摘要:

Recent studies have shown that theX¯chart with variable parameters (VpX¯chart) detects process shifts faster than the traditionalX¯chart. This article extends these studies for processes that are monitored by both,X¯andRcharts. Basically, theX¯andRvalues establish if the control should or should not be relaxed. When theX¯andRvalues fall in the central region the control is relaxed because one will wait more to take the next sample and/or the next sample will be smaller than usual. When theX¯orRvalues fall in the warning region the control is tightened because one will wait less to take the next sample and the next sample will be larger than usual. The action limits are also made variable. This paper proposes to draw the action limits (for both charts) wider than usual when the control is relaxed and narrower than usual when the control is tightened. The Vp feature improves the jointX¯andRcontrol chart performance in terms of the speed with which the process mean and/or variance shifts are detected.

ISSN:0740-817X    

DOI:10.1080/07408179808966490

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

When monitoring a process it is important to quickly detect increases and decreases in its variability. In addition to preventing any increase in the variability of the process and any deterioration in the quality of the output, it is also important to search for special causes that may result in a smaller process dispersion. Considering this, users should always try to monitor for both increases and decreases in the variability. The process variability is commonly monitored by means of a Shewhart range chart. For small subgroup sizes this control chart has a lower control limit equal to zero. To help monitor for both increases and decreases in variability, Shewhart charts with probability limits or runs rules can be used. CUSUM and EWMA charts based on the range or a function of the subgroup variance can also be used. In this paper a CUSUM chart based on the subgroup range is proposed. Its performance is compared with that of other charts proposed in the literature. It is found that for small subgroup sizes, it has an excellent performance and it thus represents a powerful alternative to currently utilized strategies.

ISSN:0740-817X    

DOI:10.1080/07408179808966491

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

An important component of the quality program of many manufacturing operations is the use of control chart for variables. Inherent in the construction of these control charts is the assumption that the sampled process is a normal distribution whose observations are independent and identically distributed (iid). Many processes such as those found in chemical manufacturing, refinery operations, smelting operations, wood product manufacturing, waste-water processing and the operation of nuclear reactors have been shown to have autocorrelated observations. Autocorrelation, which violates the independence assumption of standard control charts, is known to have an adverse effect on the average run length (ARL) performance of control charts. This paper will consider a statistical testing procedure for the change-point problem for monitoring the level parameter of the AR(1) process. This test is shown to result in a CUSUM-based control chart. Two different solutions of the change-point problem are given which result in slightly different control charts. The average run length of each of these CUSUM control charts is found via the Markov chain approach. A methodology for designing the CUSUM-based control chart is presented and the performance of these control charts is compared to other approaches in the literature.

ISSN:0740-817X    

DOI:10.1080/07408179808966492

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The assessment of multivariate yield is central to the robust design of products/processes. Currently, yield is evaluated via Monte Carlo simulation. However, it requires thousands of replications per simulation to achieve an acceptably precise estimate of yield, this is often tedious and time consuming, thereby rendering it unattractive as an evaluation tool. We propose a discrete point approximation on each design variable, using general Beta distributions, for assessing reasonably precise multivariate yield estimates, which require only a minute fraction of the Monte Carlo replications/simulations required to estimate yield (e.g., 3 and 5 design variables would require only 33= 27 and 35= 243 replications, respectively). The Beta distribution has the desirable property of being able to characterize a wide variety of processes that may or may not be symmetric and which may or may not have a finite operating range. Using an approach that computes the roots of a polynomial, whose degree is determined by the number of discrete points, discrete three point approximations are obtained and tabulated for twenty-five different Beta distributions. Based on several test examples, where design parameters are modeled as independent Beta random variates, our approach appears to be highly accurate, achieving virtually the same multivariate yield estimate as that obtained via Monte Carlo simulation. The substantial reduction in the number of replications and associated computational time required to assess yield makes the iterative adjustment of design parameters a more practical design strategy.

ISSN:0740-817X    

DOI:10.1080/07408179808966493

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A control chart based on applying a sequential probability ratio test (SPRT) at each sampling point is considered for the problem of monitoring a process proportionp. This SPRT chart can be applied in situations in which items are inspected one by one, and the results of each inspection can be conveniently recorded before the next item is inspected. Some corrected diffusion theory approximations are given for the statistical properties of the SPRT and the SPRT chart. These approximations are very accurate and provide a simple method for designing an SPRT chart for practical applications. The sample size for the SPRT chart at a particular sampling time depends on the observations at that time, but the chart can be designed to have a specified average sampling rate when the process is in control. When there is a small shift inp, the average sampling rate per unit time will increase, but for a large shift inpthe average sampling rate will decrease. For a given in-control average sampling rate and a given false alarm rate, the SPRT chart will detect changes inpmuch faster than the standardp-chart, which has traditionally been used for monitoringp. The SPRT chart will also detect changes inpmuch faster than the CUSUM chart forp. Thus, the SPRT chart can be used in place of traditional control charts to provide faster detection of changes inpor to reduce the sampling effort required to provide a given detection capability.

ISSN:0740-817X    

DOI:10.1080/07408179808966494

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The two measures of dispersion which are used in statistical quality control are ρ, the expected value of the range of samples of a uniform sizen, and σ, the standard deviation of the population from which the samples are taken. Conversion of one into the other is facilitated by use of the quantity calledd2which is taken to be the ratio of ρ to σ. Tables ofd2versusnare reproduced in all texts on statistical quality control. These tables are predicated upon the parent population being normally distributed, an assumption which may be unjustified in many instances. To understand the consequences of this assumption of normality, a short table ofd2values based upon five distributions is presented. The five distributions are: normal, uniform, triangular, Erlang ν = 1 (negative exponential), and Erlang ν = 2. The sample size varies from two through 12, plus 15, 20, and 50. It was observed that for many values ofnthe normal distribution produced the largest value ofd2, while the negative exponential distribution produced the smallest value. Depending upon the intended use, and whether Type I or Type II error is of more concern, one may wish to used2values based upon other than the normal distribution. Some recommendations are made. A derivation of the formula for computing ρ as a function ofnwhich is dependent upon the parent population distribution is given in an appendix.

ISSN:0740-817X    

DOI:10.1080/07408179808966495

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

ISSN:0740-817X    

DOI:10.1080/07408179808966496

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

ISSN:0740-817X    

DOI:10.1080/07408179808966497

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

ISSN:0740-817X    

DOI:10.1080/07408179808966498

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

ISSN:0740-817X    

DOI:10.1080/07408179808966499

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor