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1.
The process capability index C pk is widely used when measuring the capability of a manufacturing process. A process is defined to be capable if the capability index exceeds a stated threshold value, e.g. C pk >4/3. This inequality can be expressed graphically using a process capability plot, which is a plot in the plane defined by the process mean and the process standard deviation, showing the region for a capable process. In the process capability plot, a safety region can be plotted to obtain a simple graphical decision rule to assess process capability at a given significance level. We consider safety regions to be used for the index C pk . Under the assumption of normality, we derive elliptical safety regions so that, using a random sample, conclusions about the process capability can be drawn at a given significance level. This simple graphical tool is helpful when trying to understand whether it is the variability, the deviation from target, or both that need to be reduced to improve the capability. Furthermore, using safety regions, several characteristics with different specification limits and different sample sizes can be monitored in the same plot. The proposed graphical decision rule is also investigated with respect to power.  相似文献   

2.
ABSTRACT

Considerable effort has been spent on the development of confidence intervals for process capability indices (PCIs) based on the sampling distribution of the PCI or the transferred PCI. However, there is still no definitive way to construct a closed interval for a PCI. The aim of this study is to develop closed intervals for the PCIs Cpu, Cpl, and Spk based on Boole's inequality and de Morgan's laws. The relationships between different sample sizes, the significance levels, and the confidence intervals of the PCIs Cpu, Cpl, and Spk are investigated. Then, a testing model for interval estimation for the PCIs Cpu, Cpl, and Spk is built as a powerful tool for measuring the quality performance of a product. Finally, an applied example is given to demonstrate the effectiveness and applicability of the proposed method and the testing model.  相似文献   

3.
This article deals with alternative process capability indices (PCIs) to traditional basic PCIs C p , C pk , and C pm based on different fraction conforming type of probabilities. In view of various problems of constructing capability indices for univariate as well as multivariate set up, these alternative PCIs are very useful as compared to C p , C pk , and C pm . Computing aspects of proposed PCIs are discussed for normal and non normal processes when process tolerance is symmetric as well as asymmetric. Generalization of these PCIs for multivariate set up is also discussed. Some simulation study results and real life problems are given for applications of proposed PCIs.  相似文献   

4.
In this article, we investigated the bootstrap calibrated generalized confidence limits for process capability indices C pk for the one-way random effect model. Also, we derived Bissell's approximation formula for the lower confidence limit using Satterthwaite's method and calculated its coverage probabilities and expected values. Then we compared it with standard bootstrap (SB) method and generalized confidence interval method. The simulation results indicate that the confidence limit obtained offers satisfactory coverage probabilities. The proposed method is illustrated with the help of simulation studies and data sets.  相似文献   

5.
In this paper, variables repetitive group sampling plans are developed based on the process capability index C pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.  相似文献   

6.
Pearn and Chen (1996) considered the process capability index Cpk, and investigated the statistical properties of its natural estimator under various process conditions. Their investigation, however, was restricted to processes with symmetric tolerances. Recently, Pearn and Chen (1998) considered a generalization of Cpk, referred to as C? pk, to cover processes with asymmetric tolerances. They investigated the statistical properties of the natural estimator of C? pk, and obtained the exact formulae for the expected value and variance. In this paper, we consider a new estimator of C? pk, assuming the knowledge on P(LI > T) = p is available, where 0 > p > 1, which can be obtained from historical information of a stable process. We obtain the exact distribution of the new estimator assuming the process characteristic follows the normal distribution. We show that the new estimator is consistent, asymptotically unbiased, which converges to a mixture of two normal distributions. We also show that by adding suitable correction factors to the new estimator, we may obtain the UMVUE and the MLE of the generalization C? pk.  相似文献   

7.
Abstract

The use of indices as an estimation tool of process capability is long-established among the statistical quality professionals. Numerous capability indices have been proposed in last few years. Cpm constitutes one of the most widely used capability indices and its estimation has attracted much interest. In this paper, we propose a new method for constructing an approximate confidence interval for the index Cpm. The proposed method is based on the asymptotic distribution of the index Cpm obtained by the Delta Method. Under some regularity conditions, the distribution of an estimator of the process capability index Cpm is asymptotically normal.  相似文献   

8.
When the distribution of one of the characteristics of a process is non normal, methods based on empirical percentiles suggest the use of several process capability indices (PCIs) which are similar to the usual C p , C pk , C pm , and C pmk indices. However most of these PCIs apply only to the case of symmetrical tolerances. To take into account the asymmetry of the tolerances as well as the asymmetry of the process distribution, new PCIs which improve the previous ones are proposed. In the end and in order to validate the method proposed here, we apply it to a real production case.  相似文献   

9.
In this paper an attempt has been made to examine the multivariate versions of the common process capability indices (PCI's) denoted by Cp and Cpk . Markov chain Monte Carlo (MCMC) methods are used to generate sampling distributions for the various PCI's from where inference is performed. Some Bayesian model checking techniques are developed and implemented to examine how well our model fits the data. Finally the methods are exemplified on a historical aircraft data set collected by the Pratt and Whitney Company.  相似文献   

10.
Process capability index Cp has been the most popular one used in the manufacturing industry to provide numerical measures on process precision. For normally distributed processes with automatic fully inspections, the inspected processes follow truncated normal distributions. In this article, we provide the formulae of moments used for the Edgeworth approximation on the precision measurement Cp for truncated normally distributed processes. Based on the developed moments, lower confidence bounds with various sample sizes and confidence levels are provided and tabulated. Consequently, practitioners can use lower confidence bounds to determine whether their manufacturing processes are capable of preset precision requirements.  相似文献   

11.
Vannman has earlier studied a class of capability indices, containing the indices C p , C pk , C pm and C pmk , when the tolerances are symmetric. We study the properties of this class when the tolerances are asymmetric and suggest a new enlargened class of indices. Under the assumption of normality an explicit form of the distribution of the new class of the estimated indices is provided. Numerical investigations are made to explore the behavior of the estimators of the indices for different values of the parameters. Based on the estimator a decision rule that can be used to determine whether the process can be considered capable or not is provided and suitable criteria for choosing an index from the family are suggested.  相似文献   

12.
Franklin and Wasserman (1991) introduced the use of Bootstrap sampling procedures for deriving nonparametric confidence intervals for the process capability index, Cpk, which are applicable for instances when at least twenty data points are available. This represents a significant reduction in the usually recommended sample requirement of 100 observations (see Gunther 1989). To facilitate and encourage the use of these procedures. a FORTRAN program is provided for computation of confidence intervals for Cpk. Three methods are provided for this calculation including the standard method, the percentile confidence interval, and the biased - corrected percentile confidence interval.  相似文献   

13.
Process capability indices are routinely used in manufacturing industries for process monitoring. A basic assumption while using process capability indices is that there are no assignable causes of variation present. However, when variation due to an assignable cause is present and is tolerated, the conventional methods of capability measurement become inaccurate. In this article, we suggest an estimate of Cpk assuming that the process capability changes dynamically. We obtain an exact form of the sampling distribution in the presence of a systematic assignable cause. We discuss the problem of testing whether a given process is capable. The critical values for different sample sizes are obtained based on the sampling distribution. An example involving tool wear problem is presented.  相似文献   

14.
In this article, we propose a new mixed chain sampling plan based on the process capability index Cpk, where the quality characteristic of interest having double specification limits and follows the normal distribution with unknown mean and variance. In the proposed mixed plan, the chain sampling inspection plan is used for the inspection of attribute quality characteristics. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications by formulating the problem as a non linear programming in which the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.  相似文献   

15.
The process capability index C pm, sometimes called the loss-based index, has been proposed to the manufacturing industry for measuring process reproduction capability. This index incorporates the variation of production items with respect to the target value and the specification limits preset in the factory. To estimate the loss-based index properly and accurately, certain frequentist and Bayesian perspectives have been proposed to obtain lower confidence bounds (LCBs) for providing minimum process capability. The LCBs not only provide critical information regarding process performance but are also used to determine whether an improvement was made in a capability index and by extension in reducing the fraction of non-conforming items. In this paper, under the assumption of normality, based on frequentist and Bayesian senses, several existing approaches for constructing LCBs of C pm are presented. Depending on the statistical methods used, we then classify these existing approaches into three categories and compared them in terms of the coverage rates and the mean values of the LCBs via simulations. The relative advantages and disadvantages of these approaches are summarized with some highlights of the relevant findings.  相似文献   

16.
In this paper, a variables tightened-normal-tightened (TNT) two-plan sampling system based on the widely used capability index Cpk is developed for product acceptance determination when the quality characteristic of products has two-sided specification limits and follows a normal distribution. The operating procedure and operating characteristic (OC) function of the variables TNT two-plan sampling system, and the conditions for solving plan parameters are provided. The behavior of OC curves for the variables TNT sampling system under various parameters is also studied, and compared with the variables single tightened inspection plan and single normal inspection plan.  相似文献   

17.
Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCI Cp compares the output of a process to the specification limits (SLs) by forming the ratio of the width between the process SLs with the width of the natural tolerance limits which is measured by six process standard deviation units. As another common PCI, Cpm incorporates two variation components which are variation to the process mean and deviation of the process mean from the target. A meaningful generalized version of above PCIs is introduced in this paper which is able to handle in a fuzzy environment. These generalized PCIs are able to measure the capability of a fuzzy-valued process in producing products on the basis of a fuzzy quality. Fast computing formulas for the generalized PCIs are computed for normal and symmetric triangular fuzzy observations, where the fuzzy quality is defined by linear and exponential fuzzy SLs. A practical example is presented to show the performance of proposed indices.  相似文献   

18.
This article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on Cpk and the mixed variable lot size plan based on Cpk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.  相似文献   

19.
In this article, we construct an improved procedure for estimating the process capability index C pmk . We propose a new C pmk lower-bound approach based on the GCI concept, and compare it with other existing methods. Based on the comparison results, we conclude with a recommendation, and construct a step-by-step procedure for the recommended approach to estimate the actual process capability C pmk for various sample sizes. The lower bound attended by our recommended approach, indeed, improves other existing lower bound methods. We also investigate a real-world application to illustrate how we could apply the recommended approach to the actual manufacturing processes.  相似文献   

20.
In this paper, we present an optimal designing methodology for the skip-lot sampling plan (SkSP) of type SkSP-R based on the most widely used process capability index (PCI) Cpk. The SkSP-R plan is one of the SkSPs that incorporate the provision of the reinspection concept. In order to design the optimal parameters, we consider both symmetric and asymmetric fraction non conforming cases. Tables are also constructed to determine the optimal parameters by formulating an optimization problem. The advantages of the proposed plan over the existing plan are also discussed. Application of the plan is explained with a real-life example.  相似文献   

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