Diploma of Laboratory Technology. Assessment 2 Control charts. Data Analysis. MSL Analyse data and report results.

Transcription

1 Diploma of Laboratory Technology Assessment 2 Control charts Data Analysis MSL Analyse data and report results

2 PURPOSE 2 ASSESSMENT MAP 2 SUBMISSION 2 GETTING STARTED 3 TASK 1 X CHART 3 What to do 3 How to do it 3 TASK 2 DETERMINING THE CAPABILITY INDEX 4 What to do 4 How to do it 4 TASK 3 THE R CHART 6 What to do 6 How to do it 6 Chemical, Forensic, Food & Environmental Technology [ Page 1

3 Purpose This task assesses your ability to; Use calculations on raw data to determine control limits Graph control limits Apply normal distribution statistics to raw data Compare real data to the normal statistics Assessment map Each aspect of this assessment is mapped as per the table below; Unit Element Performance Criteria Performance Evidence MSL , 5.3 4, 6 na Knowledge evidence Submission All work will be completed in the one spreadsheet The spreadsheet must be ed to your assessor using the following format; DA-1-Yourname Due Date: End of term 4, 2016 Chemical, Forensic, Food & Environmental Technology [ Page 2

4 Getting started Visit the course website; Download the.pdf guide for Assessment 2 Download the Excel file linked to Assessment 2. Rename the file DA2-yourname and save it somewhere sensible. NOTE 1: All graphs must be formatted properly. Refer to the topic in Study Module 2 on the rules for formatting graphs appropriately. Task 1 X Chart The X Chart is the easiest of all the control charts to prepare, and typifies what you would do for most common laboratory applications. No data is manipulated and it uses basic descriptive statistics you have already learnt. What to do 1. Using the tab titled X Chart, enter the appropriate calculations into cells B3-B6 (you do B7 later). This will populate columns D-F; 2. Graph columns B-F (format appropriately) 3. Move chart to own sheet labelled as X 4. Save your work How to do it Use the following formulas to calculate these parameters; MEAN: STDEV: UCL: LCL: =AVERAGE(Range) =STDEV(Range) =AVERAGE + 3*STDEV =AVERAGE 3*STDEV Chemical, Forensic, Food & Environmental Technology [ Page 3

5 Task 2 Determining the capability index What to do You will need to calculate the USL, LSL, Cp and Cpk 1,2 for the X Chart data and answer a question. You need to use the rules below to establish whether the data in in process or not (using the comparison column) by using an IF function to determine the parameter. RULE How to do it 1. Calculate the upper and lower Specification Limits (USL, LSL) in cells B7-8; USL = AVERAGE + (6 x SD) LSL = AVERAGE (6 x SD) 2. Calculate the capability index, C p, in cell B9 C p = (USL - LSL) 6s 3. Caluclate the Cpk1 and 2 values in Cells B10-11; C pk1 = (USL - x ) 3s (above centre) C pk2 = ( x - LSL) 3s (below centre) 4. Add the USL and LSL lines to the X Chart 5. Using the information from the example below, answer the question in cell C10 (hover your mouse over the cell to see the question). If C p is 1, the process is capable of meeting the specifications; if C p < 1, it isn t. The C p value only tells us how the process variability compares to the limits. It doesn t tell us whether the process is within the limits. To determine whether it is, use the two Cpk equations below, where x is the population mean, not the central point of the specification. RULE If C pk1 and C pk2 are similar, the process output is centred. If C pk1 and C pk2 are different, the process should be adjusted towards the end which has the higher C pk value. Chemical, Forensic, Food & Environmental Technology [ Page 4

6 Example Process Mean Process SD USL LSL (a) (b) (a) C p = ( ) (6 x 9) = 1.1. C pk1 = ( ) (3 x 9) = 1.04 C pk2 = ( ) (3 x 9) = OK. Process spread less than specification, since C p > 1. C pk values similar so centring is Process can meet specifications. (b) C p = ( ) (6 x 0.06) = C pk1 = ( ) (3 x 0.06) = 1.1 C pk2 = ( ) (3 x 0.06) = Process spread is greater than specifications, so variability must be reduced. Also, process is poorly centred (low) and should be adjusted to increase the average. Chemical, Forensic, Food & Environmental Technology [ Page 5

7 Task 3 The R Chart The range chart is another useful chart to use in industry. Perform the following tasks to create and interpret a range chart for the data provided. What to do Use the data on the tab titled R Chart which has four columns of data from four samples which need to be manipulated. 1. Use Excel functions to determine the range for each row of four samples (Column F) 2. Find the average of the four samples (Column G) 3. Find the average of the sample averages (Cell B5) 4. Find the average for the range values (Cell B4) 5. Determine the UCL & LCL in cells B6-7 using the formulas in the table below 6. Plot columns F-I and format graph appropriately 7. Add a 7 period moving average trendline 8. Move chart to own sheet as R How to do it Equations and statistical fudge factors are employed which can be used with much small data sets. The basic principle behind the use of these statistical equations is that a number (minimum 20, preferably 50) of quality control samples are taken during a time when it is considered that the process is behaving normally. Any obvious out-of-specification product is ignored. If when the control limits are calculated, one or more points used in the calculation are found to lie outside the limits, then it/they should be removed, and the limits recalculated. x and R Charts Chart Centre UCL LCL x x x + F 1 R x - F 1 R R R F 2 R F 3 R x is the average mean from the sample sets Chemical, Forensic, Food & Environmental Technology [ Page 6

8 R is the average range from the sample sets F 1, F 2 and F 3 are fudge factors (see Table 4.3) Statistical fudge factors for x and R charts n Fudge Factor 1 (F 1 ) Fudge Factor 2 (F 2 ) Fudge Factor 3 (F 3 ) Example Determine the control limits for average and range charts, given the following data, taken during a run when the system was in control. Four samples were taken at each time and the mean and range calculated. Mean Range Mean Range Chemical, Forensic, Food & Environmental Technology [ Page 7

9 The average of the 20 means is 105 (rounded from ) = x. The average of the 20 ranges is 4 (rounded from 3.8) = R. The control chart limits and centre line for the two charts would then be: Chart Centre UCL LCL x x 3.8 = x 3.8 = 102 R x 2.28 = x 0 = 0 Note that each of the values has been rounded to the nearest whole number, because that is how the data is collected (no decimal places). NOTE With any control chart where measurements are never negative, any lower control limit calculation giving such a result is given the value of 0. Chemical, Forensic, Food & Environmental Technology [ Page 8