Statistical design of variable sample size and sampling interval $$\bar X$$ control charts with run rulescontrol charts with run rules

Abstract

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.

Robust design of adaptive control charts for manual manufacturing/inspection workstations

“…An efficient approach could be to vary the design parameters at two levels [2,18]. Tagaras [14] has presented a complete survey on the design of several adaptive charts.…”

“…Keywords: statistical process control; control chart; economic design; robust optimization; labour resource Notation n 1 smaller sample size n 2 larger sample size h 1 shorter sampling interval h 2 longer sampling interval LR 1 smaller capacity of required labour resource (LR) LR 2 higher capacity of required labour resource (LR) 182 G. Celano w width of warning limit k width of control limit δ random shift in the process mean μ 0 to μ 0 + δσ μ δ mean of the random shift in the process mean λ the number of occurrences per hour of an assignable cause (the failure rate) C p process capability index shift of the in-control process mean μ 0 with respect to the target value μ 0 = target + σ p in-control fraction nonconforming p out-of-control fraction nonconforming ARL 0 in-control average run length c LR cost of labour resource (LR) per time unit c nc cost of producing a nonconforming part r IN rate of inspection r PR rate of production C 0 cost per unit time of production when the process is in-control C 1 (δ) cost per unit time of production when the process is out-of-control d 1 indicator variable (1 if production continues during searches, 0 otherwise) d 2 indicator variable (1 if production continues during repair, 0 otherwise) W cost for locating and repairing an assignable cause Y cost per false alarm T 0 expected search time associated with a false alarm T 1 expected search time to discover an assignable cause T 2 expected time to repair the process ATS δ out-of-control average time to signal…”

An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles

“…The VSI and VSS features can be combined to give a Variable Sample Sizes and Sampling Intervals (VSSI) control chart that allows the sample sizes and sampling intervals to vary. There have been lots of research on conventional control chart using VSR features in the literature, for the X control chart, see Prabhu, Montgomery, and Runger (1994), Costa (1998), Chen and Chiou (2005) and Celano et al (2006); for the cumulative sum (CUSUM) control chart, see Reynolds, Amin, and Arnold (1990), Zhang and Wu (2007) and Wu et al (2007); for the EWMA control chart, see Reynolds (1996) and Reynolds et al (2001); for the cumulative count of conforming chart, see Liu, Xie, Goh, Liu, and Yang (2006) and for the Hotelling's T 2 control chart, see Aparisi and Haro (2001). For the X control chart, Chen and Liao (2004) study multi-criteria design and show that the design parameters of sample sizes and sampling intervals need to be adjusted.…”

Optimal condition-based maintenance policy for a partially observable system with two sampling intervals

“…The shorter sampling time is used instead, when both sample statistics fall outside the warning limits but inside the control limits. More related references can be found in [25,26] and [4].…”