The​ Solomon, Smith, and Samson law firm produces many legal documents that must be word processed for clients and the firm. Requests average pages of documents per​ hour, and they arrive according to a Poisson distribution. The secretary can word process pages per hour on average according to an exponential distribution. a. The average utilization rate of the secretary is ​% utilization. ​
b. The probability that more than four pages are waiting or being word processed is . (Enter your response rounded to three decimalplaces.)
c. The average number of pages waiting to be word processed is pages. (Enter your response rounded to two decimal places.)

Arrival rate λ= 19 pages per hour

Service rate μ = 20 pages per hour

a.  Average utilization rate P =  λ/μ

Average utilization rate P = 19/20

Average utilization rate P = 0.95

Average utilization rate P = 95%

b.  Probability that more than four pages are waiting or being word processed Pn>4 = 1 - (P0 + P1 + P2 + P3 + P4)

Pn>4 = 1 - (0.05*(1+0.95 + 0.95^2 + 0.95^3 + 0.95^4))

Pn>4 = 1 - (0.05*4.524)

Pn>4 = 1 - 0.2262

Pn>4 = 0.774.

c.  Average number of pages waiting to be word processed Lq

Lq = λ²/μ(μ-λ)

Lq = 19²/20(20-19)

Lq = 361/20

Lq = 18.05

step 1: create a plan

step 2: inventory facility equipment/assets

step 3: create preventive maintenance procedures

step 4: create preventive maintenance schedules

step 5: train your maintenanceteam

step 6: analyze – adjust - improve

or

step 1 – pm procedure design: doing the effective things

step 2 – pm procedure scheduling: efficient use of people and resources

step 3 – pm lubrication engineering

step 4 – pm training: back on the chain gang

step 5 – pm program management plan

step 6 – communicate, communicate, communicate