Quick Recap Monitoring and Controlling
Performance Management Objectives • In this training you will learn the most effective methods to create constructive performance evaluations and how to communicate with employees during the performance process. • To learn the basics of Performance Management • To understand the purpose and strategies behind Performance Appraisals • To gain knowledge of the performance management forms and tools • To gain an understanding of the merit/awards process
Lesson 13: Monitoring and Controlling Project Performance and QualityTopic 13A: Perform Quality ControlTopic 13B: Report on Project Performance
Quality Control • Quality control is a process that measures output relative to standard, and acts when output doesn't meet standards. • The purpose of quality control is to assure that processes are performing in an acceptable manner. • Companies accomplish quality control by monitoring process output using statistical techniques.
Acceptance sampling Process control Continuous improvement Phases of Quality Assurance Figure 10.1 Inspection and corrective action during production Inspection before/after production Quality built into the process The least progressive The most progressive
Inspection • Inspection is an appraisal activity that compares goods or services to a standard. • Inspection can occur at three points: - before production: is to make sure that inputs are acceptable. - during production: to make sure that the conversion of inputs into outputs is proceeding in an acceptablemanner. - after production: to make a final verification of conformance before passing goods to customers
Inputs Transformation Outputs Inspection • Inspection before and after production involves acceptance sampling procedure. • Monitoring during the production process is referred as process control Acceptance sampling Acceptance sampling Process control
Inspection • The purpose of inspection is to provide information on the degree to which items conform to a standard. • The basic issues of inspection are: 1 - how much to inspect and how often 2- At what points in the process inspection should occur. 3 - whether to inspect in a centralized or on-site location. 4- whether to inspect attributes (counts) or variables (measures)
How much to inspect and how often • The amount of inspection can range from no inspection to inspection of each item many times. • Low-cost, high volume items such as paper clips and pencils often require little inspection because: 1. the cost associated with passing defective items is quite low. 2. the process that produce these items are usually highly reliable, so that defects are rare. • High-cost, low volume items that have large cost associated with passing defective items often require more intensive inspection such as airplanes and spaceships. • The majority of quality control applications ranges between these two extremes. • The amount of inspection needed is governed by the cost of inspection and the expected cost of passing defective items.
Cost Optimal Amount of Inspection Inspection Costs Figure 10.3 Total Cost Cost of inspection Cost of passing defectives
Where to Inspect in the Process Inspection always adds to the cost of the product; therefore, it is important to restrict inspection efforts to the points where they can do the most good. In manufacturing, some of the typical inspection points are: • Raw materials and purchased parts • Finished products • Before a costly operation • Before an irreversible process • Before a covering process
Examples of Inspection Points Table 10.1
Centralized versus on-site inspection • Some situations require that inspections be performed on site such as inspecting the hull of a ship for cracks. • Some situations require specialized tests to be performed in a lab such as medical tests, analyzing food samples, testing metals for hardness, running viscosity tests on lubricants.
Statistical process control • Quality control is concerned with the quality of conformance of a process: Does the output of a process conform to the intent of design? • Managers use Statistical Process Control (SPC) to evaluate the output of a process to determine if it is statistically acceptable. • Statistical Process Control:Statistical evaluation of the output of a process during production • Quality of Conformance:A product or service conforms to specifications
Control Chart • Control Chart: an important tool in SPC • Purpose: to monitor process output to see if it is random (in control) or not (out of control). • A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means). • Upper and lower control limits define the range of acceptable variation.
Abnormal variationdue to assignable sources Out ofcontrol UCL Mean Normal variationdue to chance LCL Abnormal variationdue to assignable sources 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number Control Chart Figure 10.4
Statistical Process Control • The essence of statistical process control is to assure that the output of a process is random so that future output will be random.
Statistical Process Control • The Control Process include • Define what is to be controlled. • Measure the attribute or the variable to be controlled • Compare with the standard • Evaluate if the process in control or out of control • Correct when a process is judged out of control • Monitor results to ensure that corrective action is effective.
Statistical Process Control • Variations and Control • Random variation: Common natural variations in the output of a process, created by countless minor factors. It would be negligible. • Assignable variation: A special variation whose source can be identified (it can be assigned to a specific cause)
Sampling Distribution • The variability of a sample statistic can be described by its sampling distribution. • The sampling distribution is a theoretical distribution that describe the random variability of a sample statistic. • The goal of the sampling distribution is to determine whether nonrandom-and thus, correctable-source of variation are present in the output of a process. How?
Sampling distribution • Suppose there is a process for filling bottles with soft drink. If the amount of soft drink in a large number of bottles (e.g., 100) is measured accurately, we would discover slight differences among the bottles. • If these amounts were arranged in a graph, the frequency distribution would reflect the process variability. • The values would be clustered close to the process average, but some values would vary somewhat from the mean.
Sampling distribution (cont.) • If we return back to the process and take samples of 10 bottles each and compute the mean amount of soft drink in each sample, we would discover that these values also vary, just as the individual values varied. They, too, would have a distribution of values. • The following figure shows the process and the sampling distribution.
Samplingdistribution Processdistribution Mean Sampling Distribution Figure 10.5
Sampling distribution Properties • The sampling distribution exhibits much less variability than the process distribution. • The sampling distribution has the same mean as the process distribution. • The sampling distribution is a normal distribution regardless of the shape of the process distribution. (central limit theorem).
Process and sampling distribution Process distributionSampling distribution Mean = Mean = Variance = 2 Variance = Standard deviation = Standard deviation = Where: n = sample size
Standard deviation Mean 95.44% 99.74% Normal Distribution Figure 10.6
Control limits • Control charts have two limits that separate random variation and nonrandom variation. • Control limits are based on sampling distribution • Theoretically, the normal distribution extends in either direction to infinity. Therefore, any value is theoretically possible. • As a practical matter, we know that 99.7% of the values will be within ±3 standard deviation of the mean of the distribution. • Therefore, we could decide to set the control limit at the values that represent ±3 standard deviation from the mean
Samplingdistribution Processdistribution Mean Lowercontrollimit Uppercontrollimit Control Limits Figure 10.7
SPC hypotheses Null hypothesis H0: the process is in control Alternative hypothesis H1: the process is out of control Actual situation
SPC Errors • Type I error • Concluding a process is not in control when it actually is. The probability of rejecting H0 when it is actually true. • Type II error • Concluding a process is in control when it is not. The probability of accepting H0 when it is actually not true.
/2 /2 Mean LCL UCL Probabilityof Type I error Type I Error Figure 10.8 Using wider limits (e.g., ± 3 sigma limits) reduces the probability of Type I error
UCL LCL 1 2 3 4 Sample number Observations from Sample Distribution Figure 10.9
Types of control charts • There are four types of control charts; two for variables, and two for attributes • Attribute: counted data (e.g., number of defective items in a sample, the number of calls per day) • Variable: measured data, usually on a continuous scale (e.g., amount of time needed to complete a task, length, width, weight, diameter of a part).
Variables Control Charts • Mean control charts • Used to monitor the central tendency of a process. • X-bar charts • Range control charts • Used to monitor the process dispersion • R charts
Mean Chart (X-bar chart) • The control limits of the mean chart is calculated as follows: (first approach) • Upper Control Limit (UCL)= • Lower Control Limit (LCL) = Where: n = sample size z = standard normal deviation (1,2 and 3; 3 is recommended) = process standard deviation = standard deviation of the sampling distribution of the means = average of sample means
Mean Chart (X-bar chart) • Example A quality inspector took five samples, each with four observations, of the length of time for glue to dry. The analyst computed the mean of each sample and then computed the grand mean. All values are in minutes. Use this information to obtain three-sigma (i.e., z = 3) control limits for the means of future time. It is known from previous experience that the standard deviation of the process is 0.02 minute.
Mean chart Sample Observation
Solution • n = 4 • z = 3 • = 0.02
Control chart UCL 12.14 12.11 LCL 12.08 1 2 3 4 5 Sample
Mean chart • A second approach to calculate the control limits: • This approach assumes that the range is in control This approach is recommended when the process standard deviation is not known Where: A2 = A factor from table 10.2 Page 441 = Average of sample ranges
Example • Twenty samples of n = 8 have been taken from a cleaning operations. The average sample range for the 20 samples was 0.016 minute, and the average mean was 3 minutes. Determine three-sigma control limits for this process. • Solution = 3 min. , = 0.016, A2 = 0.37 for n = 8 (table 10.2)
Range Control Chart (R-chart) • The R-charts are used to monitor process dispersion; they are sensitive to changes in process dispersion. Although the underlying sampling distribution of the range is not normal, the concept for use of range charts are much the same as those for use of mean chart. • Control limits: Where values of D3 and D4 are obtained from table 10.2 page 441
R-chart • Example Twenty-five samples of n = 10 observations have been taken from a milling process. The average sample range was 0.01 centimeter. Determine upper and lower control limits for sample ranges. • Solution = 0.01 cm, n = 10 From table 10.2, for n = 10, D4 = 1.78 and D3 = 0.22 UCL = 1.78(0.01) = 0.0178 or 0.018 LCL = 0.22(0.01) = 0.0022 or 0.002
R-Chart • Example Small boxes of cereal are labeled “net weight 10 ounces.” Each hour, a random sample of size n = 4 boxes are weighted to check process control. Five hours of observation yielded the following:
R-Chart • Solution n = 4 For n = 4 , D3 = 0 and D4 = 2.28 Since all ranges are between the upper and lower limits, we conclude that the process is in control
Using Mean and Range Charts • Mean control charts and range control charts provide different perspectives on a process. • The mean charts are sensitive to shifts in process mean, whereas range charts are sensitive to changes in process dispersion. • Because of this difference in perspective, both types of charts might be used to monitor the same process.
x-Chart Mean and Range Charts Figure 10.10A (process mean is shifting upward) Sampling Distribution UCL Detects shift LCL UCL Does notdetect shift R-chart LCL
x-Chart Mean and Range Charts Figure 10.10B Sampling Distribution (process variability is increasing) UCL Does notreveal increase LCL UCL R-chart Reveals increase LCL
Using the Mean and Range Chart To use the Mean and Range control chart, apply the following procedure: • Obtain 20 to 25 samples. Compute the appropriate sample statistics (mean and range) for each sample. • Establish preliminary control limits using the formulas. • Determine if any points fall outside the control limits. • If you find no out-of-control signals, assume that the process is in control. If not, investigate and correct assignable cause of variation. Then resume the process and collect another set of observations upon which control limits can be based. • Plot the data on a control chart and check for out-of-control signals.
Control Chart for Attributes • Control charts for attributes are used when the process characteristic is counted rather than measured. Two types are available: • P-Chart - Control chart used to monitor the proportion of defectives in a process • C-Chart - Control chart used to monitor the number of defects per unit Attributes generate data that are counted.