The Economic Design of p-Charts to Maintain Current Control of o Process: Some Numerical Results

For two initial process levels, po ′ = 0.01 and po ′ = 0.05, minimum cost p-charts are presented for 36 sets of cost data and three degrees of shift in the process mean. Minimum cost designs are also given for other special cases. Actually minimum cost designs are derived for np-charts and converted to p-charts. The degrees of shift are expressed as 0.1, 0.5 and 1.0 multiples of the initial process standard deviation. This has some but not a full stabilizing effect. In general it is found that small shifts require larger samples taken less frequently, but generally with a lower overall intensity of sampling. It is also found that with rare exceptions charts designed to detect small shifts have acceptance limits of zero. The effects of variations in the cost parameters and in the rate of occurrence of the assignable cause are also presented in the paper and a brief comparison is made with a paper on p-charts by W. K. Chiu and another by D. C. Montgomery, J. F. Mance and R. G. Herkes.