Assignment Task: SPC and Process Capability
Choose the Best Answer
Assume alpha = 0.05 unless otherwise noted.
SPC Chart Guidelines
Select only rules 1-4 in assessing stability for Minitab SPC Charts
Select R-bar method for estimating within subgroup standard deviation for X-bar Charts
Do NOT check the 'leave gap' setting if you remove points from an SPC analysis
Part 1: General Problems
Problem 1: Which of the following best represents the purpose for using Statistical Process Control (SPC) charts?
a. SPC Charts help distinguish between common and special cause variation
b. SPC Charts always identify the root cause for all statistically significant mean shifts
c. Both A and B
d. Neither A nor B
Problem 2: An office supplies distributor ships 90-130 orders per day. Each order is either delivered on-time or late, relative to a posted schedule. The company wishes to use a control chart to monitor late deliveries per day. Their goal is a daily on-time percentage greater than 95%. Use an appropriate SPC chart to assess the stability of this process. Which of the following may be reasonably concluded about the current state of this process?
See excel file for data to create chart to answer Problem.
a. The process is out-of-statistical control using a P-Chart
b. While on-time % is not acceptable, company may reasonably expect a typical day to have a defect rate (late) of 0.127, ranging from ~0.027 to 0.227 (based on 3 sigma control limits)
c. Defect rate would be significantly lower if they used constant sample size of 110 each day
d. The process is out-of-statistical control using an X-bar Chart
Part 2: Staff Scheduling
Suppose you wish to monitor the consistency of orders received at a distribution center for the purpose of scheduling staff. You obtain data on the number of orders received every two hours. Given the available data, answer the following Problems. (Note: Hour = 2 in worksheet represents the number of orders in the first two hours of the work shift, etc.)
Problem 3: Construct an appropriate variable control chart using the variable 'Day 'to represent a subgroup. Which of the following limits would be used to determine if the average number of orders is consistent? Hint: Construct a chart to monitor BETWEEN SUBGROUP variations.
a. LCL = 16.90; UCL = 40.68
b. LCL = 0; UCL = 37.23
c. LCL = 6.90; UCL = 50.68
d. LSL = 6.90; USL = 50.68
Problem 4: Which of the following may be reasonably concluded from a stability analysis (Hint: Consider different subgroup strategies and apply other tools to stratify the data)?
a. Nothing. One should not make conclusions about stability of this process using an X-bar chart because the skewness of the individual samples (i.e., order data collected every hours) is 1.3 and do not follow a normal distribution
b. Although the number of orders per day is consistent(in statistical control), the company should schedule staff to account for more orders in the first two hours of each shift than the other three time periods as evident by a Multiple Box Plot (or interval plot).
c. The amount of orders received every 2 hours is out of statistical control per I/MR chart. Thus, the company should develop a flexible staffing plan that changes every two hours.
d. The number of orders tends to increase in the last two hours of the day, thus the company should schedule more staff at the end of the shift.
Part 3: Medication Errors
An elderly care center is concerned with medication errors in one of their departments ('5N'). Medication errors are recorded by medication passes done by staff during a work shift (three work shifts: morning-AM, afternoon-PM, or midnights-MN). Here, a staff member administers medications to a collection of patients. Some possible types of medication errors include: wrong medication, wrong amount, wrong patient, and wrong time. For each patient receiving medication, more than one error may occur during a medication pass. (Note: Historically, most errors are for 'wrong time'). Construct an appropriate attribute control chartto monitor the process for all shifts (72 subgroups).
Problem 5: Which of the following would be the LCL and UCL for your control chart? (Note: Plot all data in a one chart with 72 subgroups)
a. Individual Chart: LCL = 13.6; UCL = 25.4
b. P-Chart: LCL = 0.01; UCL = 0.26
c. U-Chart: LCL = 0.0; UCL = 0.027
d. C-Chart: LCL = 8.6; UCL = 37.3
Problem 6: Subset the data to create control charts for each individual shift. Based on this analysis (along with your control chart for all shifts above), which of the following may be reasonably concluded? (Hint: Use the Minitab split data command to subset data by shift and then create SPC charts)
a. Based on P-chart, this company has a chronic (consistent) medication error problem, spread equally across all three shifts
b. Based on U-Chart, the afternoon shift (PM) is the most consistent and thus the other shifts should replicate their process to reduce errors
c. Based on U-Chart, the midnight shift (MN), while not in statistical control, currently has the lowest overall medication error rate
d. Based on U-Chart, morning shift (AM) appears to have made a significant reduction in their error rate, and thus the company should investigate what they are doing differently compared to the other shifts
Part 4: Deliveries
Suppose you work for a customer delivery department at a large furniture company. Company policy is to guarantee delivery within 3 days. Every day, three deliveries are picked at random, and the time to delivery noted (Number of days to deliver = Delivery time - Invoice date). The results for the past month are in the following spreadsheet.
For consistency of results with solutions, use R-bar method in Minitab to estimate within group standard deviation.
Problem 7: Which of the following would be the appropriate process capability index and estimate that includes the mean of the process and uses the within subgroup standard deviation based on an in-control process? Hint: Use Process Capability Analysis - Normal.
a. St Dev = 0.75
b. Cpk = 0.36
c. Cp = 0.66
d. Ppk = 0.89
Problem 8: What is the Overall Expected PPM Defective for this process (Assume Normal)?
a. PPM Defective = 188,889
b. PPM Defective = 190,421
c. PPM Defective = 144,485
d. PPM Defective = 183,588
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