Article Contents
Article Contents

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

• * Corresponding author
• 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.

 Citation:

• Table 1.  Basic Statistics of PAC3 Waiting Time Data

 Sample Size 27,689 Min 0 (minute) 25th Percentile 21.1 (minutes) Median 40.1 (minutes) Mean 50.6 (minutes) 75th Percentile 69.6 (minutes) 95th Percentile 128.3 (minutes) Max 321.8 (minutes) Standard Deviation 39.1 (minutes) Variance 1528.7 Coefficient of Variation 0.772 Skewness 1.454

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

 $t$ the length $l$ of time interval 10 12 14 15 16 17 18 19 21 23 25 128 0.624 0.618 0.613 0.610 0.606 0.603 0.600 0.596 0.591 0.582 0.576 127 0.620 0.614 0.608 0.605 0.601 0.598 0.595 0.591 0.586 0.579 0.571 126 0.615 0.610 0.604 0.600 0.597 0.594 0.590 0.588 0.579 0.573 0.567 125 0.611 0.606 0.599 0.596 0.592 0.589 0.586 0.583 0.576 0.568 0.562 124 0.607 0.601 0.594 0.591 0.587 0.585 0.582 0.577 0.570 0.563 0.556 123 0.603 0.596 0.589 0.586 0.583 0.580 0.575 0.573 0.565 0.558 0.551 122 0.598 0.591 0.584 0.581 0.579 0.574 0.571 0.567 0.560 0.553 0.546 121 0.593 0.586 0.580 0.577 0.572 0.570 0.565 0.562 0.555 0.548 0.541 120 0.588 0.581 0.575 0.571 0.568 0.564 0.560 0.557 0.549 0.543 0.535 119 0.584 0.577 0.569 0.566 0.562 0.559 0.555 0.551 0.544 0.538 0.528 118 0.578 0.572 0.565 0.561 0.557 0.553 0.550 0.546 0.539 0.531 0.523 117 0.573 0.566 0.559 0.555 0.552 0.548 0.544 0.541 0.534 0.525 0.515 116 0.569 0.561 0.554 0.550 0.546 0.542 0.539 0.535 0.528 0.519 0.508 115 0.563 0.556 0.548 0.544 0.541 0.537 0.533 0.530 0.521 0.512 0.503 114 0.558 0.550 0.543 0.539 0.535 0.531 0.528 0.524 0.515 0.504 0.496 113 0.552 0.545 0.537 0.533 0.529 0.526 0.522 0.517 0.508 0.499 0.489 112 0.547 0.539 0.531 0.528 0.524 0.520 0.515 0.511 0.500 0.492 0.483 111 0.541 0.533 0.526 0.522 0.518 0.513 0.509 0.504 0.495 0.485 0.473 110 0.535 0.527 0.520 0.516 0.511 0.507 0.502 0.497 0.488 0.478 0.466 109 0.529 0.522 0.514 0.510 0.505 0.500 0.495 0.490 0.481 0.469 0.461 108 0.524 0.516 0.508 0.503 0.498 0.493 0.488 0.484 0.474 0.462 0.452 107 0.518 0.510 0.501 0.496 0.491 0.486 0.481 0.476 0.465 0.456 0.444 106 0.512 0.504 0.494 0.489 0.484 0.479 0.474 0.469 0.457 0.447 0.434

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

 length $l$ 12 14 15 16 17 18 19 21 23 CV 0.50 0.49 0.49 0.48 0.48 0.47 0.47 0.46 0.45 New mean 52.22 52.36 52.43 52.56 52.64 52.71 52.79 52.95 53.10 New variance 691.37 669.14 656.33 647.02 636.20 624.37 613.49 586.38 563.09 CV reduction 34.8% 36.1% 36.8% 37.4% 38.0% 38.7% 39.3% 40.8% 42.2% Mean increase 3.1% 3.4% 3.5% 3.6% 3.9% 4.0% 4.2% 4.4% 5.0% Var reduction 54.1% 55.4% 56.2% 57.1% 58.0 % 58.4% 59.2% 61.0% 62.0%

Tables(3)