Shewhart Control Chart for Monitoring Time Between Events with Estimated Parameters in Short Production Runs

Todetect upward and downward parameter changes in high-quality processes (HQPs), time between events (TBE) charts have traditionally been used. However, in practice, when the process parameter is unknown and short production runs (SPRs) occur in a smart manufacturing environment, the TBE chart’s characteristics need to be studied carefully. To circumvent this issue, a Shewhart TBE chart with an estimated parameter for monitoring SPR processes is studied. The unknown process parameter is estimated using both the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE). Then, the truncated run length (RL) properties—i. e. , truncated average RL (TARL), truncated standard deviation of RL (TSDRL), and percentiles of the truncated RL—of the Shewhart TBE chart in SPR for different parameter settings are obtained through extensive numerical simulations. These truncated RL properties are compared with properties of the Shewhart TBE chart with a known parameter in an SPR. The results show that the Shewhart TBE chart with an estimated parameter is more favorable in cases of an underestimation of the process parameter θ⁰ for the detection of upward changes or an overestimation of θ⁰ of the process parameter for the detection of downward changes.