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Minimization of the coefficient of variation for patient waiting system governed by a generic maximum waiting policy

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  • Timely access of care has been widely recognized as an important dimension of health care quality. Waiting times can affect patient satisfaction and quality of care in the emergency department (ED). This study analyzes a general patient waiting policy such that ED patients who wait beyond a threshold have their wait shortened. Assuming that the policy is implemented to accelerate the long-waiting cases within a short time interval, we transform the original waiting distribution to a piecewise distribution. The objective of this paper is to examine the reliability of the induced waiting system by minimizing the coefficient of variation (CV) of waiting time. We convert the CV minimization problem to an approximation counterpart using the sampling technique. With patient waiting time data from an emergency department in Singapore, we derive the optimal values of parameters, such as the threshold and the length of the underlying time interval, needed in the policy. Numerical results show that CV and variance of new waiting time will be reduced remarkably by 38% and 58% respectively, in comparison with the original ones.

    Mathematics Subject Classification: 90B22, 62F99, 62P99, 65C99.

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  • Table 1.  Basic Statistics of PAC3 Waiting Time Data

    Sample Size27,689
    Min0 (minute)
    25th Percentile21.1 (minutes)
    Median40.1 (minutes)
    Mean50.6 (minutes)
    75th Percentile69.6 (minutes)
    95th Percentile128.3 (minutes)
    Max321.8 (minutes)
    Standard Deviation39.1 (minutes)
    Variance1528.7
    Coefficient of Variation0.772
    Skewness1.454
     | Show Table
    DownLoad: CSV

    Table 2.  Coefficient of Variation under Different Scenarios on $t$ and $l$

    $t$the length $l$ of time interval
    1012141516171819212325
    1280.6240.6180.6130.6100.6060.6030.6000.5960.5910.5820.576
    1270.6200.6140.6080.6050.6010.5980.5950.5910.5860.5790.571
    1260.6150.6100.6040.6000.5970.5940.5900.5880.5790.5730.567
    1250.6110.6060.5990.5960.5920.5890.5860.5830.5760.5680.562
    1240.6070.6010.5940.5910.5870.5850.5820.5770.5700.5630.556
    1230.6030.5960.5890.5860.5830.5800.5750.5730.5650.5580.551
    1220.5980.5910.5840.5810.5790.5740.5710.5670.5600.5530.546
    1210.5930.5860.5800.5770.5720.5700.5650.5620.5550.5480.541
    1200.5880.5810.5750.5710.5680.5640.5600.5570.5490.5430.535
    1190.5840.5770.5690.5660.5620.5590.5550.5510.5440.5380.528
    1180.5780.5720.5650.5610.5570.5530.5500.5460.5390.5310.523
    1170.5730.5660.5590.5550.5520.5480.5440.5410.5340.5250.515
    1160.5690.5610.5540.5500.5460.5420.5390.5350.5280.5190.508
    1150.5630.5560.5480.5440.5410.5370.5330.5300.5210.5120.503
    1140.5580.5500.5430.5390.5350.5310.5280.5240.5150.5040.496
    1130.5520.5450.5370.5330.5290.5260.5220.5170.5080.4990.489
    1120.5470.5390.5310.5280.5240.5200.5150.5110.5000.4920.483
    1110.5410.5330.5260.5220.5180.5130.5090.5040.4950.4850.473
    1100.5350.5270.5200.5160.5110.5070.5020.4970.4880.4780.466
    1090.5290.5220.5140.5100.5050.5000.4950.4900.4810.4690.461
    1080.5240.5160.5080.5030.4980.4930.4880.4840.4740.4620.452
    1070.5180.5100.5010.4960.4910.4860.4810.4760.4650.4560.444
    1060.5120.5040.4940.4890.4840.4790.4740.4690.4570.4470.434
     | Show Table
    DownLoad: CSV

    Table 3.  Estimates of CV, Mean and Variance Changes with $t=106$

    length $l$121415161718192123
    CV0.500.490.490.480.480.470.470.460.45
    New mean52.2252.3652.4352.5652.6452.7152.7952.9553.10
    New variance691.37669.14656.33647.02636.20624.37613.49586.38563.09
    CV reduction34.8%36.1%36.8%37.4%38.0%38.7%39.3%40.8%42.2%
    Mean increase3.1%3.4%3.5%3.6%3.9%4.0%4.2%4.4%5.0%
    Var reduction54.1%55.4%56.2%57.1%58.0 % 58.4%59.2%61.0%62.0%
     | Show Table
    DownLoad: CSV
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