IE $305$

Assignment $6-$ Maintenance and Reliability

Question $1$

A typical retail transaction consists of several smaller steps, which are components subject to failure. A list of such components might include:

$\backslash$table$[[$COMPONENT$,$DESCRIPTION,DEFINITION OF FAILURE$],[1,\backslash$table$[[$Find products in proper size, color,$],[$etc$.]],$Can't find the product$],[2,$Enter cashier line,$\backslash$table$[[$No lines open; lines too long;$],[$line experiencing difficulty$]]],[3,\backslash$table$[[$Scan product UPC for name, price,$],[$etc$.]],\backslash$table$[[$Won$\text{'}$t scan; item not on file;$],[$scans incorrect name or price$]]],[4,$Calculate purchase total,$\backslash$table$[[$Wrong weight; wrong extension;$],[$wrong data entry; wrong tax$]]],[5,$Make payment,$\backslash$table$[[$The customer lacks cash; the check not$],[$acceptable; credit card refused$]]],[6,$Make change,Makes change incorrectly$],[7,$Bag merchandise,$\backslash$table$[[$Damages merchandise while bagging; bag$],[$splits$]]],[8,$Conclude transaction and exit,No receipt; unfriendly, rude, or aloof clerk$]]$

Let the eight probabilities of success be $\mathrm{.}92,\mathrm{.}94,\mathrm{.}99,\mathrm{.}99,\mathrm{.}98,\mathrm{.}97,\mathrm{.}95,$ and $\mathrm{.}96.$ What is the reliability of the system; that is$,$ the probability that there will be a satisfied customer? If you were the store manager, what would be an acceptable value for this probability? Which components would be good candidates for backup, which for redesign?

Question $2$

Medcomp Manufacturing, a medical equipment manufacturer, subjected $100$ heart pacemakers to $5,000$ hours of testing. Halfway through the testing, $5$ pacemakers failed. What was the failure rate in terms of the following:

a$)$ Percentage of failures?

b$)$ Number of failures per unit$-$hour of operating time?

c$)$ Number of failures per unit$-$year?

d$)$ If $1,100$ people receive pacemaker implants, how many units can we expect to fail during the following year?

Question $3$

The fire department has some failures with its oxygen masks and is evaluating the possibility of outsourcing preventive maintenance to the manufacturer. Because of the risk associated with a failure, the cost of each failure is estimated at $$2,000.$ The current maintenance policy $($with station employees performing maintenance$)$ has yielded the following history:

$\backslash$table$[[$NUMBER OF BREAKDOWNS,$0,1,2,3,4,5],[\backslash$table$[[$NUMBER OF YEARS IN WHICH$],[$BREAKDOWNS OCCURRED$]],4,3,1,5,5,0]]$

This manufacturer will guarantee repairs on any and all failures as part of a service contract. The cost of this service is $$5,000$ per year.

a$)$ What is the expected number of breakdowns per year with station employees performing maintenance?

b$)$ What is the cost of the current maintenance policy?

c$)$ What is the more economical policy?