Consolidated Cases
In Partial Fulfilment of the Requirements in MGT 428 - Production and Operations Management MWF 6:55PM – 7:55PM
Presented to: Mr. Antonio A. Emberda
Presented by: Caldoza, Tyron Troy Dadia, Hanna Diaz, Eloise Johanne Fernandez, Jasper Ferdie Go, Jacymae Kaira Pacomo, Vincent Austin Punzalan, Tamy Anthonette Surriga, Gaille Anne Group II
Bachelor of Science in Accountancy 2017
CASE: LANDMARK AUTO PARTS, INC.
1. What type of process flow structure is Landmark Auto Parts using?
The process flow structure of Landmark Auto parts is an assembly line layout. The processes are arranged progressively pr ogressively as the u-bolts are made. In this layout we can also calculate how much time it will take to complete a process and it is demonstrated by a straight line production. The u-bolts undergo every process or station which are linked to the next process. It follows a predetermined fixed sequence of steps that needs to be followed to achieve efficiency in production and to arrive at a specific production rate. In this case, 7hrs of effective production time. 2. Diagram the process in a manner similar to Exhibit 7.7
3. Analyze the current capacity of the process. Check if the capacity is equal to 18000 unit/day or not.
The capacity is not equal to 18,000 units per day. The capacity, however, is equal to 691.67 or 692 units per day or approximately 18,000 units per month using the the 25.7142 working days in a month. (Refer to the table below). The one with the least capacity to produce shall be the capacity of the entire process.
4. What is the effect of set up times on the production rate of each process?
The set up times especially heating, heat treatment and galvanizing takes longer than expected time for set up thus increasing the processing time. Out of all the processes heating, heat treatment and galvanizing take 5 minutes, 30 minutes and 15 minutes respectively to set up. Taking all these into account would result to a stall in production because it leaves the other processes unable to continue as it stacks up a large queue. The inefficiency slows down production as many resources such as time, people and machines are being paid to wait. Thus, the amount of time that was used for setting up could have been used for further manufacturing of the U bolts so that the company could have been more efficient with its operations.
5. What recommendation would you make for a short- term solution to landmark’s problem?
For Landmark to increase its capacity from 18t units to 30t per month, some of the short-term solutions we can think of are the following: 1. Extend the working days and make the employees work overtime. 2. Outsource the work from outside suppliers or manufacturers. 3. If possible, overwork machineries to produce more than theoretical capacity. 4. Purchase better equipments that would produce more units of products in order to reduce human error as a result of manual labor.
6. What long term recommendation would you make?
In a long-term perspective, the company should pursue or invest on new methods in manufacturing their products, maybe in a more capital-intensive production or a combination of capital and labor intensive production. As provided in Exhibit 7.8, the production of U-Bolt relies more on the use of the labor workforce than on the use of machinery. Although the use of labor intensive production generally provides better quality, it can be shown that relying more on machinery is more advantageous. Aside from the fact that there is greater speed in producing products when the company relies more on the use of machinery, it also provides more accuracy and consistency in the manufacture of products and eliminates the errors that are results of using labor. This would effectively reduce the processing time in every step of production and the number of inspections that are made on the production process would be minimized. As a result of these, the company would be able to produce more units of product in the effective production hours. Also, while the use of capital intensive production can be very costly at first, it is relatively less expensive in the long-run when compared to labor intensive production.
CASE: TOSHIBA’S NOTEBOOK COMPUTER ASSEMBLY LINE
1. What is the daily capacity of the assembly line designed by the engineers. Assume that the assembly line has a computer at every position when it is started at the beginning of the day.
The assembly line would be designed assuming that one notebook can be assembled in 2 minutes by 6 workers. Daily capacity would 225 units having a production time of 450 minutes per day. Assuming that one of the six workstations a computer is position in the beginning of the day. Assembly Line Position 1
Tasks Assemble Cover(75)
Workstation Labor Number
Time
1
75
2
85
3
97
4
105
6
120
Install LCD (61) 2
Prepare base Assembly(24) Install main Printed circuit Board (36)
3
Install CPU (22) Install Back up Batteries and test (39) Install Accupoint Pointing Device Wrist Rest (32)
4
Install Speaker and microphone (44) Install Auxiliary Printed Circuit Board (29) Prepare and install
5
keyboard (26) Prepare and Install DVD and HDD (52)
Install battery pack (7) Insert memory card (5) Start Software load (11) Software Load (19) 6
Software Load
7
Software Load
8
Software Load Test Video Display (60)
9
Test Keyboard (60)
10
Empty
11
Empty
12
Empty
6
120
2. When it is running at maximum capacity, what is the efficiency of the line relative to its use of labor. Assuming supporter is not included in efficiency calculations.
Initial production of Toshiba 150 units per day, increasing to 250 units per day and would reach 300 units per day Number of units
Labor Time
Cycle time
Workstations
Efficiency
250
602 sec
108
6
92.9%
300
602 sec
90
6
111.48%
269
602 sec
100.33
6
100%
The table summarizes the number of units produced per day and their respective efficiency. As we can see, the companies goal of reaching 250 units will require a 92.9% efficiency which is leaves little room for bottlenecks and idle time, The second plan is to produce 300 units it will require 111.48% efficiency which is unattainable by the plant because it assumes that all bottlenecks and idle time are totally eliminated. Based on these data, if the plant runs at 100% efficiency it can produce 269 units which is less than the desired production units.
3. How the line should be redesigned to operate at the initial production of 250 units per day, assuming no overtime will be used? What is the efficiency of the design?
The line has a bottleneck on workstation 4 and 5. Workstation 5 creates slack of 4 seconds per unit. A possible solution for this bottleneck is to assign highly skilled workers to workstation 4 to push assembly. If the plant manufactures 250 units it will create a slack time of 16.67 minutes which could have made 9.3 units already and if production was at 300 units there would be 20 minutes of slack time and could have created 13.3 units already. These highlight that workstation 4 results in major cost due to high idle time. Number of units
Labor Time
Cycle time
Workstations
Efficiency
250
602 sec
108
6
92.9%
300
602 sec
90
6
111.48%
269
602 sec
100.33
6
100%
4. What about running the line at 300 units per day? If overtime were used with the engineer’s initial design, how much time would the line need to be run each day?
If the engineers run the line at 300 units assuming that it uses 100% capacity while maintaining the same labor time per workstation. The factory will have to run for 8.36 hours. This assumption of working at 100% efficiency is close to unrealistic because it assumes no idle time for assembly time which is not practical. The plan that the plant can work on 300 units per day is only a theoretical capacity.
5. Can the assembly line produce 300 units per day without using overtime?
The assembly line cannot produce 300 units without any overtime the regular production time is 7.5 hours or 450 minutes. In order to produce 300 units, the plant needs to run for 8.36 hours or 501.67 hours at 100% efficiency.
6. What other issues might Toshihiro consider when bringing the new assembly line up to speed?
The possible issues that might be considered when bringing the new assembly line up to speed. First is the cost of labor, to release the bottleneck in workstations 4 and 5 highly skilled workers must be hired on both stations. This is the most practical solution that the company can use because changing the assembly line would require a huge overhaul that could incur higher cost and have an adverse effect on the company. Recommendation:
The assembly line should not be changed, therefore hire more skilled workers in workstation 4
Assign a supporter on workstation 4
Assign two workers on both sides of the conveyor belt in workstation 4
Split workstation 4 into 2 stations since there are free spaces in the assembly area.
CASE: A GP SURGERY IN THE UK: AN EXERCISE IN TRANSLATING CUSTOMER REQUIREMENTS INTO PROCESS DESIGN REQUIREMENTS
1. Make a list of GP practice attributes that are important to you as a customer.
a. Caring and understanding of the patient’s well -being b. Committed to provide high quality healthcare c. Conscious of their own limitations and aware of the need to be accessible to patients immediately d. Practices ethical standards required in the course of their practice e. Willing to contribute to the common good through teaching, contributing to medical advances and the like. f. GP is courteous and respectful and patient g. Skilled in making diagnosis on the patient and the corresponding treatment h. Able to examine the patient’s physical and mental state i. Skilled in communication and in the process of consultation j.
Mindful of the patient’s illness prevention and maintenance of health
k. Keeps updated medical records of the patient for clearer health background l. Quick in responding in times of emergency m. Gives proper post-operative care and discipline n. Participates and organizes effective clinical audit for the assessment of practice o. Keen to contribute in a team or a team player that is conscious to the responsibilities of each individual participant p. Knowledgeable in allocating and using resources effectively 2. Combine your list with the lists of a few other class members and categorize under a series of major headings.
Character
Competence
Caring and understanding of
Skilled in making
the patient’s well -being
diagnosis on the patient
Committed to provide high
and the corresponding
quality healthcare
treatment
Organizational Contribution Participates and organizes effective clinical audit for the assessment of practice
Conscious of their own
Able to examine the
Keen to contribute in a team
limitations and aware of the
patient’s physical and
or a team player that is
need to be accessible to
mental state
conscious to the
patients immediately
Skilled in communication
responsibilities of each
Practices ethical standards
and in the process of
individual participant
required in the course of their
consultation
Knowledgeable in allocating
practice
Mindful of the patient’s
and using resources
Willing to contribute to the
illness prevention and
effectively
common good through
maintenance of health
teaching, contributing to
Keeps updated medical
medical advances and the like. records of the patient for GP is courteous and respectful clearer health background and patient
Quick in responding in times of emergency Gives proper postoperative care and discipline
3. Make a list of GP practice process design requirements. Associate with each requirement a measure that would ensure that the process meets the requirement.
i.
Resources like equipment, supplies. These are required in order to properly accommodate present and incoming patients. These resources must be sufficient enough to provide the medical needs of a customer. Moreover, the readiness of these resources is important to immediately respond to these needs, especially during emergency times.
ii.
Medical staff. The medical staff must be competent and skilled enough to provide a high-quality health care for the customers. The staff must know the efficient and effective way of doing the things they should do. The members of the staff must also be ethical during their practice.
iii.
Professional services of a doctor. He or she must provide professional
diagnoses, prescriptions and recommendation in correspondence to the patient's situation. These must be recorded properly to minimize or avoid mistakes. iv.
Detailed and right procedure. The medical staff follows a procedure when performing its tasks. Thus, it is important to have the applicable pro cedure that corresponds to a specific situation. It must be detailed and right in accordance of what must be performed.
v.
Billing management. A billing section that does its task correctly in the facility is required for a patient to be discharged.
4. Design a process that meets your requirements. Describe it by using a flowchart like that shown in Exhibit 9.5.
Stage 1: Preliminary Activities
Medical staff and equipment must be ready always.
There must be sufficient resources to accommodate the incoming patient (sufficient staff and supplies)
Stage 2: Problem Diagnosis
The doctor will conduct a diagnosis on the condition of the patient. The diagnosis must be clearly placed in the records to avoid any mistakes.
After diagnosis, the doctor will give his recommendation. If it is serious, the patient must be admitted and further test must be conducted. If not serious, the patient may be release only upon the doctor’s advice.
Perform all necessary test for the admission of the patient if the illness is serious.
Stage 3: Perform Work
The medical staff must have a detailed procedure on what must be performed.
Experienced medical staff must handle critical patients and those inexperienced must act as support.
Medical staff executes the applicable procedure and discharge waits.
Stage 4: Settlement of Bills
The patient pays the medical bill including the doctor’s PF and other hospital
charges and patient is discharged after payment of bills and order of the doctor.
CASE: TACO BELLS RESTAURANT
1. Draw diagram of the process using format in Exhibit 9.5
Customer Arrives
Service Champs greets customer
Service Champs takes customer
Service Champs tells customer
Customer pulls ups and waits
Customer leaves with order
Customer pays
Give customer food
Line of Visibility
Service Champ prepares for arrival of customer
Service Champ enters order into s stem
Service Champ determines cost form s stem Food Champs begin making food
Food made
Order ready
Food wrapped
The above outline demoes the process by using a service blueprint drawing. The line in found in the middle of the outline represents the line of visibility and the items above
such line are things that the customer can see and the items below are the scenes activities. 2. Consider a base case where a customer arrives every 40 seconds and the customer service champion can handle 120 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour. How long should it take to be served by the restaurant (from the time a customer enters the kiosk queue until her food is delivered)? Use queuing model to estimate this.
The following data were given: ∙ Every 40 seconds a customer arrive ∙ The customer service champion can handle 120 customers per hour ∙ There are two Food Champions, each capable of handling 100 orders per hour
The queuing model below shows the calculations to answer the question. ʎ= Arrival Rate
µ= Service Rate µS= Service Champions= 120 customers per hour µF= Food Champions= (100*2) = 200 customers per hour
Average total time spent by customer in system Calculation using model 1: Ls= Average number in system Ws=Average total time in system (including time to be served)
Using Model 3 to calculate total time:
The calculation shows that it should take 152.8 seconds to be served by the restaurant. 3. On average, how busy are the customer service champions and the two food champions? ρ=Ratio of total arrival rate to service rate for a single server
The percentages above suggest that the Customer Service Champion is busier than the Food Champion given that there are two Food Champions and only one Customer Service Champion. 4. On average, how many cars do you expect to have in the drive-thru line? (Include those waiting to place orders and those waiting for food.)
The equation shown below is used to calculate the number of expected cars to have in the drive-thru line: Lq=Average number waiting in line
5. If the restaurant runs a sale and the customer rate arrival increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive-thru line?
Average total time spent by customer in system Calculation using model 1: Ls= Average number in system Ws=Average total time in system (including time to be served)
Using Model 3 to calculate total time:
Taco Bell will encounter a great difference in the aggregate time since it is now demonstrated with a 20% sale, that the average number of customers would increment from 3.82 to 10.17 clients; this is a 2.66 to 1 proportion. With this increment, the expected total time tends to increase as well, showing an increment from 152.8 seconds to 339 seconds, more than 3 minutes than before. Ascertaining the average number of cars in the drive through with sale increment:
As time increases, so as the increase of average customers waiting in line. This number increased from 2.62 customers wait to 8.73 customers waiting. This is over three times as much as before. 6. Currently, relatively few customers(less than ½%) order the crunchwrap supreme. What would happen if the restaurant ran the sale, demand jumped on the crunchwrap supreme and 30% of the orders were for this item? Take a quantitative approach to answering this question. Assume that the customer service champion never helps the food champions and that these two processes remain independent.
(Assume that the Customer Service Champion never helps the Food Champions ad that these two processes remain independent). It was given in the reading of the case that a Crunchwrap supreme takes twice as long as anything else to make. If 30% of sales were Crunchwrap Supremes’ you can expect the average wait time to increase as well. Assuming that with the 20% sale, the same amount of customers came to Taco Bell as before (108 customers per hour). Knowing that 30% of sales are going to be Crunchwrap Supremes’, this means that 70% of orders will go through the Food Champions and 30%
of orders will go through the Service Champions. The calculations below show the increase in average wait time due to the Crunchwrap Supreme taking longer to make. Under the assumption that the Customer Service Champion never helps the Food Champions advertisement and that these two processes remain independent, it is now expected the average wait time will increase if 30% of sales were Crunchwrap Supremes’.
Assuming that with the 20% sale, the same amount of customers came to Taco Bell as before (108 customers per hour). Knowing that 30% of sales are going to be Crunchwrap Supremes’, this means that 70% of orders will go through the Food Champions and 30%
of orders will go through the Service Champions. The calculations below show the
increment in average wait time given that a Crunchwrap Supreme takes twice as long as anything else to make.
but it was mentioned that it takes twice as long as any normal item therefore:
7. For the type of analysis done in this case, what are the key assumptions? What would be the impact on our analysis if these assumptions were not true?
Subsequent to taking a look at the counts that these models have given, it can concluded that there are a few different assumptions that can be made. The first assumption is that problems cannot always be solved by applying only one step of the model or even by applying every one of the three steps. In determining what model to use, it would be helpful to depend on the situation and type of problem. With regards to past, present, and future data, these models can be very valuable and useful in a way that it guide companies in achieving great success . It is true that these models cannot be easily understood, however, they are not impossible to apply and it can help teach a good lesson. One major assumption that the given calculations depicts is a large effect that a 20% sale would have. There would be a drastic increase in the number of customers. In the event that Taco Bell would not do anything about the quantity of employees or the procedure they were running they could have enormous delays in turnaround time. On the off chance that these suspicions were not true and Taco Bell acted upon them as they were, hiring more employees or changing the procedure, this
could have major monetary effect on them. Organizations must guarantee that the assumptions made by the models are exact and any moves are taken with utmost caution. 8. Could this type of analysis be used for other service-type businesses? Give examples to support your answer.
Yes. One illustration that could prove that this type of analysis can be used for other service-type businesses would be a store in a nearby shopping center. In a shopping mall, the service that can be seen by the general population is the administration of offering garments and helping clients locate the correct sizes and styles. While there are also some activities that would not be seen by the clients, for example, stocking racks and collapsing garments. Other things and circumstances could be computed like the time of clients waiting in line, the effect of sales, and the total time the customer was in the store. Thus proving that this type of analysis be used in different circumstances.
CASE: GOLDEN JADE CASINO
1. Draw a diagram of the drop process. How long should it take to empty 300 silver dollar slot machines?
Security Officer and Slot Drop Team
15 mins
Slot Machine
Cashier’s Cage
Leader
Return Key
Accounting Staff
Hard Count Room
END
Cart
1 0 m i n s
BUCKET
2. Draw a diagram of the hard count process. How long should this process take to complete for 300 such MOP$10 slot machines? Assume that each slot machine has an average of 750 MOP$10 coins when it emptied.
Assuming that there are 750 Coins per machine. The number of rolls 300 machines can take 750 (Coins/Machine) / 25 (Per Roll) = 30 Rolls/Bucket 30 Rolls*300 Machines = 9000 Rolls Time it takes to weigh and record each bunker 7 Minutes * 300 Buckets = 2100 minutes Time it takes to wrap each roll 9000 Rolls /10 Roll/Minute = 900 minutes 9000 Rolls / 40 (Rolls/Can) = 225 cans 225 Can * 5 minutes = 1125 minutes In order to calculate the time to process 300 silver dollar slot machines, the following are added together, 10 minutes from calibration, 2100 minutes weigh and rec ord each bucker, 900 minutes to wrap each roll, 1125 Minutes to place rolls into cans, 5 minutes run summary and 450 minutes manual verification of can counts. The total number would take 4590 minutes or approximately 76.5 Hours. Thus, it would take 76.5 hours to complete for 300 silver dollar slot machines assuming that each slot machine has an average of 750 MOP$10 coins when emptied.
3. The casino is considering the purchase of a second coin-wrapping machine. What impact would this have on the hard count process? Is this the most desirable machine to purchase?
By Purchasing an additional wrapping machine would save 450 minutes in the process.
750 (Coins/Machine) / 25 (Per Roll) = 30 Rolls/Bucket
30 Rolls * 300 Machines = 9000 Rolls
7 Minutes * 300 Buckets = 2100 Minutes
9000 Rolls /20 Roll/Minute = 450 Minutes
9000 Rolls / 40 (Rolls/Can) = 225 Cans
225 Can * 5 Minutes = 1125 Minutes
Time to Process 300 Silver Dollar Slot Machines = (Time to Calibrate Scale) + (Weigh and Record Each Bucket) + (Time to Wrap Each Roll) + (Time to Place Rolls into Cans) + (Run Summary) + (Manually Verify Can Counts) = 10 Minutes + 2100 Minutes + 450 Minutes + 1125 Minutes + 5 Minutes + 450 Minutes = 4140 Minutes = 69 Hours 76.5 Hours - 69 Hours = 7.5 Hours saved by the adding one additional wrapper machine. Looking at what takes the most time in the process: Weighing. If the casino purchased an additional weighing machine: 750 (Coins/Machine) / 25 (Per Roll) = 30 Rolls/Bucket 30 Rolls * 300 Machines = 9000 Rolls 3.5 Minutes * 300 Buckets = 1050 Minutes 9000 Rolls /20 Roll/Minute = 450 Minutes 9000 Rolls / 40 Rolls/Can = 225 Cans = 10 Minutes + 1050 Minutes + 900 Minutes + 1125 Minutes + 5 Minutes + 450 Minutes = 3540 Minutes = 59 Hours 76.5 Hours-59 Hours = 17.5 Hours saved by the adding one additional weighing machine
It would be, therefore a larger savings to invest in a new weigh machine instead of a new wrapper machine.
4. What would be the impact of purchasing electronic slot machines that do not use coins?
When we purchase electronic machines that do not use coins, it will impact the times and labors that are needed to conduct the drop and hard count process in large amounts. It would mean a significant reduction from theft of coins and chances of a robbery. It enables the casino management to easily monitor gamblers as they bid on a constant amount that they will not be allowed to change during gambling. Additionally, it enables gamblers to place their bids electronically which makes it more convenient for them as they do not have to bring coins wherever they go. This process also allows electronic slot machines will automatically count all customers and the total coins used in every circle. The information is then passed to the cashier and accountant. However, this becomes disadvantageous because electronic slot machines are expensive and there is a higher risk that the casino will lose money.
CASE: QUALITY MANAGEMENT – TOYOTA
1. Develop a diagram that summarizes what Toyota has done in response to its recent quality recall problems. Focus on the changes by functional area (i.e., Management, Product Design, Quality, and Manufacturing) Functional Area Manufacturing
Management
Quality
Changes Made
Operation
Factory opened in
Has the responsibility to get it right from the very
Northern Japan
beginning of quality automobile.
Managing Director
Compiles reports complaint from internet and
Quality Information
safety issues. They also gather repair reports
Center (TAQIC)
from Toyota dealers globally.
database Rapid-response teams 1,000 engineers assigned
Design
safety.
Toyota Advances
Global computer
Product
Designated to supervise issues relating to
Swift Market Analysis Response Teams (SMART)
Track vehicle repairs and out reporting times Investigates the causes of the accidents reported by complaints. Adds at least 4 weeks to new-car development schedules, manages spot-check quality and set up the troubleshooting team. Assigned for tracking down what company insiders call “S -Ketten” or safety.
2. Evaluate the statement in the case made by Toru Sakuragi that”...Toyota has been
caught between a need to cut cost to overcome the strong yen and the need to improve quality to prevent recalls,” and that “[t]hey are now pursuing both strategies, but they are essentially at odds with one another.” Is this a rea listic strategy? Do you have suggestions
for the strategies to be improved?
The strategy is realistic even though it is hard to meet. Realistic in a way that enterprises still consider maintaining the quality of the product and how it satisfies its customers while minimizing its costs. These realistic strategies of Toyota can furthermore be improved by keeping the costs focused internally instead of keeping it focused externally. Toyota has improved satisfaction through investing on external failure costfocusing activities while these costs are known to be low in the short run and become high in the long run. Instead, Toyota must invest on activities preventing defects from being sold and reaching the customers. The company should therefore focus more on investing in activities that give essentiality to materials and labor efficiency, inspection, quality checks, etc or also known as the internal failure costs. Through this proposal, the company could achieve its desired strategy, could cut costs, and could improve its product's efficiency and quality.
3. Suggest improvements that you feel could be made to Toyota’s quality program. Also,
what might Toyota do to improve its image to the consumer relative to quality?
Toyota could focus more on the inspection of its products, quality checks, give importance on the materials used and on the efficiency of the materials and labor. These activities are categorized under internal failure cost activities which are done before the products are sent to the market.
CASE: QUALITY MANAGEMENT – TOYOTA
1. If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thicknesses are distributed normally, what fraction of the output is expected to be greater than this thickness?
1.9
2
1.9
1.8
2.2
1.7
2
1.9
1.7
1.8
1.8
2.2
2.1
2.2
1.9
1.8
2.1
1.6
1.8
1.6
2.1
2.4
2.2
2.1
2.1
2
1.8
1.7
1.9
1.9
2.1
2
2.4
1.7
2.2
2
1.6
2
2.1
2.2
From these 40 sets of sample data given, the average thickness in the sample would 1.9625 which is calculated by the summation of all the given data divided by the number of data given. Also, the standard deviation would be 0.209624206. The probability, therefore, that the thickness is greater than 2.4 is: =
2.4 − 1.9625 0.209624206
= 2.087068
Thus, the fraction defective that are expected to have a thickness greater than 2.4 is .018441 or 1.8441% of the washers. 1 − NORMSDIST(2.087068) = 0.018441
2. What is the Cpk for the process? = min [ (1.9625 − 1.4) / 3(0.209624206) , (2.4 − 1.9625) / 3(0.209624206) ]
= [0.894458, 0.695689] = . The Cpk for the process is 0.695689 which is the smaller number. 3. What would be the Cpk for the process if it were centered between the specification limits (assume the process standard deviation is the same)? = min [ (1.9 − 1.4) / 3(0.209624206) , (2.4 − 1.9) / 3(0.209624206) ]
= [0.795074, 0.795074] = . Given that the center of the specification limits is 1.9, Cpk for the process is equal at the value of 0.795074.
4. What would be the Cpk for the process if it were centered between the specification limits (assume the process standard deviation is the same)? = min [ (1.9 − 1.4)/ 3(0.209624206) , (2.4 − 1.9)/ 3(0.209624206) ]
= [0.795074, 0.795074] = . Assuming that the specification limits of its center equals to 1.9, the cpk for the process will be 0.795074 5. What percentage of output would be expected to be out of tolerance if the process were centered? = 2.4 − 1.9/ 0.209624206= 2.385221
2 × (1 − NORMSDIST)(2.385221) = 0.017068876/1.7%
If the process were centered, the expected percentage of output to be out of tolerance would be about 1.7% 6. Set up X- and range control charts for the current process. Assume the operators will take samples of 10 washers at a time.
Observation Sample
1
2
3
4
5
6
7
8
9
1
1.9
2
1.9
1.8
2.2
1.7
2
1.9
1.7
1.8
1.89
0.5
2
1.8
2.2
2.1
2.2
1.9
1.8
2.1
1.6
1.8
1.6
1.91
0.6
3
2.1
2.4
2.2
2.1
2.1
2
1.8
1.7
1.9
1.9
2.02
0.7
4
2.1
2
2.4
1.7
2.2
2
1.6
2
2.1
2.2
2.03
0.8
1.9625
0.65
Mean
Highest measurement Lowest measurement Upper control limit for X bar:
2.164
Lower Limit for X Bar:
1.761
Upper Control Limit R:
1.157
Lowe Control Limit R:
0.143
10 X- bar
R
7. Plot the data on your controls charts. Does the current process appear to be in control?
X-Bar Chart
Range Chart
2.5
1.4
1.2 2 1 1.5
0.8
0.6
1
0.4 0.5 0.2
0
0 1 X-cell
2
3
UCL
Mean
4 LCL
1
2
R
UCL
3
4
Mean
LCL
We can say that the current process is in control since in the 4 samples used; there were no out of the control limits because they were within the Upper Control Limit and the Lower Control Limit. It can also be implied that the process is working without much noise because there is only a minimal amount of variation.
8. If the process could be improved so that the standard deviations were only about .10 millimeter, what would be the best that could be expected with the processes relative to fraction defective?
Consider the table below:
Considering upper spec
FRACTION
Z-SCORE
NORMDIST
1-NORMDIST
4.375
0.999993928
6.07162E-06
0.000607162%
-5.625
9.2754E-09
0.999999991
0.000608090%
5
0.999999713
2.86652E-07
0.000057330%
DEFECTIVE
Considering the lower and upper spec When centered
By looking at the table, we could observe that the best thing to do for the process is to have it centered if the standard deviation were only 0.10 millimeters. If centered, the fraction defective is only 0.000057330% of the washers compared to the other fraction defectives when considering the other specifications.
