Steady-state behavior of nonparametric control charts using sign statistic

Abstract

If process is running for a long period in an in-control condition, it will reach in a steady-state condition. In order to study the long term properties of a control chart, it is appropriate to investigate the steady-state average time to signal. In this article, we discussed runs rules representation of a nonparametric synthetic control chart using sign statistic for detecting shifts in location parameter. We compared zero-state average time to signal with steady-state average time to signal of the synthetic control chart for symmetric and asymmetric distributions. We also present the m-of-m control chart using sign statistic. For comparison study, we computed average time to signal of the m-of-m control chart, the sign chart (1-of-1 chart) and the synthetic control chart for normal, Cauchy, double exponential and gamma distributions. Steady-state and zero-state performance of the m-of-m control chart with m = 2, 3 compared with the sign chart (1-of-1 chart) and synthetic control chart. The zero-state and steady-state average time to signal of the synthetic and the m-of-m control charts computed using Markov chain approach.

One-sided precedence monitoring schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved runs-rules

“…Case K and Case U nonparametric monitoring schemes have received a lot of attention in recent SPM literature. For Case K, see for example, Human et al (2010), Khilare and Shirke (2010), Kritzinger et al (2014), Khilare and Shirke (2015), Patil and Shirke (2017), Pawar et al (2018), etc. For Case U, see for example, Chakraborti and van de Wiel (2008), Chakraborti et al (2009a), Albers and Kallenberg (2008), Graham et al (2017), Malela-Majika et al (2019), etc.…”

“…The parametric one-and two-sided schemes supplemented with runs-rules have been recently investigated in many publications, see for instance, Mehmood et al (2019), Chew et al (2019), Shongwe et al (2019a, b), and the references therein, however as far we know, there are very few nonparametric runs-rules schemes: Chakraborti and Eryilmaz (2007), Chakraborti et al (2009a), Human et al (2010), Kritzinger et al (2014), Khilare and Shirke (2015), Malela-Majika et al (2016a, b), Malela-Majika and Rapoo (2017), Pawar et al (2018), Malela-Majika et al (2019), Triantafyllou (2020 as well as the ones discussed in the book by Chakraborti and Graham (2019).…”