Dynamic Optimization Of Continuous Sampling Plan For Statistical Process Control

Continuous sampling plans（CSP）is the process control scheme and can be used to improve the process quality.There are infinite inspection schemes under the same quality requirement for the in-control process.In practice,the appropriate scheme is identified according to the production lot and the quality requirement.For the multiple concurrent processes with various process capability levels,some defeciencies have be found on the method of selecting the inspection scheme as the followings.For these concurrent processes,having the same production lots and the different process capabilities,the same inspection scheme will be identified,the outgoing process qualities for them will be conformant but different from each other.For the concurrent processes,having the same process capability but the different production lots,the disimilar inspection scheme will be identified for every process,the outgoing process quality will be also conformant but inconsistent.Some other questions exist when the continuous sampling plan is carried out for the process control.For example,the Type I and II risks are both high when the continuous sampling plan is adopted for the process control,and it is not agreed for the researchers on how to decrease the inspection cost.By analyzing the causes that the continuous sampling plan cannot satify the quality control requirement of the in-control process,and considering the proprieties of the statistical stable of the in-control process,two improved continuous sampling plans for controlling the process quality of the in-control process are proposed.One is the optimal continuous sampling plan,and the other is the process control scheme of integrating the single level continuous sampling plan and the process yield index.First,the statistical stability characteristics of the in-control process are analyzed.The methods for expressing the process state of the in-control process are presented,such as the estimator and the lower confidence limit of the process conformance,and the distributed function of the process capability indices.The various process control requirements for the in-control process are concluded.Based on the completeness of the theory of the continuous sampling plan,it is induced that it is feasible to improve the continuous sampling plan for meeting the various process control requirements of the in-control process.Secondly,by analyzing the relation between the estimator of the process conformance,the process quality control index,and the quality controlling characteristics of the continuous sampling plan,the effective work interval of the continuous sampling pan is constructed where the process quality can be improved with the affordable inspection cost.The connections between the performance measures and quality and cost constraints are depicted based on the change regular of three performance functions and the relationship among the process state,the quality control requirement,and the operation cost of the continuous sampling plan.Thirdly,the changing regulars of three performance measures in the performance equations are analyzed.The feasible continuous sampling plans and its boundary for the in-control process are proposed under the fluctuation regulars of the performance measures.It is identified that the boundary feasible continuous sampling plan is the optimal process control scheme by comparing three performance measures between the optimal scheme and the original inspection scheme from the two views of the feasible plan and the contour plan.The equation sets are constructed for solving the parameters of the four kinds of optimal continuous sampling schemes,respectively.The boundary identical equation and the contour identical equation are involved in the equation sets.The scheme parameters,process conformance,average outgoing quality limit,and average fraction inspected are one-to-one relationship for the optimal scheme.The optimal plan can meet various process control requirements of the in-control process,such as monitoring the process state,satisfying the multiple constraints,achieving the feedback control,adjusting automatically the scheme parameters,and controlling quantitively the process quality,due to the one-to-one correspondence.Fourthly,the integrated process control scheme between CSP-1 and S_pk is provided,which includes the quality control scheme and the risk control scheme.Regardless of the process quality fluctuation,the conformant quality can be obtained with the quality control scheme.However,the Type I and II risks are both high and the cost constraint cannot be satisfied under the quality control scheme.By analyzing the relation between the quality and cost constraints and the process capability,the risk control scheme is presented based on the accurate distribution of the estimator of the process yield index.The Type I and II risks can be controlled on the given level with the risk control scheme.The quality control scheme and the risk control scheme work independently and complementarily in the integrated control scheme.Four constraints,quality,cost,Type I risk,and Type II risk,are satisfied simultaneously.The one-to-one relationship exists between the scheme parameters and the four constraints.Various process control requirements are satisfied when the integrated process control scheme is adopted.Lastly,the tabulated schemes under three constraint requirements are supplied for all the proposed improvement schemes.The comparisons show the advantages of the improvement schemes against the original continuous sampling plan for the in-control process.The enterprise applications verify the effective of the improvement schemes.