The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival function before and after fuzzy work. The period of study was (May, June, July, and August). The number of patients who entered the study during the above period was 1058 patients. Six cases have been ruled out including: The number of prisoners was 26. The number of people with negative swabs was 48. The number of patients who exit status was unknown was 29. The number of patients who escaped from the hospital was 2. The number of patients transferred to other hospitals was 35. The number of patients discharged at their responsibility was 133. Then the number of patients who entered the (study) hospital which is the sample size becomes (n=785). The number of patients who died during the period of study was (m=88). The number of patients who survived during the study period was (n-m=697).
