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The present paper aims to present the results of a simulation study on the behavior of the four 95 percent bootstrap confidence intervals for estimating C_pk when collected data are from a multiple streams process.

A computer simulation study is developed to present the behavior of four 95 percent bootstrap confidence intervals, i.e. standard bootstrap (SB), percentile bootstrap (PB), biased‐corrected percentile bootstrap (BCPB), and biased‐corrected and accelerated (BCa) bootstrap for estimating the capability index C_pk of a multiple streams process. An analysis of variance using two factorial and three‐stage nested designs is applied for experimental planning and data analysis.

For multiple process streams, the relationship between the true value of C_pk and the required sample size for effective experiment is presented. Based on the simulation study, the two‐stream process always gives a higher coverage percentage of bootstrap confidence interval than the four‐stream process. Meanwhile, BCPB and BCa intervals lead to better coverage percentage than SB and PB intervals.

Since a large number of process streams decreases the coverage percentage of the bootstrap confidence interval, it may be inappropriate to use the bootstrap method for constructing the confidence interval of a process capability index as the number of process streams is large.

The present paper is the first work to explore the behavior of bootstrap confidence intervals for estimating the capability index C_pk of a multiple streams process. It is concluded that the number of process streams definitively affects the performance of bootstrap methods.

The purpose of this paper is to develop an yield-based process capability index (PCI), C _py , to overcome the shortcomings of existing PCIs that limit their use and lead to inaccurate measures of quality conformance under a variety of common conditions.

–C _py is developed conceptually to flexibly and accurately reflect conformance and then used to numerically measure inaccuracies of C _pk .

–C _py overcomes many of the problems associated with existing PCIs, including C _pk . The degree of process distribution non-normality, level of quality (the sigma level), and whether the process is centered or shifted left or right affect the direction and size of process capability error produced by C _pk . The accuracy of C _pk can be greatly affected by process data that deviate even slightly from normality.

–C _py offers numerous advantages compared to existing PCIs. It accurately reflects process conformance regardless of the process distribution. It is applicable even if the process has multiple characteristics and with both variable and attribute data. Its calculation is relatively simple and the necessary data for it are likely already captured by most organizations.

The main contributions are the development of a new PCI, C _py ; a conceptual analysis of its advantages; and a numerical analysis of the improved accuracy of C _py as compared to C _pk for shifted and non-shifted process means for normal, nearly normal, and highly non-normal distributions over a range of process variability levels.

The traditional Shewhart control chart, the X-bar and R/S chart, cannot give support to decide when it is not economically feasible to stop the process in order to remove special causes. Therefore, the purpose of this paper is to propose a new control chart design – a modified acceptance control chart, which provides a supportive method for decision making in economic terms, especially when the process has high capability indices.

The authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution of C_pk, to compare and analyze the efficiency of the proposed design.

This study suggested a new procedure to calculate the control limits (CL) of the X-bar chart, which allows economic decisions about the process to be made. By introducing a permissible average variation and defining three regions for statistical CL in the traditional X-bar control chart, a new design is proposed.

A framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (C_p and C_pk) in addition to m and n were introduced in the expected ARL equation. The C_pk is a random variable and its probability function is known. Therefore, by using a preliminary sample of a process under control, the authors can test whether the process is capable or not.

Introduces a practical method of constructing confidence intervals for the C_pk index. Constructs these confidence intervals based on the asymptotic normality of estimators for the sub‐indices of the C_pk index. As a result, the underlying distribution of the quality characteristic of interest need not be normal nor be known. Explains these sub‐indices and the Cp index and presents numerical examples and results of simulation studies of the confidence intervals.

The purpose of this paper is to propose a new mixed repetitive group sampling (RGS) plan based on the process capability index, C_pk, where the quality characteristics of interest follow the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications for both symmetric and asymmetric fraction non-conforming cases. The advantages of this proposed mixed sampling plan are also discussed. The proposed sampling plan is also compared with other existing sampling plans.

In order to determine the optimal parameters of the proposed mixed RGS plan based on C_pk, the authors constructed tables for various combinations of acceptable and limiting quality levels (LQLs). For constructing tables, the authors followed the approach of two points on the operating characteristic (OC) curve. The optimal problem is formulated as a non-linear programming where the objective function to be minimized is the average sample number (ASN) and the constraints are related to lot acceptance probabilities at acceptable quality level and LQL under the OC curve.

The proposed mixed RGS plan will be a new addition to the literature of acceptance sampling. It is shown that the proposed mixed plan involves minimum ASN with desired protection to both producers and consumers compared to other existing sampling plans. The practical application of the proposed mixed sampling plan is also explained with an illustrative real-time example.

In this paper, the authors propose a new mixed RGS plan based on the process capability index C_pk, where the quality characteristic of interest follows the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications. The proposed mixed sampling plan can be used in all production industries. This kind of mixed RGS plan is not available in the literature.

Average quadratic quality loss function (QQLF) measures quality of a given process using mean shift from its target value and variance. While it has a target parameter for the mean, it lacks a target for the variance revisable for counting any progress of the process across different quality levels, above/below the standard level; thus, it appears too general. Hence, in this research, it was initially supposed that all processes are located at two possible quality spaces, above/below the standard level. The purpose of this paper is to propose a two-criterion QQLF, in which each criterion is specifically proper to one of the quality spaces.

Since 1.33 is a literarily standard or satisfactory value for two most important process capability indices C_p and C_pk, its upper/lower spaces are assumed as high-/low-quality spaces. Then the indices are integrated into traditional QQLF, of type nominal the best (NTB), to develop a two-criterion QQLF, in which each criterion is more suitable for each quality space. These two criteria have also been innovatively embedded in the plan-do-check-act (PDCA) cycle to help continuous improvement. Finally, the proposed function has been examined in comparison with the traditional one in Feiz Hospital in the province of Isfahan, Iran.

Results indicate that the internal process of the studied case is placed on the lower quality space. So the first criterion of revised QQLF gives a more relevant evaluation for that process, compared with the traditional function. Moreover, this study has embedded both proposed criteria in the PDCA cycle as well.

Formulating the two-criterion QQLF only for observations of normal and symmetric distributions, and offering it solely for NTB characteristics are limitations of this study.

Two more relevant quality loss criteria have been formulated for each process (service or manufacturing). However, in order to show the comprehensiveness of the proposed method even in service institutes, emergency function of Feiz Hospital has been examined.

The traditional loss function of type NTB merely and implicitly targets zero defect for variance. In fact, it calculates quality loss of all processes placed on different quality spaces using a same measure. This study, however, provides a practitioner with opportunity of targeting excellent or satisfactory targets.

The purpose of this paper is to find the configuration of the number (m) and size (n) of the sample in Phase I that would make it possible to detect the out-of-control (OOC) state of the process with the smallest number of samples and ensure a capability index (C_pk) that would meet the customer’s requirements.

The suggested approach addresses this problem using simulation techniques and design of experiments (DOE). The simulation techniques made it possible to reproduce the normal operating conditions of the process. The DOE was used to construct a predictive model for control chart performance and thus to determine combinations of m and n in Phase I that would meet the capability objectives of the process. A numerical example and a simulation study were conducted to illustrate the proposed method.

Using simulation techniques and DOE, the authors can find the number (m) and size (n) of the sample in Phase I that would make it possible to detect the OOC state of the process with the smallest number of samples and ensure a C_pk that would meet the customer’s requirements.

In the real situations of many companies, choosing the numbers and sizes of samples (m and n) in Phases I and II is a crucial decision in relation to implementing a control chart. The paper shows that the simulation method and use of linear regression are effective alternatives because they are better known and more easily applied in industrial settings. Therefore, the need for alternatives to the X control chart comes into play.

In this context, process capability indices (PCI) reveal the process zones base on specification limits (SLs). Most of the research on control charts assumed certain data. However, to measure quality characteristic, practitioners sometimes face with uncertain and linguistic variables. Fuzzy theory is one of the most applicable tools which academia has employed to deal with uncertainty. The paper aims to discuss these issues.

In this investigation, first, fuzzy and S control chart has been developed and second, the fuzzy formulation of the PCIs such as C _pm ,C _pmu ,C _pml , C _pmk , P _p , P _pl , P _pu , P _pk are constructed when SLs and measurements are at both triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) stages.

The results show that using fuzzy make more flexibility and sense on recognition of out-of-control warnings.

For further research, the PCIs for non-normal data can be conducted based on TFN and TrFN.

The application case is related to a piston company in Konya’s industry area.

In the previous researches, for calculating C _p , C _pk , C _pm and C _pmk indices, the base approach was calculate standard deviation for a short term variation. For calculating these indices, the variation between subgroups are being ignored. Therefore, P _p and P _pk indices solved this fault by mentioning long term and short term variations. Therefore these two indices calculate the actual process capability.

The purpose of this paper is propose a methodology for monitoring industrial processes that cannot be stabilized, but are nevertheless capable.

The proposed procedure uses the C_P(u,v) family of capability indices proposed by Vännman (including the indices C_PK, C_PM, C_PMK) combined with one‐sided two‐out‐of‐three and three‐out‐of‐four run rules strategies.

This paper introduces a new strategy, where capability indices are monitored in place of the classical sample statistics like the mean, median, standard deviation or range.

When doing a capability analysis it is recommended to first check that the process is stable, e.g. by using control charts. However, there are occasions when a process cannot be stabilized, but is nevertheless capable. Then the classical control charts fail to efficiently monitor the process position and variability. The approach suggested in this paper overcomes this problem.

The experimental results presented in this paper demonstrate how the new proposed approach efficiently monitors capable processes by detecting decreases or increases of capability level.

Many process capability indices have been proposed to measure process performance. In this paper, we first review C_p, C_pk, C_pm and C_pmk, and their generalizations, C_Np, C_Npk, C_Npm and C_Npmk, and then propose a new index S_pmk for any underlying distribution, which takes into account process variability, departure of the process mean from the target value, and proportion of nonconformity. Proportion of nonconformity can be exactly reflected by S_pmk. Its superiority over C_Npmk, a recently developed index, also taking into account process variability and departure from the target value, is demonstrated with several non‐normal processes. A method is proposed to estimate S_pmk, with illustrations.