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Different versions of X- control chart structure are available under various ranked set strategies. In these control charts, computation of performance measures was carried out through Monte Carlo simulation method (MCSM). In this article, we have defined a generalized structure of X- control charts under variant sampling strategies followed by der...
Citations
... 53,54 For example, hazardous waste sites with different levels of contamination can be visually classified based on the color of the soil, while actual statistics of toxic chemicals and quantifying their ecological impacts are prohibitively expensive. 55 The other applications of RSS methods in SPM area are discussed in the papers such as Muttlak and Al-Sabah, 56 Al-Omari and Haq, 57 Haq et al., 58 Haq et al., 59 Riaz et al., 60 Mehmood et al., 61 Ali et al., 62 Nawaz and Han, 63 Malela-Majika et al., 64 Mehmood et al. 65 The use of the RSS method in the construction of control charts is a relatively new topic. The RSS scheme in SPM was first used by Salazar and Sinha 66 for constructing the Shewhart control chart. ...
... Da Silva et al.119 studied the effect of the NRSS method on control charts for normal and non-normal processes. Mehmood et al.61 proposed two Shewhart-type optimal control charts by using the generalized multiple dependent state plan and RSS schemes for monitoring the process mean. Abbasi 120 studied the performance of control charts based on the SRS, RSS, MRSS and ERSS schemes, by considering normal and different non-normal parent distributions. ...
Statistical process monitoring (SPM) and designing control charts include measuring quality characteristics by considering the time and cost constraints. Ranked set sampling (RSS) is a very efficient and an inexpensive approach in obtaining a more representative sample when the actual measurement of the sampling units is too expensive or destructive, where it is easier to rank the observations. Since 1997, when the first paper on designing control charts based on the RSS scheme was presented, a significant number of papers have been published in this area. This paper provides a literature review on using the RSS schemes in designing control charts. Relevant papers are classified and analyzed to identify the research gaps and provide recommendations and directions for future studies.
This article proposes efficient computational methods for designing and evaluating phases of Shewhart type control charts under runs rules. The efficient computational methods include exact equations or formulas for computing the probability of single-point and run-length properties of control charts. The run-length properties include average, variance, standard deviation, coefficient of variation, and moments. The study implements the proposed computational methods in the design and evaluation phases of well known univariate and multivariate control charts. In this regard, the research considers mean, variance, standard deviation, multivariate Hotelling and generalized variance control charts. Also, various procedures and a code in R language are provided to exemplify the applications of proposed computational methods in control charts. A comprehensive analysis of the behaviour of run-length properties of control charts under runs rules is conducted by considering various choices of factors such as sample size, amount of shift, and choice of runs rules. The proposed efficient computational methods provide the desired results with additional features such as reducing the computational burden, time efficient and being practitioner friendly. Finally, the article presents some real-life examples of univariate and multivariate control charts from manufacturing and winds turbine processes.
