In some industrial or health-related processes, it makes more practical sense to monitor either an increase only or a decrease only in the quality characteristic of interest. Consequently, in this paper, we propose four one-sided Shewhart X charts supplemented with runs-rules to monitor the mean of autocorrelated normally distributed samples using a stationary first-order autoregressive model. To counteract the negative effect of autocorrelation, we implement a sampling strategy which involves sampling of non-neighboring observations to form rational subgroups. The Markov chain technique is used to derive zero-state and steady-state closed-form expressions of the specific shift performance metric, ie, average run-length (ARL). Moreover, we compute the expected ARL metric which evaluates each monitoring scheme based on all specified range of possible values of the shift parameter, or more specifically, from a global point of view and thus gives a different perspective from the specific shift ARL metric. We observed that the steady-state improved w-of-w and the improved 2-of-(H + 1) schemes yield a better overall performance than their corresponding basic counterparts for all different levels of autocorrelation. A real-life example is provided to illustrate the implementation of the monitoring schemes proposed here.

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Distribution-free (nonparametric) control charts are helpful in applications where we do not have enough information about the underlying distribution. The Shewhart precedence charts is a class of phase-I nonparametric charts for location. One of these charts, called the median precedence chart (Med chart hereafter), uses the median of the test sample as the charting statistic, whereas another chart, called the minimum precedence chart (Min chart hereafter), uses the minimum. In this paper, we first study the comparative performance of the Min and the Med charts, respectively, in terms of their in-control and out-of-control run-length properties in an extensive simulation study. It is seen that neither chart is best as each has its strength in certain situations. Next, we consider enhancing their performance by adding some supplementary runs-rules. It is seen that the new charts present very attractive run-length properties, that is, they outperform their competitors in many situations. A summary and some concluding remarks are given. Appl. Stochastic Models Bus. Ind. 2016, 32 423-439 423 J. C. MALELA-MAJIKA, S. CHAKRABORTI AND M. A. GRAHAM Background, statistical framework and preliminaries of the precedence control chartAssume that a reference (phase-I) sample of independent and identically distributed (iid) observations, X 1 , X 2 , … , X m , of size m, is available from an IC process with an unknown continuous cumulative distribution function (cdf) F(x). Next, assume that a sample of iid phase-II observations Y 1 , Y 2 , … , Y n , of size n, is taken from an unknown continuous cdf G(x). Moreover, the phase-II observations are assumed to be independent of those from the phase-I sample. We further assume the location model G(t) = F(t + ), for all t. For the IC case, the location shift is equal to zero ( = 0), so that the two distributions are identical (F = G). For the OOC case, the distribution of the phase-II sample is taken to be the same form as that for the phase-I sample but with a shift in location parameter in units of the population standard deviation, so that ≠ 0. For example, the phase-I sample may be drawn from a normal distribution with mean 0 and standard deviation 1, whereas in the OOC case, the phase-II sample may be drawn from a normal distribution with mean different from 0 (mean = ) and standard deviation 1. We say that the shift in location (mean), , is not equal to zero ( ≠ 0).Janacek and Meikle [19] first proposed a phase-II nonparametric control chart useful in case U. The control limits for this chart are given by two selected order statistics of a phase-I reference sample, and the charting statistic is the median, M i , i = 1, 2, …, of the phase-II samples, taken sequentially. Chakraborti et al. [20] generalized the work of Janacek and Meikle [19] and proposed the class of precedence charts. The precedence chart uses the j th order statistic in the phase-II sample Y (j∶n) , j = 1, 2, … , n (such as the minimum, lower quartile, median, upper quartile and maximum) as the charting statist...

An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution‐free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (ie, double GWMA, composite Shewhart‐GWMA, mixed GWMA‐CUSUM, and mixed CUSUM‐GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA‐related schemes (ie, 66 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.