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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 (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]

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]

Abstract It is a very important topic in the manufacturing industry to evaluate whether the quality of products adhered to the desire level. The larger-the-better process capability index (PCI) C L is frequently used to measure the performance of lifetimes of products. Gompertz distribution has many applications in the lifetime data analysis. The maximum likelihood estimator for C L is utilized to develop a hypothesis testing procedure with respect to a lower specification limit based on the progressive type I interval censored sample. Finally, two practical examples are given to demonstrate the application of our proposed testing procedure to assess whether the lifetime performance reached the desire level. [ABSTRACT FROM AUTHOR]

In the competitive manufacturing markets, quality engineers frequently are dedicated to evaluate whether the quality performance of products met the desire level. The lifetime performance index (LPI) C L is used to monitor the larger-the-better performance of lifetimes of products. Chen lifetime distribution with bathtub shape or increasing failure rate function has many applications in the lifetime data analysis. The maximum likelihood estimator for C L is derived and used to propose a hypothesis testing procedure under a lower specification limit based on the progressive type I interval censored sample. Finally, two practical examples are given to demonstrate the application of our proposed testing procedure to assess whether the lifetime performance reached the desire level. [ABSTRACT FROM AUTHOR]

It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices C L is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Rayleigh distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also developed. We use this estimator to build the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

The assessing of the lifetime performance is a very important topic in manufacturing or service industries. Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. The lifetimes of products are assumed to have Weibull distribution with a known shape parameter and the larger-the-better lifetime performance index is considered. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

The objective of the article is to increase the probability of achieving a joint of cylindrical machine parts, through appropriate orientation of the robot gripper of the assembly robot, while ensuring the best parameters of the assembly process and the required process capability, without unnecessarily increasing the accuracy of the assembly workstation equipment. The presented methodology for the summation of errors, besides its simplicity, has an additional advantage compared with the method of the summation of variance or error vectors separately in regard to each axis of the adopted coordinate system, because it takes into account the nature of the relationships between variables (covariance). The analysis showed that by rotation of the gripper around an oriented axis of the machine cylindrical part, the probability of the joint and process capability index C p value can be increased from C p = 1.17 to C p = 1.33 . The optimal orientation of the robot gripper enables the clearance fit between mating parts to be reduced by 8% and 19% with respect to its extreme unfavourable setting. However, this setting of the robot gripper reduces the sensitivity of the system to the effects of systematic errors. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose three novel capability indices for multidimensional machining processes. [•] Consider the variances of machining results on different directions may not be equal. [•] The statistical properties of the point estimators for the new indices are derived. [•] The simulation results show that the new indices outperform the predecessors. [•] Two numerical examples further demonstrate the usefulness of our proposed indices. [ABSTRACT FROM AUTHOR]

Abstract: An important topic in the manufacturing industries is the assessing of the lifetime performance. In this paper, it is supposed the lifetimes of products are independent and have a common Weibull distribution with a known shape parameter. The lifetime performance index () proposed by Montgomery (1985) [1], is used for evaluating the performance of a process with respect to a lower specification limit (). The maximum likelihood estimate of is obtained on the basis of the progressive first-failure censored data. This estimate is then used for developing a confidence interval for . The behavior of the confidence interval for the parameter given a significance level is investigated and also two illustrative examples and a sensitivity analysis are given. For the exponential distribution as a special case of Weibull distribution, a comparison study for various estimates of based on mean squared error (MSE) and Pitman measure of closeness (PMC) criteria is done. [Copyright &y& Elsevier]

Abstract: Process capability indices (PCIs) can be viewed as the effective and excellent means of measuring product quality and process performance. They are very useful statistical analysis tools to summarize process dispersion and location by using process capability analysis (PCA). However, there are some limitations which prevent a deep and flexible analysis because of the crisp definition of PCA’s parameters. In this paper, the fuzzy set theory is used to add more information and flexibility to PCA. For this aim, fuzzy process mean, and fuzzy variance, , which are obtained by using the fuzzy extension principle, are used. Then fuzzy specification limits (SLs) are used together with and to produce fuzzy PCIs (FPCIs). The fuzzy formulations of the indices C p , C pk , C a , C pm , and C pmk which are the most used traditional PCIs, are developed and a numerical example for each from an automotive company is given. The results show that fuzzy estimations of PCIs have much more treasure to evaluate the process performance when it is compared with the crisp case. [Copyright &y& Elsevier]

Abstract: Process capability indices measure the ability of a production process to produce items within specification limits. The calculation of process capability indices has been focusing on using traditional frequency approach, which requires a large sample size for an accurate estimation. In order to eliminate this defect of traditional frequency approach on multi-batch and low volume production, Bayesian approach was used. The conjugate Bayesian approach is chosen to estimate the process distribution parameters. The algorithm with these conjugate Bayes estimators is proposed for measuring the process capability for multi-batch and low volume production. A case study is presented to demonstrate how the approach can be applied to actual data collected in practice. [Copyright &y& Elsevier]

Abstract: The index C pmk is a well-known loss-based process capability index. It can reveal more information about the location of the process mean compared with other classic process capability indices. This index is also more sensitive than other capability indices to any deviations from process mean. When there are some uncertainties in observations, fuzzy logic can be employed to manage these uncertainties. There is some research on different fuzzy process capability indices and this paper is an extension of for the process capability index C pmk of fuzzy numbers. In order to find the membership function of process capability index C pmk , the α-cuts of the fuzzy observation were employed. An example of fuzzy process capability C pmk calculator was illustrated and compared with other classic fuzzy process capability indices and . Results showed that fuzzy has the advantages of both and . Since the index C pmk is a more sensitive index compared with other classic indices, the fuzzy process capability index can be a more sensitive fuzzy index compared with and . [Copyright &y& Elsevier]

Abstract: Process performance can be analyzed by using process capability indices (PCIs), which are summary statistics to depict the process location and dispersion successfully. Although they are very usable statistics, they have some limitations which prevent a deep and flexible analysis because of the crisp measurements and specification limits (SLs). If the specification limits or measurements are expressed by linguistic variables, traditional PCIs cause some misleading results. In this paper, the fuzzy set theory is used to add more information and flexibility to process capability analyses (PCA). For this aim, linguistic definition of the quality characteristic measurements are converted to fuzzy numbers and fuzzy PCIs are produced based on these measurements and fuzzy specification limits (SLs). Also fuzzy control charts are derived for fuzzy measurements of the related quality characteristic. They are used to increase the accuracy of PCA by determining whether or not the process is in statistical control. The fuzzy formulation of the indices C p and C pk , which are the most used two traditional PCIs, are produced when SLs and measurements are both triangular (TFN) and trapezoidal fuzzy numbers (TrFN). The proposed methodologies are applied in a piston manufacturer in Konya’s Industrial Area, Turkey. [ABSTRACT FROM AUTHOR]

Abstract: Process capability indices (PCIs) are very a useful statistical analysis tool to summarize process’ dispersion and location by process capability analysis (PCA). Additionally PCA produces another two more important results that show us the process ability satisfying specification limits (SLs) and the ratios of conforming (CIs) and nonconforming (NCIs) items which are the probabilities of producing within and out of SLs. However, there are some limitations which prevent a deep and flexible analysis because of the crisp definition of SLs. In this paper, the fuzzy set theory is used to add more sensitiveness to PCA including more information and flexibility. For this aim, fuzzy normal distribution with crisp SLs is first used to calculate the fuzzy percentages of conforming (FCIs) and nonconforming (FNCIs) items by taking into account fuzzy process mean, and fuzzy variance, which are obtained by using fuzzy extension principles. The calculation of the percentages of CIs and NCIs items in fuzzy numbers gains more flexible evaluation ability for the process engineer. Then fuzzy SLs are used together with and to produce fuzzy PCIs (FPCIs) and fuzzy normal distribution. The fuzzy formulation of the indices and , most used two traditional PCIs, are produced when SLs are either triangular (TFN) or trapezoidal fuzzy numbers (TrFN). The proposed methodologies are applied in a piston manufacturer in Konya’s Industrial Area, Turkey. FPCIs, FCIs, and FNCIs ratios are determined for piston diameter measurements. The results show that fuzzy estimations of PCIs, CIs, and NCIs have much more treasure to evaluate the process when it is compared with the crisp case. [Copyright &y& Elsevier]

Abstract: This paper proposes a procedure for assessing a measurement system and manufacturing process capabilities using Gage Repeatability and Reproducibility (GR&R) designed experiments with four quality measures. In this procedure, a GR&R study is conducted to obtain replicate measurements on units by several different operators. The gage and part variance components are then estimated by conducting analysis of variance (ANOVA) on the GR&R measurement observations. Finally, the acceptance and rejection criteria of the precision-to-tolerance ratio (PTR), signal-to-noise ratio (SNR), discrimination ratio (DR), and process capability index (Cp or Cpk ), are employed to assess the measurement and process capabilities. Three previously studied case studies are provided for illustration; in all of which the procedure provided efficient capability assessments at minimal computational and statistical efforts. In conclusion, the procedure proposed in this research using GR&R designed experiments provides valuable procedure and helpful guidelines to quality and production managers in assessing the capabilities of a measurement system and manufacturing process, and deciding the needed actions for improving performance. [Copyright &y& Elsevier]

Abstract: Process capability indices (PCIs) are used to measure process potential and performance. Since the lifetime of products generally may possess an exponential, gamma or Weibull distribution, etc., so under a two-parameter exponential distribution, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the right type II censored sample. Then the UMVUE of the lifetime performance index is utilized to develop the new hypothesis testing procedure in the condition of known L. Finally, a practical example is illustrated to employ the testing procedure to determine whether the process is capable. [Copyright &y& Elsevier]

Abstract: Process capability indices (PCIs) are used to measure process potential and performance. Since the lifetime of products generally may possess an exponential, gamma or Weibull distribution, etc., so under a two-parameter exponential distribution, this study constructs a maximum likelihood estimator (MLE) of the lifetime performance index based on the right type II censored sample. Then the MLE of the lifetime performance index is utilized to develop the new hypothesis testing algorithmic procedure in the condition of known L. Finally, a practical example is illustrated to employ the testing algorithmic procedure to determine whether the process is capable. [Copyright &y& Elsevier]