two methods for constructing confidence intervals for the ratio of the values of process capability index Cpm for two processes are proposed. The suggested techniques are based on a two-step approximation of the doubly non-central F distribution. Their performance is tested via simulation. Findings: The performance of the suggested techniques seems to be rather satisfactory even for small samples, as illustrated through the use of simulated data. Practical implications: The practical implication of the suggested techniques is that they can be implemented in real-world applications, since they can be used for comparing the capability of any pair of competitive processes. Originality/value: The paper presents two new methods for constructing confidence intervals for the ratio of the values of process capability index Cpm for two processes. [ABSTRACT FROM AUTHOR]

In this study we propose a sequential test for hypothesis testing on the C pmk process capability index. Furthermore, we propose a sequential sampling plan for lot acceptance based on C pmk . We compare the statistical properties of the sequential procedures with the performance of the corresponding non-sequential methodologies by carrying out an extensive simulation study. The results show that the proposed sequential methods make it possible to reach decisions much more quickly, on average, than the fixed sample size procedures with the same discriminating power. [ABSTRACT FROM AUTHOR]

This paper presents two approaches for testing quality to make a decision based on the extended process capability indices. Common methods in measuring quality of the manufactured product have widely focused on the precise specification limits, but in this study the lower and upper specification limits are considered as non-precise/fuzzy sets. Based on a general statistical approach using an extended process capability index, the purpose of this study is estimating a critical value to determine whether the process meets the customer requirements. Moreover, a simulation approach to analyze the manufacturing process capability has been suggested for testing quality based on fuzzy specifications by normal data. Meanwhile, this paper discusses how well the Monte Carlo simulation approach can be used for non-normal data. Finally, the real application of the proposed methods is investigated in a real case study. [ABSTRACT FROM AUTHOR]

Durability, one of the dimensions of quality, is the important criterion for comparing suppliers. In many industries, durability is widely measured by lifetime data modeled with Weibull distribution becauseof its flexible shape. The process capability indices (PCIs) is an appropriate tool for comparing suppliers regarding quality aspect. Many methods for comparing suppliers using the PCIs are developed to correspond to manufacturing conditions. However, themethods cannot apply with the lifetime data since they are developed under the normality assumption. The mentioned violation leads to probably misleading results in comparison. To consider the lifetime, this paper proposes the new supplier comparison using the PCIs for Weibull distribution model. Two parameters (scale and shape) of the Weibull distribution are studied. Since the shape parameter is sensitive to the PCIs estimation, this paper emphasizes on various shape parameters, e.g. symmetric, right, and left skewed. Regarding the lifetime, this paper studies single quality characteristic and the lower PCIs (Cpl). The producer’s risk and the power of test obtained from Monte Carlo simulation are used to evaluate the performance of theproposed method. This method is compared with supplier comparison methods applying percentile PCIs and Box-Cox transformation for the PCIs estimation.

We present a two-phase methodology based on the concept of depth to measure the capability of processes characterized by the functional relationship of multivariate nonlinear profile data, treated as multivariate functional observations. In the first phase, the modified tolerance region is estimated using a historical data set, while in the second, a current process is assessed using the proposed three-component vector, where the first component measures the volume ratio between the current process region and the modified tolerance region; the second measures the probability that the median of the current process is within the modified tolerance region, and the third measures the probability that the current process region is inside the modified tolerance region. To facilitate interpretation, a single index is derived from this capability vector. A simulation study is carried out to assess the performance of the proposed method. An real example illustrates the applicability of this approach. [ABSTRACT FROM AUTHOR]

A swingarm is the most crucial component of modern motorcycles use to provide suspension, hold the rear axle firmly, manage load distribution and maintain the centre of gravity. Boring is one of the most critical operation in swing arm manufacturing. The objective of this research work is to conduct a case study on process capability and its improvement for the most critical operation in swingarm. The boring operation was performed on swingarm using CNC boring machine and observations were recorded. X and R Control charts were plotted and commented on process control. The process capability indices Cp, Cpk, Cpm and Cpmk were calculated using MINITAB 19 statistical software. Among all indices, Cpmk was found to be more trustworthy with respect to the process output. Process improvement was suggested by changing the process mean towards the goal. Further analysis of such data is possible using Taguchi's loss function for quality improvement.

Process capability indices are a powerful tool used by quality control engineering to measure the degree to which the process is or is not meeting the requirements. This paper studies the application of process capability indices in the evaluation of a process with asymmetric tolerances. The analyzed collected data of the cleaning liquid “Zahi”, was used to investigate the ability of the filling process to meet the requested specifications. Matlab software was used to plot ̅ ̅ control charts, normal probability, and histogram of the data gathered from the production line and further performed statistical calculations. It was observed from the control charts that the filling process is under control. In addition, it was revealed by the process capability indices that the process of filling the cleaning liquid bottle is not fitted with the target value but it is adequate.

Process capability analysis (PCA) is a tool for measuring a process's ability to meet specification limits (SLs), which the customers define. Process capability indices (PCIs) are used for establishing a relationship between SLs and the considered process's ability to meet these limits as an index. PCA compares the output of a process with the SLs through these capability indices. If the customers' needs contain vague or imprecise terms, the classical methods are inadequate to solve the problem. In such cases, the information can be processed by the fuzzy set theory. Recently, ordinary fuzzy sets have been extended to several new types of fuzzy sets such as intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets. In this paper, a new extension of intuitionistic fuzzy sets, which is called penthagorean fuzzy sets, is proposed, and penthagorean fuzzy PCIs are developed. The design of production processes for COVID-19 has gained tremendous importance today. Surgical mask production and design have been chosen as the application area of the penthagorean fuzzy PCIs developed in this paper. PCA of the two machines used in surgical mask production has been handled under the penthagorean fuzzy environment. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) have been extensively applied to study product potential and performance. The quality control engineers use these process capability indices greatly to magnify the actual performance of the process from the predetermined specifications of the product. A control chart for the process monitoring is developed using the Gini's mean difference as a measure of variability under the Weibull distribution. We consider the control chart process capability index, Cpk has been used for the efficient monitoring of the manufacturing process. It has been observed that the proposed chart is comparatively better than the existing chart. An example of the practical application of the proposed chart has also been presented. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) have been extensively applied to study product potential and performance. The quality control engineers use these process capability indices greatly to magnify the actual performance of the process from the predetermined specifications of the product. A control chart for the process monitoring is developed using the Gini's mean difference as a measure of variability under the Weibull distribution. We consider the control chart process capability index, Cpk has been used for the efficient monitoring of the manufacturing process. It has been observed that the proposed chart is comparatively better than the existing chart. An example of the practical application of the proposed chart has also been presented. [ABSTRACT FROM AUTHOR]

Process Capability Indices (PCIs) are not only a good communication tools between sales departments and customers but also convenient tools for internal engineers to evaluate and analyze process capabilities of products. Many statisticians and process engineers are dedicated to research on process capability indices, among which the Taguchi cost loss index can reflect both the process yield and process cost loss at the same time. Therefore, in this study the Taguchi cost loss index was used to propose a novel process quality evaluation model. After the process was stabilized, a process capability evaluation was carried out. This study used Boole's inequality and DeMorgan's theorem to derive the (1 − α) × 100 % confidence region of (δ , γ 2) based on control chart data. The study adopted the mathematical programming method to find the (1 − α) × 100 % confidence interval of the Taguchi cost loss index then employed a (1 − α) × 100 % confidence interval to perform statistical testing and to determine whether the process needed improvement. [ABSTRACT FROM AUTHOR]

The performance and potential of a process of industrial products is assessed under lower specification limit L by lifetime performance index (CL). In this paper, under consideration the independent lifetimes Chen products with known one shape parameters the CL of the performance of a process is evaluated. For the hybrid censoring scheme the maximum likelihood (ML) estimate of CL is constructed as well as confidence interval for CL is developing. Also, Bayesian approach is adopted to estimates CL and credibly interval is constructed. Some theoretical results of hypothesis tests of CL is adopted. Finally, our obtaining results will be assessed and compared through Monte Carlo simulation study and numerical example.