排序方式: 共有11条查询结果,搜索用时 312 毫秒
1.
A Bayesian-like estimator of the process capability index Cpmk 总被引:1,自引:0,他引:1
Pearn et al. (1992) proposed the capability index Cpmk, and investigated the statistical properties of its natural estimator for stable normal processes with constant mean μ. Chen and Hsu (1995) showed that under general conditions the asymptotic
distribution of is normal if μ≠m, and is a linear combination of the normal and the folded-normal distributions if μ=m, where m is the mid-point
between the upper and the lower specification limits. In this paper, we consider a new estimator for stable processes under a different (more realistic) condition on process mean, namely, P (μ≥m)=p, 0≤p≤1. We obtain the
exact distribution, the expected value, and the variance of under normality assumption. We show that for P (μ≥m)=0, or 1, the new estimator is the MLE of Cpmk, which is asymptotically efficient. In addition, we show that under general conditions is consistent and is asymptotically unbiased. We also show that the asymptotic distribution of is a mixture of two normal distributions.
RID="*"
ID="*" The research was partially supported by National Science Council of the Republic of China (NSC-89-2213-E-346-003). 相似文献
2.
3.
Pearn et al. (Commun. Stat. Theory Methods, 27(4):985–1000, 1998) introduced the process accuracy index C
a
to measure the degree of process centering, the ability to cluster around the center. In this paper, we derive an explicit
form of the cumulative distribution function for the estimator [^(C)]a{\hat{C}_a } with the case of symmetric tolerances. Subsequently, the distributional and inferential properties of the estimated process
accuracy index C
a
are provided. Calculations of the critical values, P-values, and lower confidence bounds are developed for testing process accuracy. Further, a generalization of C
a
for the case with asymmetric tolerances is proposed to measure the process accuracy. Based on the results practitioners can
easily perform the testing of the process accuracy, and make reliable decisions on whether actions should be taken to improve
the process quality. An application is given to illustrate how we test the process accuracy using the actual data collected
from the factory. 相似文献
4.
Process precision index Cp has been widely used in the manufacturing industry to provide numerical measures on process potential. Pearn et al. (1998) considered an unbiased estimator of Cp for one single sample. They showed that the unbiased estimator is the UMVUE. They also proposed an efficient test for Cp based on one single sample, and showed that the test is the UMP test. In this paper, we consider an unbiased estimator of Cp for multiple samples. We show that the unbiased estimator is the UMVUE of Cp, which is asymptotically efficient. We also consider an efficient test for Cp, and show that the test is the UMPtest for multiple samples. The practitioners can use the proposed test on theirin-plant applications to obtain reliable decisions. 相似文献
5.
6.
Process yield is the most common criterion used in the manufacturing industry for measuring process performance. A measurement index, called Spk, has been proposed to calculate the yield for normal processes. The measurement index pk establishes the relationship between the manufacturing specifications and the actual process performance, which provides an exact measure on process yield. Unfortunately, the sampling distribution of the estimated pk is mathematically intractable. Therefore, process performance testing cannot be performed. In this paper; we consider a normal approximation to the distribution of the estimated pk, and investigate its accuracy computationally. We compare the critical values calculated from the approximate distribution with those obtained using the standard simulation technique, for various commonly used quality requirements. Extensive computational results are provided and analyzed. The investigation is useful to the practitioners for making decisions in testing process performance based on the yield. 相似文献
7.
The process capability index Cpk has been widely used in the manufacturing industry to provide numerical measures on process performance. Since Cpk is a yield-based index which is independent of the target T, it fails to account for process centering with symmetric tolerances, and presents an even greater problem with asymmetric tolerances. Pearn and Chen (1998) considered a new generalization Cpk which was shown to be superior to other existing generalizations of Cpk for processes with asymmetric tolerances. In this paper, we investigate the relation between the fraction nonconforming and the value of Cpk. Furthermore, we derive explicit forms of the cumulative distribution function and the probability density function for the natural estimator pk, under the assumption of normality. We also develop a decision making rule based on the natural estimator pk, which can be used to test whether the process is capable or not. 相似文献
8.
Process capability indices have been widely used in the manufacturing industry. Those capability indices, quantifying process
potential and performance, are important for any successful quality improvement activities and quality program implementation.
Because of the simplicity and easy of understanding, the precision index Cp has gained its popularity for measuring process consistency. However, the quality of data on the process characteristics
relies very much on the gauge measurement. Conclusions about capability of the process just only based on the single numerical
value of the index are not reliable. In this paper, we not only conduct the performance of the index Cp with gauge measurement errors, but also present adjusted confidence interval bounds and critical values for capability testing
purpose of Cp with unavoidable measurement errors. Our research would help practitioners to determine whether the factory processes meet
the capability requirement, and make more reliable decisions. 相似文献
9.
Process capability indices have been proposed in the manufacturing industry to provide numerical measures on process reproduction
capability, which are effective tools for quality assurance and guidance for process improvement. In process capability analysis,
the usual practice for testing capability indices from sample data are based on traditional distribution frequency approach.
Bayesian statistical techniques are an alternative to the frequency approach. Shiau, Chiang and Hung (1999) applied Bayesian
method to index Cpm and the index Cpk but under the restriction that the process mean μ equals to the midpoint of the two specification limits, m. We note that this restriction is a rather impractical assumption for most factory applications, since in this case Cpk will reduce to Cp. In this paper, we consider testing the most popular capability index Cpk for general situation – no restriction on the process mean based on Bayesian approach. The results obtained are more general
and practical for real applications. We derive the posterior probability, p, for which the process under investigation is capable and propose accordingly a Bayesian procedure for capability testing.
To make this Bayesian procedure practical for in-plant applications, we tabulate the minimum values of Ĉpk for which the posterior probability p reaches desirable confidence levels with various pre-specified capability levels. 相似文献
10.
In this paper, we consider two newsboy-type products with unequal prices and costs. Both demands are independent and follow normal distributions with unknown parameters μ and σ. We study the product selection problem which deals with comparing two products and selecting the one that has a significantly higher profitability, in which the profitability is defined to the probability of achieving a target profit under the optimal ordering policy. The statistical hypothesis testing methodology is performed to tackle this selection problem. Critical value of the test is calculated to determine the selection decision. Sample size required for a designated power and confidence level is also investigated. An application example on comparing English-teaching magazines is presented to illustrate the practicality of our approach. 相似文献