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A novel approach for production scheduling of a high pressure die casting machine subjected to selective maintenance and a sampling procedure for quality control

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Abstract

Effective maintenance keeps machines in good working condition, improving the machine availability during production. It also minimizes the process failure rate due to component failure, resulting into improved product quality. In this paper the interrelationship between maintenance, production scheduling and quality control is captured using an integrated approach. A mathematical model comprising of total cost of selective maintenance, process quality control using a sampling procedure and production scheduling is developed for a single machine manufacturing system. Simultaneous optimization using the proposed integrated model results into the decision on maintenance actions namely repair, replace and do-nothing for each component, along with the values of parameters for the sampling procedure and the optimal production schedule. A numerical study is presented to demonstrate the applicability of the proposed model. A simulated annealing algorithm is used for obtaining the near optimal solution to the decision parameters. The effectiveness of the proposed approach is compared with the conventional approach of decision making for maintenance, quality control and production scheduling. The results indicate that integrated approach is better as compared to the conventional approach.

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Abbreviations

AReq :

Required system availability

α:

Age reduction factor for component

β:

Weibull shape parameter for component

η:

Weibull scale parameter for component (h)

CC:

Cost of component (Rs.)

Cf :

Failure cost for component (Rs.)

CLP :

Cost of lost production (Rs.)

CLM :

Labour cost of maintenance (Rs./h)

Csp :

Cost of sub-components and consumables (Rs.)

CR :

Replacement cost for component (Rs.)

Cr :

Repair cost for component (Rs.)

CRL:

Cost of loss of residual life (Rs.)

E[Nf]FC2 :

Expected number of failure of the machine during the operating period leading to FC2

E(DT):

Expected downtime (h)

E[TC]M :

Expected total cost of selective maintenance (Rs.)

E[TC]M/Q :

Expected total cost of maintenance with quality control(M/Q) decision (Rs.)

ML:

Mean life (h)

MRL:

Mean residual life (h)

MTTrA:

Mean time to repair for component (h)

MTTRA:

Mean time to replacement for component (h)

MTTCA:

Mean time to corrective action for component (h)

PR:

Production rate (units/h)

ℜ i :

Index of i-th component undergoing replacement work

ri :

Index of i-th component undergoing repair work

Ri :

Reliability of i-th component

Ri(t/T):

Conditional reliability of i-th component having survived upto time T

RF:

Restoration factor for component

TPMS :

Time between the current maintenance and next expected opportunity (h)

TAvl :

Time available to carry out maintenance work (h)

TLM :

Time elapsed between the last maintenance and opportunity (h)

TCf :

Total cost of random failures (Rs.)

TCR :

Total cost of replacement (Rs.)

TCr :

Total cost of repair (Rs.)

vi :

Effective age of i-th component at the end of any period (h)

(vi)o :

Effective age of i-th component at the opportunity (h)

(v’i)o :

Effective age of i-th component after maintenance at the opportunity (h)

αs :

Type 1 error of sampling procedure

βs :

Type 2 error of sampling procedure

τ:

Expected time of occurrence of assignable cause (h)

ARLIn :

Average run length in in-control state

ARLOut :

Average run length in out-of-control state

ATS:

Average time to signal

C s :

Acceptance number

Cins :

Cost of inspection (Rs.)

Cac :

Cost of investigating the assignable cause (Rs./h)

CF :

Cost of investigating the false alarm (Rs./h)

CRej :

Cost of rejection per piece (Rs.)

CRes :

Cost of repairing/restoring the process (Rs.)

CRew :

Cost of rework (Rs. per unit)

E[Csampling]:

Expected total cost of sampling per cycle (Rs.)

E[CFalse Alarm]:

Expected total cost of false alarms per cycle (Rs.)

E[CRejections]:

Expected total cost of rejections (Rs.)

E[CACD]:

Expected total cost of assignable cause detection (Rs.)

E[CRestore]:

Expected total cost to restore the process (Rs.)

E[CPQC]cycle :

Expected cost of process quality control per cycle (Rs.)

E[CRework]:

Expected total cost of rework. (Rs.)

E[N]cycles :

Expected number of cycles

E[T]cycle :

Expected cycle length of process quality control

E[T]false :

Expected total time for investigation of false alarm (h)

E[TC]PQC :

Expected total cost of process quality control (Rs.)

Hs :

Time between samples (h)

Ns :

Sample Size

P1 :

Average proportion of defectives during in-control

P2 :

Average proportion of defectives during out-of-control

Sin :

Expected number of samples in in-control state

TF :

Time required to investigate false alarm (h)

TS :

Time required for sampling (h)

T1:

Expected time to search the assignable cause (h)

T2:

Expected time to restore the process (h)

λ:

Overall process failure rate

λE :

Process failure rate due to external causes

λM :

Process failure rate due to machine component failure

bk :

k-th batch in production schedule

Ch:

Inventory holding cost per item per unit time (Rs./item/h)

CT:

Completion time of a batch (h)

DD:

Due date for a batch (h)

E[TC]PS :

Expected total schedule penalty cost (Rs.)

E[TC]Integrated :

Expected total cost of integrated model (Rs.)

F(bk)i :

Probability of failure of i-th component during k-th batch processing

IHC:

Inventory holding cost (Rs.)

LT:

Lateness of a batch (h)

LTF :

Lateness of a batch due to component failure (h)

P:

Processing time of a batch (h)

ST:

Start time of the batch

Tk :

Tardiness penalty of k-th batch

Td :

Delay time due to component failure (h)

W:

Penalty cost for the batch (Rs./h)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    Pravin P. Tambe & Makarand S. Kulkarni

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  1. Pravin P. Tambe
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  2. Makarand S. Kulkarni
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Correspondence to Pravin P. Tambe.

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Tambe, P.P., Kulkarni, M.S. A novel approach for production scheduling of a high pressure die casting machine subjected to selective maintenance and a sampling procedure for quality control. Int J Syst Assur Eng Manag 5, 407–426 (2014). https://doi.org/10.1007/s13198-013-0183-4

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