Design of economically and statistically optimal sampling plans

Year 2018, Volume: 47 Issue: 3, 685 - 708, 01.06.2018

Mohammad Saber Fallah Nezhad Faeze Zahmatkesh Saredorahi Mohammad Saleh Owlia Mohammad Ali Vahdat Zad

Abstract

This paper attempts to develop four types of acceptance sampling plans under the objectives of minimizing the total loss to the producer and consumer and maximizing the rate of approaching to the ideal operating characteristic (OC) curve when the quality characteristic follows a normal distribution and has lower specication limit. To provide the desired protection for both the producer and the consumer, two constraints are considered that balance both producer and consumer risks by using two specied points on OC curve. The first objective function of this model is constructed based on the total expected loss by incorporating the one-sided minimum specication Taguchi loss function, and the second one is constructed based on conformity to the ideal OC curve by using minimum angle method. Also, the optimal solution of the proposed plans is determined for 10 different scenarios of process parameters. Furthermore, the optimal solution of these plans is determined when only one of the objective functions is considered.

Keywords

Quality control, Acceptance sampling plan, Loss function, Minimum angle method, Acceptable quality level, Limiting quality level

References

• Aslam, M. and Yen, C.H. and Jun, C.H. Variable repetitive group sampling plans with process loss consideration, Journal of Statistical Computation and Simulation 81 (11), 1417- 1432, 2011.
• Balamurali, S. and Jun, C.H. Repetitive group sampling procedure for variables inspection, Journal of Applied Statistics 33 (3), 327-338, 2006.
• Balamurali, S. and Jun, C.H. Multiple dependent state sampling plans for lot acceptance based on measurement data, European Journal of Operational Research 180, 1221-1230, 2007.
• Bowling, S.R. and Khasawneh, M.T. and Kaewkuekool, S. and Cho, B.R. A Markovian approach to determining optimum process target levels for a multi-stage serial production system, European Journal of Operational Research 159, 636-650, 2004.
• Fallahnezhad, M.S. and Aslam, M. A new economical design of acceptance sampling models using Bayesian inference, Accreditation and Quality Assurance 18 (3), 187-195, 2013.
• Fallahnezhad, M.S. and Niaki, S.T.A. A new acceptance sampling policy based on number of successive conforming items, Communications in Statistics-Theory and Methods 42 (8), 1542-1552, 2013.
• Fallahnezhad, M.S. and Niaki, S.T.A. and Abooie, M.H. A new acceptance sampling plan based on cumulative sums of conforming run-lengths, Journal of Industrial and Systems Engineering 4 (4), 256-264, 2011.
• Ferrell, W.G. and Chhoker, J.A. Design of economically optimal acceptance sampling plans with inspection error, Computers and Operations Research 29 (10), 1283-1300, 2002.
• Govindaraju, K. and Ganesalingam, S. Sampling inspection for resubmitted lots, Commu- nications in Statistics  Simulation and Computation 26 (3), 1163-1176, 1997.
• Liao, C.N. and Kao, H.P. Supplier selection model using Taguchi loss function, analytical hierarchy process and multi-choice goal programming, Computers and Industrial Engineering 58 (4), 571-577, 2010.
• Liu, S.W. and Lin, S.W. and Wu, C.W. A resubmitted sampling scheme by variables in- spection for controlling lot fraction nonconforming, International Journal of Production Research 52 (12), 3744-3754, 2014.
• Liu, S.W. and Wu, C.W. Design and construction of a variables repetitive group sampling plan for unilateral specication limit, Communications in Statistics - Simulation and Com- putation 43 (8), 1866-1878, 2014.
• Moskowitz, H. and Tang, K. Bayesian Variables Acceptance Sampling Plans: Quadratic Loss Function and Step Loss Function, Technometrics 34 (3), 340-347, 1992.
• Pearn, W.L. and Wu, C.W. Variables sampling plans with PPM fraction of defectives and process loss consideration, Journal of the Operational Research Society 57, 450-459, 2006.
• Sherman, R.E. Design and evaluation of repetitive group sampling plan, Technometrics 7, 11-21, 1965.
• Soundararajan, V. and Christina, A.L. Selection of single sampling variables plans based on the minimum angle, Journal of Applied Statistics 24 (2), 207-218, 1997.
• Wu, C.W. An ecient inspection scheme for variables based on Taguchi Capability index, European Journal of Operational Research 223 (1), 116-122, 2012.
• Wu, C.W. and Aslam, M. and Jun, C.H. Variables sampling inspection scheme for resubmit- ted lots based on the process capability index Cpk, European Journal of Operational Research 217 (3), 560-566, 2012.
• Yazdi, A.A. and Fallahnezhad, M.S. An Optimization Model for Designing Acceptance Sam- pling Plan Based on Cumulative Count of Conforming Run Length Using Minimum Angle Method, Hacettepe Journal of Mathematics and Statistics, 2014.
• Zhang, C.W. and Xie, M. and Goh, T.N. Economic design of cumulative count of conforming charts under inspection by samples, International Journal of Production Economics 111, 93- 104, 2008.