Logistiikka 35A00310 Tuotantotalouden perusteet HARJOITUS- PAKETTI C (8 pistettä) TUTA 18
Luento 10.Laatujohtaminen Cranston Nissan 2 pistettä 1
Q&A 3-kohdassa haetaan tunnilla esiteltyä Ishikawan syy-seuraus -diagrammia. Helpoimmalla pääsee, kun ajattelee seurauksen "korjaustapahtumaan tyytymätön asiakas" ja miettii siihen mahdollisia syitä ja syiden syitä jne.. Kalanruotoonhan ei ole tarkoitus listatta suosituksia / miten ongelma korjataan, vaan ainoastaan "hypoteeseja" joita sitten lähdetään selvittämään (eli onko ollut vai ei) 2
Luento 11.Tilastollinen laadunvalvonta Scion Capital Scion Capital is interested in monitoring the performance of the mortgage process. Fifteen samples of six completed transactions each were taken during a period when the process was believed to be in control. The times to complete the transaction were measured. The means and ranges of the mortgage process transaction times, measured in days, are as follows. Sample Mean Range 1 15 12 2 13 13 3 14 6 4 10 9 5 14 5 6 12 12 7 11 8 8 15 6 9 16 15 10 12 4 11 11 8 12 13 14 13 15 7 14 10 12 15 14 4 Subsequently, the samples of size six were taken from the process every week for the next 10 weeks. The times were measured and the following results obtained. Sample Mean Range 16 14 8 17 16 5 18 15 11 19 19 4 20 16 12 21 12 14 22 13 10 23 15 6 24 20 11 25 11 8 a. Construct the control charts for the mean and the range, using the original 15 samples. Were these samples sufficient for developing the control chart? Explain your answer. b. On the control charts, plot the sample values subsequently obtained and comment on whether the process is in control. 3
Dolce Soap Dolce Soap is conducting a study to assess the capability of its 250-gram bar soap production line. As a part of study, 20 samples of 4 were collected by the quality assurance group and the observation were recorded (table below). A critical quality measure is the weight of the soap bars after stamping. The upper and lower tolerance limits are 245 and 255 grams, respectively. Sample Obs.1 Obs.2 Obs.3 Obs.4 1 253,30 248,40 249,70 247,00 2 245,70 249,10 248,40 249,60 3 252,90 250,90 249,50 247,50 4 247,80 251,40 244,90 247,50 5 251,00 249,90 249,20 251,90 6 252,40 249,60 252,20 249,80 7 249,40 247,50 246,90 250,60 8 248,90 250,00 246,50 244,60 9 249,00 248,60 250,20 246,20 10 249,10 250,50 249,50 250,90 11 246,80 248,60 246,00 253,80 12 246,90 247,70 246,50 249,30 13 252,20 250,70 250,70 248,80 14 249,20 248,20 249,30 247,70 15 249,40 247,20 250,40 248,60 16 254,10 250,60 252,10 248,00 17 250,40 249,40 250,60 249,20 18 245,80 249,80 246,00 251,20 19 248,30 249,50 251,40 247,60 20 249,10 248,20 250,20 248,50 a. Draw the control charts for the data obtained and verify that the process is in statistical control b. Calculate Cpk and Cp values for the current process and comment its capability based on three-sigma quality standard firm is seeking c. If production would be able to improve the process standard deviation to 1,50 grams, how would your comments change (include re-calculate Cpk and Cp values to your answer) d. What kind of changes would be needed to a current process if customers wanted four-sigma quality Q&A tehtävä mekaaninen ratkaisu oikeastaan vaatii ymmärryksen kontrollista ja kyvykkyydestä (UCL ja UTL täysin eri asioita jne.) d-kohdassa vaaditaan hieman kaavan pyörittelyä, eli ideana laskea 1) mikä keskihajonnan pitäisi maksimissaan olla jotta nykyisellä prosessin keskiarvolla päästään haluttuun laatutasoon 2) mikä keskihajonnan pitäisi maksimissaan olla jotta keskittämällä prosessi päästään haluttuun laatutasoon 4
Chastain Park Memorial Hospital A hospital administrator of the Chastain Park Memorial Hospital is concerned with the absenteeism among nurses. The issue has been raised by doctors, who feel they often have to perform work normally done by nurses. To get the facts, absenteeism data were gathered for the last two weeks, which is considered a representative period for future conditions. After taking random samples of 120 personnel files each day, the following data were produced: Day Absent Mon 5 Tue 7 Wed 2 Thu 9 Fri 12 Sat 2 Sun 3 Mon 7 Tue 2 Wed 4 Thu 13 Fri 11 Sat 2 Sun 2 Since administrator s assessment of absenteeism is likely to come under careful scrutiny, she would like a type I error of only 1 percent. She wants to be sure to identify any instances of unusual absences. a. Determine control limits for analyzing absenteeism b. Draw a control chart and comment Chastain Park s nurse process Q&A jos ei erityisesti mainita, niin ominaisuuksien kontrollilaskuissa käytetään yleensä z:n arvoa 3 (99,74% luottamus ). Tässä tehtävässä halutaan ottaa kantaa vaihtelun satunnaisuuteen hieman alhaisemmalla luottamuksella (99%) eli z-arvo pitää määrittää normaalijakauman avulla (2-laitainen jakauma) toisin kuin x-kartat, ominaisuuksien p- ja c-kartat eivät välttämättä ole symmetrisiä. "Virheiden" osuus/määrä ei voi olla yli maksimin/negatiivinen eli silloin "raja" vain pyöristetään maksimiin tai nollaan. 5
Gunn Fashions Gunn Fashions makes upscale dress shirts. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Tim took one shirt per hour from production line to closer inspection, with the following results: Shirt Flaws 1 4 2 7 3 1 4 2 5 6 6 2 7 4 8 6 9 3 10 5 a. Assuming that 10 observations are adequate for these purposes, determine the three-sigma control limits for the flaws per shirt b. Draw a control chart and comment Gunn s quality c. Suppose that the next shirt has 9 flaws. What can you say about the process now? 6
Luento 12&13.Varastointi Mountain Man Mountain Man, a sporting goods store, is trying to figure out continuous review order policy for infuser water bottle. The bottle has following characteristics: Length of a year 52 weeks Demand per week (d) 50 units per week Supply (ordering/setup) cost (S) 77 per order Holding cost (H) 10 per unit per year Lead-time (L) 3 weeks Standard deviation of weekly demand (σ t ) 6 units Cycle-service level (z) 91 % a. What is the EOQ for the bottle? b. What is the desired safety stock? c. What is the reorder point? d. What is the total inventory costs for the bottle for Mountain Man? e. What are the cost implications if the current policy for bottle is Q = 350 and R = 190? Q&A määriteltäessä varmuusvaraston kokoa palvelutasolla tarkoitetaan todennäköisyyttä, että tilattaessa jäljellä oleva määrä riittää tilaus-toimitusviiveen aikaiseen kysyntään. Laskemisessa tarvittava z-arvo pohjautuu 1- laitaiseen normaalijakaumaan e-kohdassa kannattaa muistaa huomioida tilauspolitiikan vaikutus varmuusvaraston kokoon (ja sen aiheuttamiin säilytyskustannuksiin) 7
Couch Boy Couch Boy, an e-sports store, is trying to figure out periodic review order policy for infuser water bottle. The bottle has following characteristics: Length of a year 52 weeks Demand per week (d) 50 units per week Supply (ordering/setup) cost (S) 77 per order Holding cost (H) 10 per unit per year Lead-time (L) 3 weeks Standard deviation of weekly demand (σ t ) 6 units Cycle-service level (z) 91 % a. What value of P gives the same approximate number of orders per year as the EOQ? b. What is the desired safety stock? c. What is the order-up-to / target inventory level? d. What is the total inventory costs for the bottle for Couch Boy? Q&A Mountain Manin ja Couch Boyn lähtötiedot ovat samat, joten kannattaa verrata ovatko lasketut tulokset keskenään linjassa 8
Xena s Swords Xena s Swords produces specialty sword for larping enthusiasts. The annual demand for a particular type of sword is 11250 units. The demand is uniform over the 250 working days in a year. Xena produces this type of sword in lots and, on average, can produce 60 swords a day. The cost to set up a production lot is $2000, and the annual holding cost is $80 per sword. Demand per year 11250 swords Number of working days 250 days Production rate (p) 60 swords per day Setup cost (S) 2000 per lot Holding cost (H) 80 per sword a. What is the economic production lot size (ELS) for this sword? b. How much is the total annual holding and setup cost? c. What is the TBO, or cycle length, for the ELS? d. What is the production time per lot? e. How much is the maximum cycle inventory? f. Draw a graph showing how inventory volumes develop over time (include the key figures calculated in c, d and e to the graph) Q&A laskua ratkaistaessa huomioitava, että ELS:n kaava eroaa hieman EOQ:sta kuvan voi piirtää myös käsin, mutta onnistuu melko helposti Excelin scatter/xy-muodossa 9
University Bookstore University Bookstore at a prestigious private university buys mechanical pencils from a wholesaler. The wholesaler offers discounts for a large orders according to the following price schedule: Order Quantity Price per Unit 0 to 200 $ 4,00 201 to 2000 $ 3,50 2001 or more $ 3,25 The bookstore expects an annual demand of 2500 units. It costs $10 to place an order, and the annual cost of holding a unit in stock is 30 percent of the unit s price. Determine the best order quantity. Q&A suositus halvimmaksi tilausvolyymiksi perustuu luonnollisesti kokonaiskustannuksiin (säilytys+tilaaminen+tuotteista maksettu hinta) 10
Parts Emporium 2 pistettä 11
Q&A numeropuolella hyvässä vastauksessa on kummankin nimikkeen osalta nykyisen ja suositellun systeemin keskeiset varastonhallintaluvut (tyyliin tilausmäärä ja tilauspiste (sis. varmuusvarasto)) ja kustannuserien suuruus (säilytys+tilaaminen+varmuusvarasto+puute). Erinomaisessa vastauksessa löytyy myös luvut sekä Q- että P-systeemille. tuotteiden katteiden osalta kannattaa huomata (kun lasketaan omakustannushintoja ym.), että kateprosentit on ilmoitettu anglosaksisesti eli prosenttina myyntihinnasta (kun taas meillä usein ilmoitetaan päinvastoin eli prosenttia omakustanushinnan päälle) laskemisen lisäksi kannattaa suosituksessa pohtia eri systeemien sopivuutta nimikkeille ja case-yritykselle (esim. kysynnän määrän/rakenteen, implementoinnin ym. kannalta). 12