An Attribute Control Chart Based on the Birnbaum-Saunders Distribution Using Repetitive Sampling

Aslam, Muhammad; Arif, Osama H.

doi:10.1109/access.2016.2643692

Cited by 17 publications

(14 citation statements)

References 39 publications

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“…In this section, the performance of the control charts built with the statistics

\overset{δ_{i}}{true}

i =

SM, MM, and ML, is compared with some competitors found in the literature, specifically the

n p^{'} s

control charts proposed by Leiva et al and by Aslam et al In both control charts, a sample of

normaln

units is taken, and let

Y = # X_{i} > δ_{0}

. The control limits of

n p

chart presented in Leiva et al are

n p_{0} \pm K \sqrt{n p_{0} false(1 - p_{0} false)}

, with

p_{0} = P false(X > δ_{0} false)

K

, a constant searched to meet some performance metric.…”

Section: Comparison With Other Proposalsmentioning

confidence: 99%

“…If

L C L = n p_{0} - K \sqrt{n p_{0} false(1 - p_{0} false)} \leq Y \leq U C L = n p_{0} - K \sqrt{n p_{0} false(1 - p_{0} false)}

, the process is declared in control. In Aslam et al's proposal, the two sets of control limits are the outer as

n p_{0} \pm K_{1} \sqrt{n p_{0} false(1 - p_{0} false)}

and the inner as

n p_{0} \pm K_{2} \sqrt{n p_{0} false(1 - p_{0} false)}

K_{1} > K_{2}

constants searched to meet performance criteria. If

L C L_{2} = n p_{0} - K_{2} \sqrt{n p_{0} false(1 - p_{0} false)} \leq Y \leq U C L_{2} = n p_{0} - K_{2} \sqrt{n p_{0} false(1 - p_{0} false)}

, the process is declared in control; if

Y < L C L_{1} = n p_{0} - K_{1} \sqrt{n p_{0} false(1 - p_{0} false)}

Y > U C L_{1} = n p_{0} - K_{1} \sqrt{n p_{0} false(1 - p_{0}}

…”

Section: Comparison With Other Proposalsmentioning

confidence: 99%

“…Leiva et al suggested

n p

attribute control chart to monitor the BS mean. Aslam et al presented also an attribute control chart on the basis of BS distribution using repetitive sampling. Khan et al studied the attribute control chart for the BS distribution under the accelerated hybrid censoring.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

Bourguignon

Fernandes

2020

Quality & Reliability Eng

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In this paper, we propose control charts for monitoring the Birnbaum-Saunders (BS) median parameter (scale parameter) on the basis of three estimators. Comparison of the control charts in terms of average run length using probability control limits and those based on asymptotic distribution of three estimators for the median parameter is developed. We also present guidelines for practitioners about the minimum sample size needed to match out-of-control average run length with the asymptotic control limits in function of the median parameter after an extensive simulation study. Numerical example illustrates the applied monitoring of BS median parameter. KEYWORDS asymptotic normal distribution, average run length, maximum likelihood estimator, modified moment estimator, simulation 4 2 ).

show abstract

“…In this section, the performance of the control charts built with the statistics

\overset{δ_{i}}{true}

i =

SM, MM, and ML, is compared with some competitors found in the literature, specifically the

n p^{'} s

control charts proposed by Leiva et al and by Aslam et al In both control charts, a sample of

normaln

units is taken, and let

Y = # X_{i} > δ_{0}

. The control limits of

n p

chart presented in Leiva et al are

n p_{0} \pm K \sqrt{n p_{0} false(1 - p_{0} false)}

, with

p_{0} = P false(X > δ_{0} false)

K

, a constant searched to meet some performance metric.…”

Section: Comparison With Other Proposalsmentioning

confidence: 99%

“…If

L C L = n p_{0} - K \sqrt{n p_{0} false(1 - p_{0} false)} \leq Y \leq U C L = n p_{0} - K \sqrt{n p_{0} false(1 - p_{0} false)}

, the process is declared in control. In Aslam et al's proposal, the two sets of control limits are the outer as

n p_{0} \pm K_{1} \sqrt{n p_{0} false(1 - p_{0} false)}

and the inner as

n p_{0} \pm K_{2} \sqrt{n p_{0} false(1 - p_{0} false)}

K_{1} > K_{2}

constants searched to meet performance criteria. If

L C L_{2} = n p_{0} - K_{2} \sqrt{n p_{0} false(1 - p_{0} false)} \leq Y \leq U C L_{2} = n p_{0} - K_{2} \sqrt{n p_{0} false(1 - p_{0} false)}

, the process is declared in control; if

Y < L C L_{1} = n p_{0} - K_{1} \sqrt{n p_{0} false(1 - p_{0} false)}

Y > U C L_{1} = n p_{0} - K_{1} \sqrt{n p_{0} false(1 - p_{0}}

…”

Section: Comparison With Other Proposalsmentioning

confidence: 99%

See 1 more Smart Citation

Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

Bourguignon

Fernandes

2020

Quality & Reliability Eng

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show abstract

“…Ho and Quinino [4] proposed an attribute chart to control the variation in the process. Aslam et al [5] and Aslam et al [6] worked on a time-truncated chart for the Birnbaum-Saunders distribution and the Weibull distribution respectively. Jeyadurga et al [7] worked on an attribute chart under truncated life tests.…”

Section: Introductionmentioning

confidence: 99%

Classification of the State of Manufacturing Process under Indeterminacy

Aslam

Arif

2019

Mathematics

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In this paper, the diagnosis of the manufacturing process under the indeterminate environment is presented. The similarity measure index was used to find the probability of the in-control and the out-of-control of the process. The average run length (ARL) was also computed for various values of specified parameters. An example from the Juice Company is considered under the indeterminate environment. From this study, it is concluded that the proposed diagnosis scheme under the neutrosophic statistics is quite simple and effective for the current state of the manufacturing process under uncertainty. The use of the proposed method under the uncertainty environment in the Juice Company may eliminate the non-conforming items and alternatively increase the profit of the company.

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“…Aslam et al [16] designed a time truncated attribute control chart using the Pareto distribution. Aslam et al [17] deigned a time truncated control chart for the Birnbaum-Saunders distribution under repetitive sampling. More details about such control charts can be read in Aslam et al [18], Arif et al [19], Khan et al [20], and Shafqat et al [21].…”

Section: Introductionmentioning

confidence: 99%

A Variable Control Chart under the Truncated Life Test for a Weibull Distribution

2018

Self Cite

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In this manuscript, a variable control chart under the time truncated life test for the Weibull distribution is presented. The procedure of the proposed control chart is given and its run length properties are derived for the shifted process. The control limit is determined by considering the target in-control average run length (ARL). The tables for ARLs are presented for industrial use according to various shift parameters and shape parameters in the Weibull distribution. A simulation study is given for demonstrating the performance of the proposed control chart.

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An Attribute Control Chart Based on the Birnbaum-Saunders Distribution Using Repetitive Sampling

Cited by 17 publications

References 39 publications

Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

Classification of the State of Manufacturing Process under Indeterminacy

A Variable Control Chart under the Truncated Life Test for a Weibull Distribution

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