Joint optimization of production, maintenance, and quality control considering the product quality variance of a degraded system

doi:10.1007/s42524-024-3103-1

Front. Eng

2024, Vol. 11

Issue (3) : 413-429 https://doi.org/10.1007/s42524-024-3103-1

Industrial Engineering and Intelligent Manufacturing

Joint optimization of production, maintenance, and quality control considering the product quality variance of a degraded system

Xiaolei LV¹, Liangxing SHI¹, Yingdong HE¹(

), Zhen HE¹, Dennis K.J. LIN²

¹. College of Management and Economics, Tianjin University, Tianjin 300072, China; Laboratory of Computation and Analytics of Complex Management Systems (CACMS), Tianjin University, Tianjin 300072, China
². Department of Statistics, Purdue University, West Lafayette, IN 47907, USA

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Abstract

The joint optimization of production, maintenance, and quality control has shown effectiveness in reducing long-term operational costs in production systems. However, existing studies often assume that changes in the mean value of product quality characteristics in a deteriorating system follow a specific distribution while keeping variance constant. To address this limitation, we propose an innovative method based on the continuous ranking probability score (CRPS). This method enables the simultaneous detection of changes in mean and variance in nonconformities, thus removing the assumption of a specific distribution for quality characteristics. Our approach focuses on developing optimal strategies for production, maintenance, and quality control to minimize cost per unit of time. Additionally, we employ a stochastic model to optimize the production time allocated to the inventory buffer, resulting in significant cost reductions. The effectiveness of our proposed joint optimization method is demonstrated through comprehensive numerical experiments, sensitivity analysis, and a comparative study. The results show that our method can achieve cost reductions compared to several other related methods, highlighting its practical applicability for manufacturing companies aiming to reduce costs.

Keywords joint optimization degraded system CRPS control chart uncertain buffer stocking time

Corresponding Author(s): Yingdong HE

Just Accepted Date: 02 July 2024 Online First Date: 26 July 2024 Issue Date: 26 September 2024

Cite this article:

Xiaolei LV,Liangxing SHI,Yingdong HE, et al. Joint optimization of production, maintenance, and quality control considering the product quality variance of a degraded system[J]. Front. Eng, 2024, 11(3): 413-429.

URL:

https://academic.hep.com.cn/fem/EN/10.1007/s42524-024-3103-1
https://academic.hep.com.cn/fem/EN/Y2024/V11/I3/413

Fig.1 The process of joint production, maintenance, and quality control.

n	(Decision variable) Sample number
k	(Decision variable) Inspection frequency
h	(Decision variable) Time interval between successive samples
UCL	(Decision variable) Control chart’s limits
S	(Decision variable) Safety stock levels in the buffer zone
X	(Random variable) Transition time from the in-control state to the out-of-control state
f(x)	Probability density function (PDF) of x
F(x)	Cumulative distribution function (CDF) of x
$F ¯$ (x)	1 – F(x)
Y₁	(Random variable) Time required for preventive maintenance
g₁(y₁)	PDF of Y₁
G₁(y₁)	CDF of Y₁
Y₂	(Random variable) Time required for corrective maintenance
g₂(y₂)	PDF of Y₂
G₂(y₂)	CDF of Y₂
γ	Set to zero when production halts during the false alarm analysis; otherwise, set to one
t_f	Analyze and rectify false alarm durations
t_s	Duration of time per sample inspection
t_a	Assignable cause analysis duration
q₁	Productivity of normal production
q₂	Replenishment rate of buffer zone inventory (q₂ > q₁)
C_f	Fixed cost for sample inspection
C_v	Variable cost for sample inspection
C_in	Operational cost per time unit in the in-control state
C_out	Operational cost per time unit in the out-of-control state
C_I	Cost of the false alarm analysis
C_h	Inventory holding cost per unit item per time unit
C_s	Cost of stockouts per time unit
C_CM	Corrective maintenance cost
C_PM	Preventive maintenance cost (C_CM > C_PM)
Q_in	Cost per unit of the quality lost when the production process is in the in-control state
Q_out	Cost per unit of the quality lost when the production process is in the out-of-control state
ARL₀	Average run length when the production process is in the in-control state
ARL₁	Average run length when the production process is in the out-of-control state
α	Probability of occurrence of Type I errors
β	Probability of occurrence of Type II errors

Fig.2 Graphical representation of the four scenarios.

Fig.3 The quality control strategy.

Fig.4 The maintenance strategy.

Fig.5 The production strategy.

Fig.6 The buffer stock holding state.

$γ$	$t f$	$t s$	$t a$	$C C M$	$C P M$	$C h$	$C S$	$C i n$	$C o u t$	$C f$
1	1	0.01	1	5000	2400	0.5	3	100	300	1

$C v$	$C I$	$Q i n$	$Q o u t$	$q 1$	$q 2$	$λ 1$	$λ 2$	$λ$	$v 1$	$v 2$	$v$
0.2	200	0	0	90	160	0.4	0.4	0.3	2	2	2

Tab.1 The parameters’ values.

Tab.2 The results of Case 1

Fig.7 The CRPS value range in Case 1.

Fig.8 The CRPS values in Case 2.

Tab.3 The results of Case 2

Fig.9 The CRPS values in Case 3.

Tab.4 The results of Case 3

$γ$	$t f$	$t s$	$t a$	$C C M$	$C P M$	$C h$	$C S$	$C i n$	$C o u t$	$C f$
1	1	0.01	1	5000	2400	0.5	3	100	300	1

$C v$	$C I$	$Q i n$	$Q o u t$	$q 1$	$q 2$	$λ 1$	$λ 2$	$λ$	$v 1$	$v 2$	$v$
0.2	200	0	0	90	160	0.4	0.4	0.3	2	2	2

Tab.5 Parameter values

$λ$	n	h	k	UCL	S	ECT
0.2	5	50	4.6374	0.5	348.7862	328.6117
0.3	5	50	4.6518	0.5	347.4615	328.5618
0.4	5	50	4.6637	0.5	316.9654	328.4249

Tab.6 Sensitivity analysis results for

λ

$v$	n	h	k	UCL	S	ECT
1	5	50	4.6170	0.5	339.0196	328.4801
2	5	50	4.6518	0.5	347.4615	328.5618
3	5	50	4.6223	0.5	342.2853	328.5144

Tab.7 Sensitivity analysis results for

v

$λ 1$	n	h	k	UCL	S	ECT
0.3	5	50	4.6350	0.5	342.2019	328.5166
0.4	5	50	4.6518	0.5	347.4615	328.5618
0.5	5	50	4.6170	0.5	344.1313	328.5166

Tab.8 Sensitivity analysis results for

λ 1

$v 1$	n	h	k	UCL	S	ECT
1	5	50	4.6163	0.5	349.7860	328.5169
2	5	50	4.6518	0.5	347.4615	328.5618
3	5	50	5.6577	0.5	341.5521	328.5167

Tab.9 Sensitivity analysis results for

v 1

$λ 2$	n	h	k	UCL	S	ECT
0.3	5	50	4.5604	0.5	372.0660	329.6455
0.4	5	50	4.6518	0.5	347.4615	328.5618
0.5	5	50	4.6858	0.5	320.0389	327.7921

Tab.10 Sensitivity analysis results for

λ 2

$v 2$	n	h	k	UCL	S	ECT
1	5	50	4.6930	0.5	366.1123	328.8817
2	5	50	4.6518	0.5	347.4615	328.5618
3	5	50	4.6149	0.5	323.6984	328.5246

Tab.11 Sensitivity analysis results for

v 2

$γ$	$t f$	$t s$	$t a$	$C C M$	$C P M$	$C h$	$C S$	$C i n$	$C o u t$	$C f$	$δ$
1	1	0.01	1	5000	2400	0.5	3	100	300	1	1

$C v$	$C I$	$Q i n$	$Q o u t$	$q 1$	$q 2$	$λ 1$	$λ 2$	$λ$	$v 1$	$v 2$	$v$
0.2	200	0	0	90	160	0.4	0.4	0.3	2	2	2

Tab.12 Data used in the comparative study

	n	h	k	$l$ (UCL)	S	ECT
Hadian et al. (2021)	26	2.2604	27	3.1616	101.0751	315.9644
Shi et al. (2023)	1	10	100	3.5	205.8511	304.3147
This study	5	50	100	1	303.1824	301.0150

Tab.13 Comparison results of the three models

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