Control Charts monitoring Product's Loss to Society

Celano, Giovanni; Faraz, Alireza; Saniga, Erwin M.

doi:10.1002/qre.1562

Cited by 7 publications

(9 citation statements)

References 21 publications

(28 reference statements)

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“…This coefficient may be deduced from a replacement/repair cost function A 0 = Loss(T ± d) pertaining to a nonconforming part and expressed as below [10,11],…”

Section: Effects On the Process Capability Index C Pmmentioning

confidence: 99%

Control chart limits based on true process capability with consideration of measurement system error

Amara

Dhahri

Fredj

2016

Int. J. Metrol. Qual. Eng.

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Abstract. Shewhart X and R control charts and process capability indices, proven to be effective tools in statistical process control are widely used under the assumption that the measurement system is free from errors. However, measurement variability is unavoidable and may be evaluated by the measurement system discrimination ratio (DR). This paper investigates the effects of measurement system variability evaluated by DR on the process capability indices C p and C pm , on the expected non conforming units of product per million (ppm), on the expected mean value of the Taguchi loss function (E(Loss)) and on the Shewhart charts properties. It is shown that when measurement system variability is neglected, an overestimation of ppm and underestimation of E(Loss) are induced. Moreover, significant effects of the measurement variability on the control chart properties were made in evidence. Therefore, control charts limits calculation methods based on process real state were developed. An example is provided in order to compare the proposed limits with those traditionally calculated for Shewhart X, R charts.Keywords: process capability indices / expected non conforming units of product per million (ppm) / mean value of Taguchi loss function E(Loss) / measurement system discrimination ratio / Shewhart X, R control chart parameters

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“…This coefficient may be deduced from a replacement/repair cost function A 0 = Loss(T ± d) pertaining to a nonconforming part and expressed as below [10,11],…”

Section: Effects On the Process Capability Index C Pmmentioning

confidence: 99%

Control chart limits based on true process capability with consideration of measurement system error

Amara

Dhahri

Fredj

2016

Int. J. Metrol. Qual. Eng.

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“…Taguchi loss function is usually assumed to be well approximated by the symmetric squared error loss function defined as:

italicLoss ((), Y) = k {(Y - T)}^{2}

where k [$/ unit ] expresses the quality loss per produced unit and Y is the measured part dimension. k may be deduced from a repair cost function Loss ( T ± d ) pertaining to a nonconforming part and expressed as below:

italicLoss ((), T \pm d) = A_{0} = k {((T \pm d) - T)}^{2}

where d is the half width of tolerance ( d = Tol / 2 ). Therefore,

k = \frac{A_{0}}{d^{2}} .

…”

Section: Process Capability Indices and The Mean Value Taguchi Loss Fmentioning

confidence: 99%

“…The mean value of the Taguchi loss function (average quality loss) is expressed as:

E ((), Loss) = k ([], σ_{p}^{2} + {(μ - T)}^{2}) .

…”

Section: Process Capability Indices and The Mean Value Taguchi Loss Fmentioning

confidence: 99%

“…The observed capability index, the process mean and the A 1 ratio computed using this data are C p , Obs = 1.6835, μ = 74.0012 mm and A 1 = 0.12, respectively. On the other hand, the same value of the repair cost of non‐conforming piston rings, A 0 = 10 $, mentioned by Celano et al . is used in the present work.…”

Section: Illustrative Examplementioning

confidence: 99%

“…In order to extend the expression of C pk , given by equation (2) to a process with a predefined target value (T) that could be different from the midpoint M, a loss function is used to reflect the economic loss associated to the process departure from the target value. Taguchi loss function is usually assumed to be well approximated by the symmetric squared error loss function defined as [33][34][35] :…”

Section: Process Capability Indices and The Mean Value Taguchi Loss Fmentioning

confidence: 99%

See 2 more Smart Citations

Process True Capability Evaluation with the Consideration of Measurement System Variability and Expected Quality Loss

Amara

Dhahri

Fredj

2016

Quality & Reliability Eng

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Process capability indices are widely computed under the assumption that the measurement system is free from errors. However, measurement variability is unavoidable and has a significant impact in process capability evaluation. From an economic point of view, Taguchi loss function is an effective tool to measure the quality loss of a product characteristic deviated from target value that is extensively used without taking into account the effect of the measurement system. This paper investigates the influence of measurement system variability on the process capability analysis through the calculation of process capability indices. A new quality loss function, integrating the measurement system errors, is developed to compute the optimal true process capability regarding to the expected mean value of the Taguchi loss function and the loss resulting from the control of the true process capability. Copyright © 2016 John Wiley & Sons, Ltd.

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Control charts with random interarrival times between successive samplings

Koutras

Rakitzis

2018

Appl Stoch Models Bus & Ind

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In the classical setup used in process monitoring, the times between the collection of successive plotted samples are considered as nonrandom. However, in several real-life applications, it seems plausible to assume that the time needed to collect the necessary information for plotting a point in the control chart has a stochastic nature. Under this scenario, instead of focusing on the number of points plotted on the chart until an out-of-control signal is initiated, the appropriate statistic to look at is the total time until a signal is generated. If we denote by L the run length of a control chart and by Y t , t = 1, 2, … , the times between successive plotted points, then the compound random variable S L = ∑ L t=1 Y t expresses the time to signal of a monitoring scheme, under a particular sampling policy. In this paper, we illustrate how S L can be exploited to study various charts that are suitable for monitoring Poisson observations. We provide some results for the exact distribution of S L that may facilitate the task of the performance assessment of a control chart with random plotting times; illustrations and several numerical comparisons that are useful for quality control experts who wish to practice them are presented, and finally, an illustrative example elucidating the implementation of the proposed model is also provided.

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Control Charts monitoring Product's Loss to Society

Cited by 7 publications

References 21 publications

Control chart limits based on true process capability with consideration of measurement system error

Control chart limits based on true process capability with consideration of measurement system error

Process True Capability Evaluation with the Consideration of Measurement System Variability and Expected Quality Loss

Control charts with random interarrival times between successive samplings

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