Question
Another rejected shipment! exclaimed Bill Roberts.That makes four in the past twenty days ! Tony Escalera knew that Roberts would not take the news well.Something
"Another rejected shipment!"exclaimed Bill Roberts."That makesfour in the past twenty days!" Tony Escalera knew that Roberts would not take the news well.Something was wrong, and things were going to be uncomfortable for everybody atPackemuntil the problem was resolved. Packemproduces magnetic data storage devices and media for the computer industry. A few years ago, they began producing thePackemDS1000, a compact hard drive with the capability of storing 1 gigabyte (1,000 megabytes) of information.Most of the drives they produce are sold to companies that resell the drives under their own product label to consumers and commercial businesses. Packem'smain buyer is Four-D Office Products.Four-D is a national retailer that sells the drives under its own product label to final consumers and some computer companies.This arrangement with Four-D has been very profitable forPackem. Bill Roberts has been vice-president in charge of sales atPackemfor the past four years.His rapid rise up the company's management ladder was due in large part to his role in developing the partnership with Four-D Office Products.Four-D was impressed with Roberts andPackem'scommitment to quality. In thePackem DS 1000 hard drivemanufacturing process, each of thethree 8-hour shifts produces approximately 120 drives per day.As part of the quality inspection process, one drive is sampled each hour and subjected to the PDQ (Performance and Drive Quality) test, originally developed byPackem.The PDQ is a rigorous test of a hard drive that measures the performance of the drive in a variety of conditions, checks the accuracy and speed of the drive in storing and retrieving information, and tests for defects in the drive's mechanism and storage media.The PDQ is a relatively expensive test and takes up to twenty minutes to complete.At the conclusion of the test, an overall test score based on drive characteristics is computed.PDQ test scoresfor the hard drives produced at Packem have historically followed anormal distribution with a mean value of 7.0 and a standard deviation of .30 when the process has been in control.Each hour, the new PDQ value is added to a control chart used in monitoring the process for early detection of drive quality problems.Signals from test scoresbelow the lower control limit (LCL) may indicate a drop in quality, while signals from test scores above the upper control limit (UCL) may indicate a potential improvement in the process. Shipments ofPackemDS 1000 hard drives are made to Four-D once each day.Before Four-D accepts a shipment, they subject arandom sample of 10 drives to the PDQ test as a final inspection.At Four-D, a drive is judged to benonconforming if its performance test score falls below 6.2. If one or more drives in the sample of 10are found to be nonconforming, the entire shipment is judged to be "unacceptable" and returned toPackem.Under the arrangement with Four-D,Packemis required to pay a penalty to Four-D and must replace the unacceptable shipment within 24 hours.Further penalties are assessed for each additional day that passes before the shipment is replaced. The production engineers atPackemhave told Bill Roberts that "zero defect"' production is virtually impossible, but that the percentage of defects has been reduced to the point that only rarely will a shipment be judged unacceptable.In recent weeks, however, there has been a noticeable increase in the frequency of returned shipments from Four-D. Tony Escalera, the chief production engineer atPackem, brought word of the latest returned shipment to Bill Roberts. Roberts:"Another rejected shipment!That makes four in the past twenty days!What's going on, Tony?" Escalera:"At this point, I don't know any more than you do, Mr. Roberts.To borrow some statistical terminology, it's possible that we're just experiencing a few 'false rejections.' After all, there is variability in any process.Even if the actual quality levels are on target, we expect a few inspections to indicate otherwise.
Roberts:"The number of rejections still seems to be much higher than we have experienced in the past.Do you think that Four-D has become more demanding in their acceptable level of quality?"
Escalera:"That's possible, but surely they would have let us know first.Maybe they are making mistakes when they conduct the PDQ tests or when they interpret the results."
Roberts:"Or maybe we're the ones making the mistakes.Do we have evidence of any quality problems here?"
Escalera:"As you know,we sample one drive each hour of each shift and run the PDQ test.In the past, we plotted the individual test scores on a control chart to monitor the process for early warning signals of problems.Recently, though, we began plotting the average of the eight PDQ test values collected over each shift on our charts instead of the individual values.Our new quality control person told us that this approach should result in a more sensitive warning system.'
Roberts:"Have your control charts indicated any problems?"
Escalera:"No.As you can tell from this latesttwo-sigma control chart, there have not been any out-of-control signals in the past 150 shifts.That's a surprising performance record.We would normally expect about seven or eight values out of 150 to fall outside the two-sigma control limits.If anything, it looks like the variability in process quality is much lower than it has been in the past.
Roberts:"Yes, but if the variability has actually decreased, why haven't we seenfewerreturned shipments?Are we plotting and interpreting these shift averages on the charts correctly?"
Escalera:"I think so. I'll go back and let the quality control person take a look at what we've been doing."
Roberts:"Maybe the problem really is at Four-D.Wait a minute!We're forgetting something.If everything looks good on our end, but Four-D is finding nonconformances in our shipments, could the problem be due to damage during shipment?"
Escalera:"Someone else suggested that possibility to me earlier.But it's pretty unlikely given the protective packaging we use."
Roberts:"Tony, we need to resolve this problem, if there is one, as quickly as possible.Check out our side first for the source of the problem.If you can't turn up anything here, make some inquiries with your contacts at Four-D."
Case Questions: Packem Company
- If thePackem DS1000hard drive production process atPackem Companyis in control, what percentage of the drives produced would be considered in nonconformance by Four-D?
- If thePackem DSIOOOhard drive production process atPackem Companyis in control, how often would shipments be found unacceptable by Four-D?
- What is the probability of four rejected shipments in the past twenty days assuming that the process has been in control all this time?
- Speculate as to the source of the problem atPackem Company.Has the problem with unaccepted shipments been due to an increase in drive nonconformances atPackem, to increased quality requirements by Four-D Office Products, to damage during shipment, or is it simply due to random variation?Be as specific as possible.What evidence leads you to your conclusion?Attach any supporting evidence from your data analysis.
AssignmentThe data from the drive quality tests conducted atPackemover the past 150 shifts are provided.
Variable | Coding |
Week | 1-10 |
Day | 1=Monday 2=Tuesday 3=Wednesday 4=Thursday 5=Friday |
Shift | 1=1stshift 2=2ndshift 3=3rdshift |
Hours | Total number of hours worked by production employees during the shift |
Drives | Total number of drives produced per shift |
Shift PDQ | The average PDQ test score recorded for the eight drives tested during the shift.One randomly selected drive is tested each hour of every shift |
Using this data set and other information given in the case, help Bill Roberts and Tony Escalera solve the quality problem they are experiencing atPackem.TheCase Questionswill assist in the analysis of the data.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started