Risk-Adjusted Control Charts for Health Care Monitoring

Algorithm 1

(1) Before the monitoring phase starts, take the following preliminary steps:

 (a) Select a desired ARL=1/𝛼 and a degree of change 𝜃 during OoC that

 should be optimally protected against.

 (b) Apply rule of thumb (2.2) to obtain 𝑟 (typically truncate at 5 in practice).

 (c) Find 𝜆 such that 𝑃(𝑍_𝜆≥𝑟)=𝑟𝛼, where 𝑍_𝜆 is Poission, or simply use its

 approximation 𝜆 from (A.2).

 (d) Wait till 𝑚 failures have occurred. Take for example, 𝑚=100 (or use Section 4

  (e.g., see (D.6)) to make a more elaborate choice).

 (e) From this Phase I sample, evaluate the fraction of failures 𝑝_𝑗 for each of the

 categories 𝑗=1,…,𝑘.

(2) Now wait till 𝑌₁, the moment at which the 𝑟th failure occurs.

(3) Obtain the corresponding numbers 𝑔_𝑗 from category 𝑗 (i.e., Σ^𝑘_𝑗=1𝑔_𝑗=𝑌₁).

(4) Give a signal if Σ^𝑘_𝑗=1𝑔_𝑗𝑝_𝑗≤𝜆; otherwise go back to Step  2, leading to 𝑌₂,𝑌₃,….