摘要:

An economic design model for an-chart which uses a variable sample size feature is developed in this paper. In a variable sample size control chart the sample size at each sampling time depends on the value of the previous sample statistic, whereas the sample size is set to be fixed constant in traditional control charts. In order to detect shifts quickly, the variable sample size chart takes a larger sample if there is any indication that the process is running in an out-of-control state and a smaller sample otherwise. for practical purposes only two possible sample sizes are considered. The objective of the econo,ic design is to find the optimal sampling interval, control limit and sample sizes to minimize the expected cost per unit operating time. The determination of the optimal design requires the computation of the averge number of samples and the average number of observations taken when the process is in control and out of control. The characteristics can be computed using the Markov chain property of the control procedure. Application of the variable sample size fezture of the-chart for the case in which there are multiple assignable causes shows improved efficiency and statistical performance compared to the fixed sample size chart

ISSN:0361-0918    

DOI:10.1080/03610919408813182

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

Designs of cumulative sum (CUSUM) control charts have traditionally been based on the average run length (ARL). However,interpretatios based on the ARL can be misleading as the in-control run length distribution of a CUSUM chart is highly skewed. Any meaningful interpretation based on the ARL is complicated by the fact that the form of the ren length distribution changes according to the shift in the process mean, and for certain shifts, the run length distributions are almost symmetric. For a run length distribution which can vary from a bighly skewed distribution to an almost symmetric distribution with respect to the sift, the median run length (MRL) is a more meaningful quantity to depend on since interpretation based on the MRL is more readily understood. An important reason for the wide sqread and easily. On the other hand, the MRL and in general, percentage points of run length distribution of a CUSUM chart can be computed accurately and easily. On the other hand, the MRL and in general, percentage points of run length distribution of a CUSUM chart are much harder to compute. Two methods of computing the MRL of a CUSUM chart are examined with emphasis given to the numerical accuracy. An optional design of CUSUM chart based on the MRL is proposed and graphs are provided such that the chart parameters of an optimal CUSUM chart can be determined easily, A normal process is assumed.

ISSN:0361-0918    

DOI:10.1080/03610919408813183

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

The speed of convergence of the distribution of the normalized maximum, of a sample of independent and identically distributed random variables, to its asymptotic distribution is considered in this article. Assuming that the cumulative distribution function of the random variables is known, the error committed replacing the actual distribution of the normalized maximum by its asympotic distribution is studied. Instead of using the arithmetical scale of probabilities, we measure the difference between the actual and asympotic distribution in terms of the double-log scale used for building the probability plotting paper for the the latter. We demonstrate that the difference between the double-log values corresponding to two probabilities in the upper tail is almost exactly equal to the logarithm of the distribution may not be uniform in this double-log scale and that the difference between the actual and asymptotic distributions, on the probebility plotting paper, may be a logarithmic, power, or even exponential function in the upper tail when the latter distribution is of Fisher-Tippett type I, but that difference is at most logarithmic in the upper tail for type II and III distributions. This fact is exploited to obtain transformed variables that converge tothe asymptotic distribution faster than the original variable on the probabilites plotting paper

ISSN:0361-0918    

DOI:10.1080/03610919408813184

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

A nonparametric test procedure is proposed for the analysis of randomized complete block designs. Such a procedure may be carried out graphically in the form of a Shewhart control chart. Exact and asymptotic critical values are given for the implementation of the proposed procedure. A Monte Carlo study is made to compare the powers of the proposed procedure to those of analysis of variance, the analysis of means, and the Friedman procedures. Results of the study indicate that the proposed procedure has superior power performance when testing against slippage alternative hypotheses under heavy-tailed distributions such as the Cauchy distribution. However, when testing against symmetric alternatives under light-tailed distributions, the proposed procedure does not perform well

ISSN:0361-0918    

DOI:10.1080/03610919408813185

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610919408813171

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor