Optimal designs of the double sampling X¯ chart with estimated parameters

► We study the impact of Phase-I parameter estimation on the DS X¯ chart's properties. ► The performance of the DS X¯ chart is adversely affected by parameter estimation. ► A theoretical method for the DS X¯ chart with estimated parameters is developed. ► Optimal designs for minimizing ARL1(δopt), ASS0 and AEQL are proposed. ► New optimal parameters, based on practical number of Phase-I samples are given.