Systems & Logistics Support Management

1 BetaC 2021 by Dr. Paul Battaglia as prepared at Florida Tech

MGT5061-FA21 Systems & Log Support Mgt

note15-W05 Chapter 2 RMA (aka RAM)

We are here

Introduction to the Course Ch 1 - Introduction to logistics Ch 2 - Reliability, Maintainability, and Availability Measures Ch 3 - Measures of Logistics and System Support Ch 4 -The Systems Engineering Process Ch 5 - Logistics and Supportability Analysis Ch 6- Logistics in System Design and Development Ch 7 - Logistics in the Production/Construction Phase Ch 8- Logistics in the System Utilization, Sustaining Support, and Retirement Phases Ch 9- Logistics Management

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We originally skipped chapter 2 (reliability, maintainability, and availability measures). We jumped from chapter 1 (introduction) to chapter 3 (measures of logistics and system support). Chapter 3 is a more general case of systemic metrics. On the other hand, Chapter 2 on reliability, maintainability, and availability is pretty specific. It seemed to me that Chapters 2 and 3 were in reverse sequence in the subject matter as addressed by Blanchard. At any rate, here we are in chapter 2.

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On page iv look at how chapter 2 is developed. ** We know there is an introduction 2.1 Then Reliability measures & factors 2.2 Maintainability measures and factors 2.3 Availability (measures) and factors That is RMA. -=-= Often referred to in a slightly different sequence, yes? RAM.

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On page 73, in section 2.4 look at the summary. ** Back on page 11 in figure 1.4 we saw that there are a wide variety of logistics and system support activities for both

** forward; and ** reverse flows.

** How well the system successfully accomplishes these activities is due, in large part, to how the system is designed. *** BUT do note that design is not the entire story. There are other factors!

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One big considerations is the behavior of employees/people in general. An example? GTYA! We can make an electrical connector so that it only fits one way. Thereby helping to ensure that the circuit is “always” connected properly and will work. But inevitably [some] people will try to force the connector in an improper orientation. ** It is very hard to make a system or product that is entirely employee proof (or aka GI proof). -=-= Glad that you asked.

** Availability is a function of reliability and maintainability and “other” considerations A = f (R,M,O) Now we see why the chapter is titled reliability, maintainability, and then availability. It aligns better with the equation. In this view, the term RAM basically has the sequence not-quite-correct. ** Also we should to look at a “systems approach”. Consider other factors such as

** software ** people ** facilities ** data ** etc (all the factors mentioned in the work so far)

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** Chapter 2 focuses on terms and metrics for reliability & maintainability & (in invisible ink) availability. After all, availability has a section in the chapter; but for some reason availability was omitted from the summary.

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On page 46 we have a few introductory paragraphs. ** One view of logistics is all considerations needed to (help-see note) ensure effective and economical support of a system throughout the system's life cycle. ** We want the system to:

** perform (work) as intended (to meet the need) ** be available when required ** be cost-effective when being used

Indeed, be cost-effective even when not being used! ** Further, Blanchard tenants (which seems reasonable) that meeting these characteristics is heavily influenced by the goals and characteristics in the system design. -=-=-=- More than wordsmithing? In a probabilistic world we can only “help ensure” a particular action. We cannot ensure (make 100% certain!) that an event will happen. Even 6-sigma is not 100%? The best laid plans of mice and men .......

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** A key measure is availability. ** And availability is a function of reliability and maintainability (and as he said in the summary, the “others” of the system). hence our “old friend” A = f (R, M, O) The sequence in the book is reliability, maintainability, and then availability. So we flip the equation and have f (R, M, O) = A Of course, the book then drops “other” so f (R, M) = A

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On page 46 in footnote 1 Blanchard comments on the use of statistics, probability density functions, and the like. Hopefully you recall some of this.

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In the following notes I am not going to make an extensive effort to cover every point or equation. You can read along and follow the algebra (and where he has quantitative examples you should do the math). I will try to hit the major takeaways.

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On page 47, 2.1 addresses reliability. Reliability is the ** probability that a system or product ** will perform in a satisfactory manner ** for a given period of time ** when used under specified operating conditions. Reliability can be expressed as R(t).

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Recall that the total probability of all possible outcomes should total to 1. *** Actually for most probability functions it will be close to 1. Remember that depending upon the probability distribution being used the tail or tails are asymptomatic to the x-axis (or the y-axis if so oriented). So the tail or tails stretch to infinity. So we will get close to 1, but never actually reach 1. Ta -da. For our purposes the difference is so small that we can use 1! So if we define F(t) as the probability that the system will fail, then the reliability is 1 less the probability of failure R(t) = 1 - F(t) (2.1)

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On page 47, follow the progression from equation 2.1 to equation 2.5. If you cannot see the math, then just take it on faith that equation 2.5 is valid. It might be easier to see if we eliminate that “minus” in the exponent. We do that by moving the term from the numerator to the denominator. R(t) = ____1______ (modified 2.5) e t/m Reliability at time t is the constant number one divided by the natural log base (e) raised to the power of t divided by m (the mean time between failure).

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As a slight detour (an aside) .... This is one of the main reasons why logisticians who are involved with maintenance place so much emphasis on the mean time between failure (MTBF). MTBF is an integral part of the reliability function!!! And as we shall see MTBF appears in many, many of the other key formulas.

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Recall that e has a value of about 2.718 (the value goes on indefinitely without repetition as far as we know). At the bottom of page 47 we ask the equivalent question --- What is the reliability if the running time (t) is equal to the mean time between failure (m)? The exponential function applies. R(t) = 1/ ( e t/m ) if the run time is equal to the MTBF (or m) then t/m = 1

example. MTBF for a system/product is 5 hours. We start the system/product at time zero. At exactly 5 hours the system/product fails.

t = 5 hours = 1 m 5 hours

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So R(t) = 1 / ( e 1 ) Get out your spreadsheet or calculator. 2.718 raised to the first power => 2.718 1 = 2.718 R(t) = 1/2.718 = 0.3679 = 0.37 (the answer in the book!) If we operate the system starting at time zero and until t reaches the MTBF, the reliability is 37% (not as we might expect say 50%). Figure 2.1 is simply the graph of the function R(t).

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On page 48, the book goes on to generalize the situation in terms of lambda (or the number of failures divided by the total operating hours). lambda = (# failures / total time) Do the problem at the bottom of page 48.

REVISED

Hours

1 75 2 125 3 130 4 325 5 525 6 525 7 525 8 525 9 525 10 525 Tot 3,805

** The 5 failures are easy to see. ** We set up 10 components. ** All 10 start running at the same time. ** First failure after 75 hours. ** Second failure after 125 hours. ** etc to fifth failure at 525 hours. ** Stop the test. ** 3,805 hours is the total running hours of the TEN components that were being tested.

The test stops after the fifth failure

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On page 49, we note that this is an equation with THREE variables. lambda = (# failures) / (total time) In any equation, if we know the values of any TWO variables, then we can solve for the value of the THIRD variable. -=-= Simple example of 3 variables and we know 2 distance = rate * time d=10 miles and rate = 5 mph what is the time? 10 miles = 5 mph * time time = 10 miles/ 5 mph = 2 hours Piece of cake

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Lesson for the rest of eternity No matter the number of variables, as long as there is only 1 unknown we can solve for the unknown. might not be easy, but it can be done If there are 100 variables and we know the values for 99 of them, then we can solve for number 100!

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On page 52, in figure 2.4 for semi-obvious reasons the top part is referred to as the “bathtub” curve. Notre that we have THREE sections.

0

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The left-hand section is often referred to as the “infant mortality period”. Time 0 is when the system or product starts. If not DOA, then it takes time to “work out the bugs”. If DOA, then the curve starts at the y-axis! So the failure rate is expected to decrease as the system/product is debugged.

0

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The center section has the period that we just discussed. A (relatively) constant failure rate. Or we can assume pretty constant. As a system/product ages, then the failure rate typically increases a bit. Hence the slight upward slope at the bottom. And the exponential failure function applies. MTBF is most important in this section..

0

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The right-hand section shows the period as the system/product is getting “older”. The failure rate is increasing. It is getting more difficult to keep “that old car repaired”. The maintenance needs are increasing! Getting near system/product retirement?

0

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Put the three sections together and we have ----

0

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On page 52, at the bottom of Figure 2.4 we see some “subsets”. The failure rates for electronic equipment tends to be different from the rates for mechanical equipment. *** Electronic equipment tends to “burn out” (operate until it just gives up the ghost). Like most light bulbs. No example is perfect? We know that some fluorescent bulbs tend to dim over time. *** In large part, mechanical equipment tends to “wear out”. There is a gradual decrease in performance. e.g., piston rings wearing out

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As an aside, here is the Centennial Light Bulb. It has been burning almost continuously since 1901. Gaps of only minutes in that period! This is an extreme example of reliability for a particular item. Really “messing up” that reliability function! The bulb is in the fire department in Livermore California. There is a live cam where you can watch this. Search for Livermore Centennial light bulb.

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On page 52, in 2.1.2 we take note that most systems do not have only ONE component. There are multiple components. In a simple case (electrical circuits are easy to use as an example) these can be either #1 SERIES or #2 PARALLEL Later #3 a combination of series and parallel

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On page 53, #1 covers a SERIES system with THREE components (A, B, C) Reliability = (Ra) (Rb) (Rc) (2.8) Reliability is the product of the reliability of the three components. Ra, Rb, and Rc do NOT need to be equal. Do the quick problem at the bottom of page 53.

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On page 54, #2 covers PARALLEL networks with THREE components (A, B, C) Reliability = 1 - (1-Ra) (1-Rb) (1-Rc) (2.11) Reliability is the PRODUCT of the terms. Again, Ra, Rb, and Rc do NOT need to be equal. Do the quick problem at the bottom of page 55.

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On page 55, in #3 we have a system with BOTH SERIES and PARALLEL. Follow along. Note that this is typical of complex systems or products.

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The main takeaways are ** Reliability is not “a given” or “fixed”. ** We can manage (to varying extent) the reliability of the system and/or the product!

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BUT (a big but) improving the reliability is not totally “free”. For example, we can increase the reliability of a system by incorporating a redundant system. ** have parallel circuits so if one fails the other still can carry the load. ** Alas, that means we need to have at least TWO of everything. ** If three deep, then we need 3, and so on. More weight Greater cost Likely increased size (need to house all the paths). Makes sense for high impact systems. ** Such as hydraulics on an airplane. Even a non-aviator strongly suspects that it is NOT a good idea to lose hydraulic control at 30,000 feet.

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We can also improve reliability by using heavier, more capable parts. ** Such as higher rated capacitor --- but the capacitor also costs just a bit more.

** A flat-free tire, but again costs a bit more (and might be heavier degrading performance).

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Of course it is also possible that a slightly more expensive part will help to avoid costly, inconvenient repairs. ** The electronic equipment with the bigger capacitor does not burn out when being used on the job.

** The flat-free tire means your bike does not get a flat in the middle of a century ride in a remote area (100-mile ride). -=-=- So we need to weigh costs and benefits! As in so many of our actions.

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An example of better reliability and the use of available data. The Boeing 737 Max had TWO exterior Angle of Attack (AOA) sensors, one on each side of the cockpit. In simple terms, alas, Boeing made the decision to use the signal from only ONE sensor on a given flight. Then on the next flight they switched sensor. On flight #1 use sensor A. On flight #2 use sensor B.

On flight #3 use sensor A. In retrospect (but even in advance?) why not use redundancy for sensors that were already installed? Certainly the slightly more complex software needed to use both sensors and compare results would not seem to be a major problem!

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In other cases improving the reliability can also help to reduce costs (or at least make “life easier”). Recall the olden days when going from the US to another country usually meant lugging around a heavy transformer to change 220-240 VAC to US 110-120 VAC? Nowadays, many electronics (e.g., laptop computer) are dual voltage. ** Make the wiring able to withstand 240 VAC. ** Then with an inexpensive circuit design the system can automatically adjust to the input voltage 110-120 or 220-240. ** Easier: no special equipment (transformer). The power supply is a matter of ounces (rather than pounds). ** Might be able to get negative (or at least low marginal cost). Due to operating with a battery as an electric supply, most smaller electronics (e.g., laptop computer) operate at lower voltage than even 110. So an in-line step down transformer was needed anyways. One power supply can work world-wide. Less need for multiple models. ** The user may still need a plug adapter for the wall socket. But that is a much smaller matter.

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On page 58, 2.2 maintainability. Maintainability (from page 34) pertains to the ease, accuracy, safety, and economy when performing maintenance actions. Ideally, the design should enable maintenance to be done without major investments in time, cost, or other resources. Maintainability is the ability of the system or product to be maintained. [A very poor academic definition, no?] The good news is that much of this can be expressed in terms of probability!

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On page 58, maintenance can be classified into two major categories.

#1 Corrective maintenance to restore to required level of performance. On page 59, figure 2.11 shows a typical “corrective maintenance cycle”.

#2 Preventative maintenance to retain a system or product at the required level of performance.

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Again statistics can play a big role in quantifying these. So we should not find it unusual to see terms such as

** mean (average) ** median (half above, half below)

** maximum

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Rearranging, the sequence of the “measures” or “metrics” might make a bit more sense. The definitions, etc are pretty straightforward.

p58 #1 mean corrective maintenance time

p66 #3 median corrective maintenance time

p67 #5 mean active maintenance time

p67 #6 Maximum active corrective maintenance time

p65 #2 mean preventative maintenance time

p65 #4 median active preventative maintenance time

Note also some “other” time periods that should be addressed.

p68 #7 logistics delay time

p68 #8 administrative delay time

p68 #9 maintenance downtime

p68 maintenance labor-hour factors per operating hour/cycle/month/action

p70 maintenance frequency factors mean time between maintenance/replacement

p72 maintenance costs per action/operating hour/month/,mission/life-cycle

42

On page 60, speaking of repair times these normally follow one of three distributions. -- If for some reason another distribution is a better fit, then use the better distribution.

Distribution Typical characteristics

#1 normal distribution * simple repair * remove & replace with fairly constant time

#2 exponential distribution * excellent built-in test or otherwise easy to diagnosis * remove & replace * maintenance rate is constant.

#3 log-normal distribution. * most actions * task times vary; and/or * frequency of repair varies

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For a log-normal curve, the logarithmic the value of the function is normally distributed. Which means the shape is a bit different from the usual “normal curve”. See next slide

44

normal exponential

log-normal

45

From pages 58 to 67 there a number of examples. You should be able to follow along pretty easily. -=-=- One comment on data collection. On page 60 in table 2.2 I was confused at first. This is supposed to be a sample of 50 observations of the time to perform corrective maintenance (in minutes). The 50 points are displayed as a 10 x 5 array. The array itself is meaningless. Better to collect and display as the 50 data points Even better in the sequence collected.

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That would be something like so .....

Observation time in min.

1 40

2 71

3 75

4 67

.....

49 63

50 63

Six reasons to collect and present the information in this way. #1 It makes more “sense”. #2 It is easier to plot without resorting to midpoints, etc. #3 It is easier to test for the distribution, compute the mean-median-mode-variance-standard deviation-etc. #4 It is easier to translate into “quality oriented metrics” assuming we are in a “quality management environment” #5 Easier to spot a time-or-cycle related trend. #6 In case of a question on a value (e.g., seems high, an outlier), then it is much easier to track to the paperwork.

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Also, I suspect that it would also be easier to spot some “apparent contradictions, or at least questions”. For example, ** on page 60 the normal distribution is described as usually applying to straightforward maintenance with a (relatively) standard time to “remove and replace”. ** however, a quick review shows a range in value of 67 minutes. between 30 minutes and 97 minutes ** That does not strike me as being “relatively standard time”. ** If we expected this repair to take whatever minutes, then we might want to look into “Why the large variability in time to repair?” -=-=- Fascinating stuff, no?

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On page 72, 2.3 availability factors #1 Can be used in the sense of READINESS (3 views) ** Probability will be available for use when needed. ** Probability will be available for use when needed AND will complete the mission. ** Probability that all is satisfactory at any give point in a mission. #2 always depends on the scenario.

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As implied by the sequence R-M-A, the availability factors are based on the metrics for ** reliability; and ** maintainability

Metrics for reliability & maintainability used to calculate availability

Mean time between failure MTBF

Mean corrective maintenance time M-bar ct

Mean time between maintenance MTBM

Mean active maintenance time M-bar

Maintenance down time MDT

50

Availabil ity

Support environment

Probability

2.3.1 Inherent availability

ideal will operate as required at any point in time

Excludes scheduled preventive maintenance, logistics delay time, admin delay time

2.3.2 Achieved availability

ideal will operate as required at any point in time

includes scheduled preventative maintenance

2.3.3 Operational availability

actual will operate as required when called upon (needed)

Here is a quick summary table

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On page 73. Already back to 2.4 and the summary. That is it for Chapter 2.