Efficient power computation for r out of m runs rules schemes

Abstract

In this article we develop a power computation code in the R language which provides an easy to use tool to researchers in designing Shewhart control charts. It enables researchers to use different existing and newly introduced sensitizing rules and runs rules schemes designed for Shewhart-type control charts for location and spread. The code provides researchers to compute the power for different options of r out of m rules/schemes. The code is flexible to apply for any sample size, false alarm rate, type of control limits (one-or two-sided), amount of shift in the process parameters and a variety of popular distributions for commonly used Shewhart-type control charts (i.e.X , R, S and S 2 charts). These mentioned benefits of the developed functional code are only partially found in features of the existing software packages and these programs may be enhanced by adding the features of the developed code as a function in their libraries dealing with quality control charting.

On the Performance of Linear Profile Methodologies Under Runs Rules Schemes

“…redefined these rules for the sake of providing each rule an independent identity and at the same time handling the aforementioned issues. Later, Mehmood et al . provided an efficient computational code for these runs rules schemes.…”

“…Riaz et al . and Mehmood et al An out‐of‐control signal is received if at least r‐w points of r consecutive points (where 0 ≤ w ≤ r‐1) fall outside the control limits of the sampling distribution of the control charting statistic.…”

“…Researchers have explored many aspects of different runs rules schemes with Shewhart's, EWMA and cumulative sum type control charting strategies. The relevant literature in the said direction may be seen in Montgomery, Riaz et al ., Abbas et al ., Mehmood et al ., and the references therein. By getting motivation from these authors, particularly Riaz et al .…”

“…By getting motivation from these authors, particularly Riaz et al . and Mehmood et al ., we implement these rules to the simple and multiple profile methodologies for the monitoring of process parameters including intercept, slope, and process variance under special process scenarios.…”

Control charting and survey sampling techniques in process monitoring

“…In case of unspecified parameters, the estimated versions may also be used. On the basis of the above-mentioned structures for T i charts, the next step is to differentiate between in-control and out-of-control states using any of the sensitizing rules (Abbas, Riaz, and Does 2011;Does 2013b). In our study, we use first sensitizing rule: select random samples of size n (univariate-y i , bivariate-ðy i ; x i Þ, and trivariate-ðy i ; x i ; z i Þ ∀(i = 1, 2, … , n)) from the normal and t distributions.…”