Control $-$ Reliability

You are designing a system for a pharmacy mixing chemotherapy for cancer patients. There are three process steps, all in series. The processes are "reading the patient characteristics," "entering the proper patient characteristics into the chemo mixing process," and "labeling patient name." Assuming that the successful completion of each of the processes is $0\mathrm{.}92,0\mathrm{.}95$ and $0\mathrm{.}98$ respectively, what is the overall system reliability?

For the previous problem, the required system reliability is $0\mathrm{.}999.$ Assume that each process can be increased at only a constant percentage $($i$.$e$.,$ you can increase them all $5\%[$e$.$g$.,$ the new proposed reading patient characteristics $=1\mathrm{.}05*0\mathrm{.}92]).$ What is the best system performance you can attain? What is the highest percentage increase you can impose? Remember, you can not exceed $1\mathrm{.}0$ for any system component.

Assume that you can not attain the required system reliability of $0\mathrm{.}999.$ Design a parallel process for each of the three processes $($i$.$e$.,$ a double check for each of the three processes, such as that a second pharmacist will inspect each process in parallel$).$ What would be the necessary increase in each of the processes to achieve the necessary system performance?

Assume that you can not attain the required system reliability of $0\mathrm{.}999.$ Design a parallel process to double check again the complete process as defined in Problem $6,$ above. In this scenario, the pharmacist$-$manager will double check the complete process. Assuming the original process reliabilities and the parallel processes for each of the three steps, have the identical process reliability as their parent process, what would be the necessary reliability of the pharmacy manager to achieve the necessary goal $($to $3$ significant digits$)?$

Clearly, assuming known reliability for any process is foolhardy! Given this, assume the following probabilities for each of the three steps: "reading the patient characteristics $($uniformly distributed $0\mathrm{.}900\mathrm{.}94),"$ "entering the proper patient characteristics into the chemo mixing process $($uniformly distributed $0\mathrm{.}940\mathrm{.}99),"$ and "labeling patient name $($uniformly distributed $0\mathrm{.}970\mathrm{.}99)."$ Assume these probabilities for their respective parallel process also. Assume the distribution for the reliability for the pharmacy supervisor is uniformly distributed $0\mathrm{.}850\mathrm{.}95.$ Develop a Monte Carlo simulation with $1000$ iterations. What are the $25$th$,50$th and $75$th percentiles for system reliability? What is the pr you will meet the $0\mathrm{.}999$ required system reliability? Sove in Excel