Run Sum Chart for the Mean with Auxiliary Information

Quality & Reliability Eng

Yeong

et al. 2021

Self Cite

This article studies the economic and economic‐statistical designs of the auxiliary information (AI) based side sensitive group runs (SSGR‐AI) chart. The regression estimator that consists of information not only from the primary variable but also from the auxiliary variable is integrated into the control charting statistic. Optimal designs of the SSGR‐AI chart, for the minimization of the expected cost function with and without statistical constraints, are developed based on (i) average run length (ARL) and (ii) expected average run length (EARL). Furthermore, sensitivity analyses are conducted, that is, the impact of various input parameters on the optimal parameters and costs for different values of correlation coefficients (ρ) between the primary and auxiliary variables are investigated. In addition, the effects of incorrect specification of the size of the shift on the optimal cost of the SSGR‐AI chart are studied. The comparative study reveals that the SSGR‐AI chart is superior to the exponentially weighted moving average‐AI (EWMA‐AI) and synthetic‐AI (Syn‐AI) charts, for both designs, by giving the smallest costs.

“…The

E A R L_{1}

formula in Equation () integrates over the distribution function

f_{δ} false(δ false)

for the interval

(δ_{\min}, δ_{\max})

, where

δ_{\min}

and

δ_{\max}

denote the lower and upper bounds of the shift sizes in the process mean, respectively. As the exact shape of

f_{δ} false(δ false)

is often hard to be identified due to insufficient information about the distribution of δ , the process mean shifts are assumed to be uniformly distributed over the interval

(δ_{\min}, δ_{\max}),

that is, the occurrence probability for each value of δ in the interval

(δ_{\min}, δ_{\max})

is assumed to be equal 7,18 . Consequently, the

E A R L_{1}

formula in Equation () becomes

E A R L_{1} = \frac{1}{δ_{\max} - δ_{\min}} \int_{δ_{\min}}^{δ_{\max}} A R L_{1} ((), δ, L, n, k) d δ .

The in‐control EARL (

E A R L_{0}

) value is set to be similar to the ARL 0 value to ensure that both measures of performance have a similar in‐control run length performance.…”

Section: Auxiliary Information Based Side Sensitive Group Runs (Ssgr‐ai) Chartmentioning

confidence: 99%

Section: Numerical Analysesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Economic and economic‐statistical designs of the side sensitive group runs chart with auxiliary information

Quality & Reliability Eng

Yeong

et al. 2021

Self Cite

“…Haq and Khoo (2016) proposed a synthetic control chart with auxiliary information (SYN-AI). Meanwhile, Ng et al (2018) proposed the run sum chart with auxiliary information (RS-AI) and showed that the RS-AI chart outperforms the SH-AI, SYN-AI and EWMA-AI charts for all shifts given that the correlation ρ is large. Saha et al (2018) developed the VSSI chart with auxiliary information (VSSI-AI) which surpasses the EWMA-AI and SYN-AI charts.…”

Section: Introductionmentioning

confidence: 99%

A variable parameters auxiliary information based quality control chart with application in a spring manufacturing process: The Markov chain approach

Chong

Castagliola

et al. 2020

Quality Engineering

Self Cite

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

“…Haq and Khoo (2018) proposed a DS chart using AI while a VSSI chart using AI was presented by Saha et al (2019). Additionally, Ng et al (2018) presented the AI-based run sum (RS-AI) chart.…”

Section: Introductionmentioning

confidence: 99%

A combined variable sampling interval and double sampling control chart with auxiliary information for the process mean

Umar

Transactions of the Institute of Measurement and Control

Saha

et al. 2019

Self Cite

In recent years, the suitable use of auxiliary information technique in control charts has shown an improved run length performance compared to control charts that do not have this feature. This article proposes a combined variable sampling interval (VSI) and double sampling (DS) chart using the auxiliary information (AI) technique (called VSIDS-AI chart, hereafter). The plotting-statistic of the VSIDS-AI chart requires information from both the study and auxiliary variables to efficiently detect process mean shifts. The charting statistics, optimal design and performance assessment of the VSIDS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) are considered as the performance measures. The ssATS and ssEATS results of the VSIDS-AI chart are compared with those of the DS AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The results of comparison show that the VSIDS-AI chart outperforms the charts under comparison for all shift sizes, except the EWMA-AI and RS-AI charts for small shift sizes. An illustrative example is provided to demonstrate the implementation of the VSIDS-AI chart.