The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Remove Redundant Left Joins (modified query below): Redundant LEFT JOINs (e.g. `CLARITY_DEP`) were detected in the query. Removing them will result in a performance improvement. In some cases, JOINs become redundant after an optimization is applied, such as when converting OR conditions to a UNION clause.

Optimal indexes for this query:

ALTER TABLE `IP_FLWSHT_MEAS` ADD INDEX `ip_meas_idx_fsd_id` (`FSD_ID`);
ALTER TABLE `PATIENT_3` ADD INDEX `patient_3_idx_pat_id` (`PAT_ID`);
ALTER TABLE `PAT_ENC_HSP` ADD INDEX `pat_hsp_idx_inpatient_id` (`INPATIENT_DATA_ID`);

The optimized query:

SELECT
        REC.INPATIENT_DATA_ID,
        RANK() OVER (PARTITION 
    BY
        PATS.PAT_ENC_CSN_ID,
        MEAS.FLO_MEAS_ID 
    ORDER BY
        MEAS.RECORDED_TIME) 'VITALS_RANK',
        MEAS.RECORDED_TIME,
        PATS.PAT_ENC_CSN_ID,
        PATS.PAT_ID,
        PATS.CONTACT_DATE,
        MEAS.FLO_MEAS_ID,
        PATS.DEPARTMENT_ID,
        PAT.IS_TEST_PAT_YN,
        PATS.HOSP_DISCH_TIME,
        PATS.HOSP_ADMSN_TIME 
    FROM
        CLARITY.DBO.IP_FLWSHT_REC REC 
    LEFT OUTER JOIN
        CLARITY.DBO.PAT_ENC_HSP PATS 
            ON PATS.INPATIENT_DATA_ID = REC.INPATIENT_DATA_ID 
    LEFT OUTER JOIN
        CLARITY.DBO.PATIENT_3 PAT 
            ON PAT.PAT_ID = PATS.PAT_ID 
    LEFT OUTER JOIN
        CLARITY.DBO.IP_FLWSHT_MEAS MEAS 
            ON REC.FSD_ID = MEAS.FSD_ID