Monitoring the coefficient of variation using a variable sample size control chart in short production runs

Amdouni, Asma; Castagliola, Philippe; Taleb, Hassen; Celano, Giovanni

doi:10.1007/s00170-015-7084-4

Cited by 57 publications

(37 citation statements)

References 21 publications

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“…As for the VSS T 2 short‐run chart, f TRL ( i ) and F TRL ( i ) of the TRL criterion can be obtained as follows:

f_{TRL} ((), i) = ({, \begin{array}{l} f_{RL} ((), i) normalif i = 1, 2, \dots, I \\ normal1 - F_{RL} ((), I) normalif i = I + 1 \end{array}),

and

F_{TRL} ((), i) = ({, \begin{array}{l} F_{RL} ((), i) normalif i = 1, 2, \dots, I \\ normal1 normalif i = I + 1 \end{array}),

where the probability mass function f RL ( i ) and cumulative distribution function F RL ( i ) of the usual run length (RL) are

f_{RL} ((), i) = q^{T} Q^{i - 1} bold-italicr,

and

F_{RL} ((), i) = normal1 - q^{T} Q^{i} bold1 monospace,

respectively. The TARL 1 ( δ ) of the VSS T 2 short‐run chart can be obtained from the expected value of the TRL, ie, E(TRL), which can be shown to be

{TARL}_{1} ((), δ) = q^{T} ((), \sum_{i = 0}^{I} Q^{i}) bold1 bold-italic,

where q in Equation is a 2 × 1 vector of initial probabilities for the transient states.…”

Section: Statistical Measures Of Performancementioning

confidence: 99%

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Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Chong

Khoo

Haq

et al. 2018

Quality & Reliability Eng

Self Cite

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Short production runs are common in enterprises that require a high degree of flexibility and variety in manufacturing processes. To date, past research on short production runs has little focus on the multivariate control charts. In view of this, fixed sample size (FSS) and variable sample size (VSS) Hotelling's T2 charts are designed to monitor the process mean when the production horizon is finite. Optimal parameters to minimize the out‐of‐control (1) truncated average run length (TARL) and (2) expected TARL (ETARL) are provided such that the in‐control TARL is equal to the number of inspections (say I). The numerical study considers the run length performances of the FSS and VSS T2 short‐run charts for both known and unknown shift sizes. The VSS T2 short‐run chart performs well in swiftly detecting various mean shifts in comparison with the FSS T2 short‐run chart. Additionally, the VSS T2 short‐run chart is superior to the FSS T2 short‐run chart, in terms of the truncated standard deviation of the run length, expected truncated standard deviation of the run length, probability that the chart signals an alarm within the I inspections, ie, P(I) and expected P(I). A case study on the impurity profile of a crystalline drug substance illustrates the implementation of the VSS T2 short‐run chart.

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“…As for the VSS T 2 short‐run chart, f TRL ( i ) and F TRL ( i ) of the TRL criterion can be obtained as follows:

f_{TRL} ((), i) = ({, \begin{array}{l} f_{RL} ((), i) normalif i = 1, 2, \dots, I \\ normal1 - F_{RL} ((), I) normalif i = I + 1 \end{array}),

and

F_{TRL} ((), i) = ({, \begin{array}{l} F_{RL} ((), i) normalif i = 1, 2, \dots, I \\ normal1 normalif i = I + 1 \end{array}),

where the probability mass function f RL ( i ) and cumulative distribution function F RL ( i ) of the usual run length (RL) are

f_{RL} ((), i) = q^{T} Q^{i - 1} bold-italicr,

and

F_{RL} ((), i) = normal1 - q^{T} Q^{i} bold1 monospace,

respectively. The TARL 1 ( δ ) of the VSS T 2 short‐run chart can be obtained from the expected value of the TRL, ie, E(TRL), which can be shown to be

{TARL}_{1} ((), δ) = q^{T} ((), \sum_{i = 0}^{I} Q^{i}) bold1 bold-italic,

where q in Equation is a 2 × 1 vector of initial probabilities for the transient states.…”

Section: Statistical Measures Of Performancementioning

confidence: 99%

“…As for the VSS T 2 short‐run chart, the second moment of the TRL is

normalTRL normal2 = q^{T} ((), \sum_{i = 0}^{I} ((), 2 i + 1) Q^{i}) bold1 .

…”

Section: Statistical Measures Of Performancementioning

confidence: 99%

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Chong

Khoo

Haq

et al. 2018

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the SPC literature, Shewhart‐type control chart for monitoring the coefficient of variation (CV), which is defined as the ratio of the population standard deviation to the population mean, has already been investigated by Kang et al; subsequently, several control charts have been developed in the literature for monitoring the CV. For further details, see, for instance, Castagliola et al, Calzada and Scariano, Castagliola et al, Castagliola et al, Zhang et al, Castagliola et al, Castagliola et al, Amdouni et al, You et al, and Tran and Tran among others. For example, in textile manufacturing industry, the variation among tensile strength measurements from thin thread is significantly smaller than measurements taken from heavy thread because of the inherent physical properties of fiber.…”

Section: Introductionmentioning

confidence: 99%

On the performance of coefficient of variation charts in the presence of measurement errors

Tran

Heuchenne

2018

Quality & Reliability Eng

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In the literature, coefficient of variation control charts have been introduced under the assumption of no measurement errors. However, measurement errors always exist in practice, and they do affect the performance of control charts in the detection of an out‐of‐control situation. In this paper, we therefore study the performance of a coefficient of variation Shewhart‐type control chart (Shewhart‐CV chart) and also one‐sided coefficient of variation exponentially weighted moving average–type control charts (EWMA‐γ2 charts) using a model with linear covariates. Moreover, we propose and study the performance of a two‐sided EWMA‐γ2 chart using a model with linear covariates. Several figures and tables are provided and analyzed to evaluate the statistical performance of these control charts for different sources of measurement errors. The obtained results show that the precision and accuracy errors significantly affect the performance of both the Shewhart‐CV and EWMA‐γ2 control charts. An example illustrating the use of this study is finally presented.

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“…In recent years, a large number of researchers have developed new control charts, some more recent ones were made by Amdouni et al . , Tran et al . , Yeong et al .…”

Section: Introductionmentioning

confidence: 99%

“…, the literature has proposed several CV control charts. For further details, see, for instance, to name a few.…”

Section: Introductionmentioning

confidence: 99%

The efficiency of CUSUM schemes for monitoring the coefficient of variation

Tran

2016

Appl Stoch Models Bus & Ind

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Continuous surveillance of the coefficient of variation is a quality control issue worthy of consideration in several manufacturing and service‐oriented companies. In this paper, we present a new method to monitor the squared coefficient of variation by means of two one‐sided cumulative sum‐type control charts. We study the run length properties of the proposed charts using a Markov chain approach. Several tables are given in order to show the sensitivity of the proposed charts for different deterministic shift sizes and their performance for the random shift size condition. The results show that the proposed control charts have attractive performance compared with some competing charts and are better in many cases. An illustrative example is discussed on a real dataset. Copyright © 2016 John Wiley & Sons, Ltd.

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Monitoring the coefficient of variation using a variable sample size control chart in short production runs

Cited by 57 publications

References 21 publications

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

On the performance of coefficient of variation charts in the presence of measurement errors

The efficiency of CUSUM schemes for monitoring the coefficient of variation

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Monitoring the coefficient of variation using a variable sample size control chart in short production runs

Cited by 57 publications

References 21 publications

Hotelling's T2 control charts with fixed and variable sample sizes for monitoring short production runs

Hotelling's T2 control charts with fixed and variable sample sizes for monitoring short production runs

On the performance of coefficient of variation charts in the presence of measurement errors

The efficiency of CUSUM schemes for monitoring the coefficient of variation

Contact Info

Product

Resources

About

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs