Introduction to Maintainability

Transcription

1 Itroducto to Mataablty The cocept of mataablty ecompasses: A operatoal measure of effectveess A characterstc of desg A egeerg specalty that supports desg A cost drver A plaed actvty each stage of product lfe-cycle Itroducto (cot) Mataablty - s the ablty of a tem to be mataed; ths ablty stems from the aggregate of all desg features whch promote servceablty. Mateace - s a seres of actos of approprate character (cotet, tmg, qualty) to restore or reta a tem a operatoal state. Cotrast: Relablty s tme to falure, probablty of o falure Mataablty s tme to dagose ad repar a falure or tme to prevet future falure

2 Mataablty s Iheretly a Probablstc Measure Detecto, dagoss, repar, check-out all volve ucertaty Huma skll ad learg are volved Dffereces due to dvduals Dffereces due to experece Cosder other deftos of mataablty: The probablty that: Item wll be restored to operatoal status T hours Mateace wll ot be requred more tha X tmes per tme perod Mateace cost wll ot exceed $Z per tme perod 3 Mataablty the System Lfe-Cycle The Mataablty Pla s developed durg coceptual desg, revewed terally ad by customer, ad cludes: Fuctos to be performed (p ) Stadards/ Procedures/ models to be used Schedule Documets/ Reports Orgazato, resposbltes, terfaces wth your compay ad wth customer, suppler 4

3 Mataablty the System Lfe-Cycle The Systems Egeerg Pla has a major secto devoted to tegrato of the egeerg specaltes to the desg process. The SE s resposble for assurg adequate partcpato, fluece, vsblty, etc. s grated to mataablty, ad others. 5 Qualtatve Mataablty Measures Especally mportat early desg whe lmted data exst Examples: Skll level reducto Ease of access Smplcty of task Idetfcato, markgs, codg Stadardzato Safety durg mateace Clearly wrtte, easy to follow structos Ease of fault solato 6 3

4 Qualtatve Mataablty Measures(cot) Some ways these get corporated to desg Maagemet emphass Expereced mateace chefs o each team Checklsts (see hadout) Degree to whch quattatve measures/ models are sestve to these 7 Quattatve Measures of Mataablty Mateace Elapsed-Tme Factors Mea Correctve Mateace Tme (MTTR) Mea Prevetatve Mateace Tme M ct M pt Meda Correctve Mateace Tme M ~ ct Meda Prevetatve Mateace Tme M ~ pt Mea Actve Mateace Tme M 8 4

5 Quattatve Measures of Mataablty Mateace Labor-Hour Factors Mateace labor-hours per operatg cycle Mateace labor-hours per cycle Mateace labor-hours per moth Mateace labor-hours per mateace acto Mateace Frequecy Factors Meatme betwee mateace MTBM Uscheduled (correctve) ad Scheduled ( prevetve) Meatme betwee replacemet MTBR 9 Mataablty Fucto Defto: Let T Repar Tme Radom Varable. The Mataablty Fucto M(t) s defed by M(t) P(T t) Example: Suppose T s expoetal wth repar rate λ. Mea tme to repar: MTTR λ M ( t) λ t e e t MTTR 0 5

6 Other Dstrbutos Used Normal - Smple, remove ad plug. Logormal - complex repar; multplcatve degradato model. Webull - Varety of stuatos most versatle. A geeralzato of the expoetal, whch has costat falure rate. Ofte used for worst lk or frst of may flaws to produce a falure. Propertes of Webull Dstrbuto b Iveted 95; tred to create h( t) at, t 0 β Set, H t λ t, β cotrols shape of h(t), The, () ( ) dh ( t) h( t) β λ dt β ( λ t) Ht Ft e e e β s expoetal t β θ β ( λ t) (), θ λ Adjo a thrd shft parameter δ 0, whch shfts left edpot of rage of dstrbuto:[δj+ ]. Requre θ>δ 0 6

7 Propertes of Webull Dstrbuto(cot) Fal Result β( t δ) ht () θ δ ( ) ( β ) β β t δ θ δ Ft () e R(t) e - β t-δ θ-δ MTTR or MTBF δ + ( θ δ) Γ( + ) β t y Γ() t y e dy M θ( l ) β + δ 0 3 How β Cotrols Shape of h(t) For Webull Dstrbuto Ths s a hadout 4 7

8 Webull Closure Property Recall for expoetal-lfe compoets wth rates λ, λ,..., λ ad a seres system λ λ If a seres system has: depedet parts, each Webull wth the same β θ, θ,..., θ λ λ λ The respectve characterstc lves s 5 Webull Closure Property(cot) The System Lfetme Dstrbuto s Webull wth shape parameter β ad, β β β β λs λ θs λ 6 8

9 Example 5 Hoses a Ege Coolg System have β.8, Respectve θ 95, θ 0, θ330, θ430, θ550 moths, the O s R 48.6(l) moths MTBF 48.6Γ moths 7 Propertes of Logormal Dstrbuto Defto - X s logormal wth rage space (0, + ), parameters µ ad σ IFF Y l X, s ormal wth parameters µ ad σ Mode of X at Meda of X at Mea of X at Varato of X s x e x µ σ y x e u y µ e y µ y + σ y y y y ( ) µ + σ σ σ x e e 8 9

10 Propertes of Logormal Dstrbuto (cot) Propertes. If X logormal µ y, σ ( y), X logormal( µ y, σy) ad X, X depedet; the W X *. If Xj, j,, are logormal ad depedet, µ y, σ y the the geometrc mea s logormal µ σ y y, x j X s logormal wth ( µ + µ σ + σ ) j y y, ( ) y y 9 Example pp Assumes ormal Takes X, s to be µ,σ. Is ths ok? What s wrog wth equato 4.? 0 0

11 Example Suppose Compoets seres, each expoetal wth λi falure rate for compoet I; Let Mct tme to repar system whe th compoet fals. The M ct MTTR for system s estmated by (4.) XM ct Repar tme/ut tme Mct System falure/ut tme Repar tme per falure If there are of type the system, the use: λ M ct λ M ct λ Example (cot) 3 3. λ *0 hrs M (hr) Repar Tme per 0 hr Assembles Compoets λ M MTTR hours 6 ct ct

12 Mea Prevetatve Mateace Tme Icludes Ispecto Servcg, Cleag Replacemets Calbrato Overhaul M pt ( fpt )( M ( fpt ) pt) Where fpt frequecy of the th prevetve mateace acto Mpt elapsed tme for th prevetve mateace acto 3 Meda (Actve) Correctve Mateace Tme For sample of sze o Mct for oe compoet l M ct Mct e For m classes of correctve mateace o system, wth respectve falure rates λ Note: It s possble to do the m computatos usg log0 λ l Mct M ct e m λ x versus 0 versus e x 4

13 Meda (Actve) Prevetatve Mateace Tme M pt e ( fpt )( l M pt ) fpt 5 Mea (Actve) Mateace Tme M λm ct + λ + fptm fpt pt λ Overall Correctve Mateace Rate λ fpt Prevetve Mateace Rate fpt 6 3

14 Maxmum(Actve) Correctve Mateace Tme M max e l M ct + Zασ y Where; ( l M ) ct σ y S y [ ( l Mct )] 7 Other Mateace Elapsed-Tme Measures Logstcs delay tme (LDT), watg for faclty, equpmet Spare part Tool Trasport Admstratve delay tme (ADT) Orgazatoal (people, paper, prortes, etc) No-physcal 8 4

15 Other Mateace Elapsed-Tme Measures(cot) Mateace Dowtme (MDT) MDT M +LDT+ADT MDT λm + λldt + λ3adt λ + λ + λ 3 where λ frequecy of respectve acto/ delay 9 Mateace Labor Hour Factors Together wth skll levels ad ther day rates, these factors determe labor cost of mateace ad umber each skll level per mateace faclty MLH/OH MLH/cycle MLH/moth MLH/MA 30 5

16 Mateace Labor Hour Factors(cot) Ay of above ca be expressed as average over all subsystems Ca apply to correctve, prevetve, pr total actve Ca apply to total mateace dowtme Coceptually, wat to select skll levels ad mateace dffculty to mmze mateace costs 3 Mateace Frequecy Factors Meatme Betwee Mateace (MTBM) MTBM + MTBM u MTBM s MTBMu s approxmately MTBF, the relablty factor, although geeral MTBF MTBMu 3 6

17 Mateace Frequecy Factors(cot) Meatme Betwee Replacemet (MTBR) A part, compoet, or a subsystem must be replaced by a spare part from vetory. Major lk betwee mateace actos ad logstcs support system 33 7