STATISTICAL PROCESS CONTROL: CONTROL CHARTS for ATTRIBUTES What is attribute?, refers to quality characteristics that conform or do not conform to specifications (e.g. OK-NG, Accept-Reject) Attributes control charts use pass – fail information for charting. 2 types of usage: 1. Measurements not possible – for example, visually inspected items such as color, missing parts, scratches, and damage 2. Measurements can be made but are not made because of time, cost, or need (e.g. use go-no-go gauge, fitting jig) 2 important terms to differentiate 1. Defect - items that contribute to nonconformity of a quality characteristics 2. Defective - part/product inspected not conforming or meeting specification (can have > 1 defects)

CONTROL CHARTS for ATTRIBUTES The types of attributes control charts include the following: 1. p charts - a single chart that tracks the percentage of nonconforming item in each sample - sample sizes are large, usually 100 pieces or more 2. np charts - tracks the number of nonconforming items in each sample - easier to use than the p chart because the percentage of defective items does not have to be calculated, but it has one restrictions - all the samples must be the same size 3. c charts - graphs the total number of nonconformance found in each piece or unit that is inspected 4. u charts - samples are taken and the total number of nonconformance in the sample is determined - tracks the average number of nonconformance per unit

CONTROL CHARTS for ATTRIBUTES

CONTROL CHARTS for ATTRIBUTES

CONTROL CHARTS for ATTRIBUTES Control Charts for Nonconforming Units Control charts for Fraction Defective for nonconforming units based on Binomial Distribution - p Chart (proportion nonconforming in sample or subgroup) - np Chart (number nonconforming) Objectives - Determine the average quality level – this information provides the process capability in terms of attributes - Bring to the attention of management any changes in the average – once the average quality is known, changes, become significant - Improve the product quality – p chart can motivate operating and management personnel to initiate ideas for quality improvement - Evaluate the quality performance of operating and management personnel – supervisors of activities and especially the CEO should be evaluated by a chart for nonconforming units - Determine acceptance criteria of a product before shipment to the customer – knowledge of the proportion nonconforming provides management with information on whether or not to release an order

CONTROL CHARTS for ATTRIBUTES p Chart Used for data consists of proportion of number of occurrences to total number of occurrences Reports fraction nonconforming in a product, quality characteristics, or group of quality characteristics Fraction nonconforming: Fraction nonconforming usually quite small i.e. about 0.15 or less If > 0.15 problem, need take drastic action Since p is small n must be big to produce meaningful chart e.g. 450 books inspected from a production if 15000 books at the end of inspections 5 book found defectives notice n large The subgroup sizes of the p chart can be either: (a) constant size (same through out) (b) variable size (changes)

CONTROL CHARTS for ATTRIBUTES Construction of p Chart (constant subgroup size) General procedure same as variable control chart 1. Select quality characteristic - determine use of control chart - p chart can control (one quality characteristic, group of quality characteristic, a part, an entire product, a number of products) - performance control for operator, department, shift, etc. 2. Determine subgroup size and method size subgroup depends on p - NOT A If p = 0.001 and n = 1000 GOOD average number nonconforming np = 1 per subgroup CHART many zeroes - GOOD p = 0.15, n = 50 CHART np = 7.5 minimum n = 50, usually 1000

CONTROL CHARTS for ATTRIBUTES 3. Collect the data - al least 25 subgroup - for each subgroup p = np/n; np = number of defectives n = number of samples 4. Calculate the trial limits

CONTROL CHARTS for ATTRIBUTES

CONTROL CHARTS for ATTRIBUTES 5. Establish revised limits - remove data points out of control - establish revised limits out of control situation present (discard) limits can only be calculated until finish inspection

CONTROL CHARTS for ATTRIBUTES

CONTROL CHARTS for ATTRIBUTES 6. Achieve the objective - the first five step are planning - the last step involves action and leads to the achievement of the objective - some representative values of inspection results for the month of June are shown in Figure above - analysis of the June results shows that the quality improved and also for entire month of July and August

CONTROL CHARTS for ATTRIBUTES Construction of p Chart (variable subgroup size) There are situations when you cannot obtain constant subgroup size - e.g. using 100% inspection results with output quantity varying day to day It is undesirable, but it exists – how to handle? - construction step 1 and 2 is same - step 3 – collect data Additional columns needed: Each day fraction defective calculated by inspector using np/n

CONTROL CHARTS for ATTRIBUTES

CONTROL CHARTS for ATTRIBUTES 4. Determine trial limits - first, average proportion nonconforming - since n changes, limits calculated for each subgroup - DO IT DIFFERENT n

CONTROL CHARTS for ATTRIBUTES - SINCE n is only changing simplify - Note: as n CL are closer n CL gets wider

CONTROL CHARTS for ATTRIBUTES 5. Establish revised central line and control limits - remove data points out of control - establish revised limits out of control situation present (discard) - DO IT CALCULATIONS for MAY 4 and MAY 5

CONTROL CHARTS for ATTRIBUTES Two techniques to minimize effect of variable subgroup size 1. Using average subgroup size - calculate individual limits when subgroup size not within ± 15% of nav

CONTROL CHARTS for ATTRIBUTES 2. Establish control limits for different subgroup sizes

CONTROL CHARTS for ATTRIBUTES Control Charts for Count of Nonconformities Nonconformities (defects) chart controls the count of nonconformities within product 2 types of chart: - c chart – count of nonconformities - u chart – count of nonconformities per unit 2 conditions must be met (due to Poisson distribution) 1) average count of nonconformities must be far less than total possible count of nonconformities if everything went wrong 2) occurrences are independent – opportunity for defects same Examples - imperfections in a large roll paper - appearance on rubber mat - imperfect soldering in a PCB - rust spots on sheets/rolls of steel - mould marks - short mould of rubber seal Same as nonconforming control chart, the CL ± from centerline

CONTROL CHARTS for ATTRIBUTES Objective - Determine the average quality level as a benchmark or starting point – gives the initial process capability - Bring to the attention of management any changes in the average - Improve the product quality – charts can motivate operating and management personnel to initiate ideas for quality improvement - Evaluate the quality performance of operating and management personnel. - Provide information concerning the acceptability of the product prior to shipment Because of the limitations of the charts for count of nonconformities, many organizations do not have occasion for their use

CONTROL CHARTS for ATTRIBUTES Construction of c chart 1. Select the quality characteristics 2. Determine the subgroup size and method For c chart n = 1 - one aeroplane - one dozen of pencils, etc. method – audit or on-line 3. Collect data, calculate trial limits

CONTROL CHARTS for ATTRIBUTES 4. Draw the centerline and control limits on the chart

CONTROL CHARTS for ATTRIBUTES 5. Interpret the chart - point 6 is out of control and should be investigated to determine the cause of so many nonconformities - except for point 6, the chart is performing in a very steady manner 6. Revising the c chart - the reasons behind special-cause situations have been identified and corrected, c charts can be revised using this formula:

CONTROL CHARTS for ATTRIBUTES Construction of u chart (count of defects per unit) For unit > 1 For varying sample size Also if subgroup size constant u chart is developed same as c chart, collect 25 subgroup data, calculate trial limits and revise limits Data: Hose Connection Formula

CONTROL CHARTS for ATTRIBUTES

CONTROL CHARTS for ATTRIBUTES Interpret the chart - except for point 16, the chart appears to be under statistical control - there are no runs or unusual patterns - point 16 should be investigated to determine the cause of such a large number of nonconformities per unit Revising the u chart

CONTROL CHARTS for ATTRIBUTES ANALYSIS STATE OF CONTROL SAME AS VARIABLE CONTROL CHART Selection of Control Chart