تخمين نقطۀ تغيير پله‌اي در نمودارهاي كنترل g و h در حوزۀ بهداشت و درمان

Step Change Point Estimation in g and h Control Charts in Healthcare

يكي از اهداف اصلي كنترل فرايند آماري كشف زمان دقيق وقوع تغيير در فرايندها، تحت عنوان نقطة تغيير است. با توجه به رابطة مهندسي كيفيت و اپيدميولوژي بيمارستاني، تخمين نقطة تغيير در فرايندهاي بهداشت و درمان اهميت بسزايي دارد؛ از اين‌رو در اين پژوهش، ضمن ارائة نمودارهاي كنترل g و h براي مراقبت‌هاي درماني، به تخمين نقطة تغيير پله‌اي با استفاده از برآورد حداكثر درست‌نمايي پرداخته شده است. به‌منظور ارزيابي عملكرد روش‌هاي پيشنهادي از شبيه‌سازي مونت‌كارلو براساس معيارهاي صحت و دقت استفاده شده، همچنين تعداد اعضاي مجموعة اطمينان و احتمال پوشش آن‌ها، براساس لگاريتم تابع درست‌نمايي ارائه شده است. نتايج شبيه‌سازي حاكي از آن است كه تخمين‌زننده‌هاي پيشنهادي تحت شيفت پله‌اي، عملكردي رضايت‌بخش تحت انواع شيفت‌ها دارند.

There is considerable interest in the use of Statistical Process Control (SPC) in healthcare in the recent years because SPC tools lead to continual improvement in healthcare process. Control chart is one of the main tools of the SPC, however, they usually signal the out-of-control status with delay respect to real time of the change known as change point. Hence, change point estimation is important in healthcare with considering relationship between quality engineering and hospital epidemiology. There are varieties of quality characteristics in healthcare which are should be monitored over time. Therefore, in this paper, first, g and h control charts are described since these control charts are famous tools for monitoring events in healthcare. Then, corresponding step change point estimators using Maximum Likelihood Estimation (MLE) are proposed. In this regard, Mont Carlo simulation is used to evaluate performances of the proposed estimators based on accuracy and precision measures under all kinds of shifts. In addition, cardinality and coverage probability of confidence set are presented for the proposed estimators based on the logarithm of the likelihood function. The simulation studies are conducted under different magnitudes of the step shifts to evaluate performances of the proposed change point estimators in both control charts. The results show that as the magnitude of the step change in the parameter of the distributions increase, the performance of the proposed change point estimators improve significantly in terms of precision and accuracy measures. Also, cardinality and coverage percentage of confidence set estimators are calculated and plotted to show the relationship among these measures and increasing and decreasing shifts under the given reference values. In addition, the simulation studies demonstrate that as the magnitude of the step change in the parameters of the distributions enlarge, cardinality of set estimators reduces and coverage percentage of confidence set estimators increases under the given references values. In general, results show that the proposed change point estimators perform satisfactory under all types of shifts. Finally, the performance of one of the proposed change point estimators is illustrated through an applied example in healthcare.