Chapter 4 Process Measurement

Effective Metrics SMART Simple Measurable Actionable (they provide a basis for decision-making) Related (to customer requirements and to each other) Timely

Identifying and Selecting Process Metrics Identify all customers and their requirements and expectations Define work processes Define value-adding activities and process outputs Develop measures for each key process Evaluate measures for their usefulness

Process Mapping A process map (flowchart) identifies the sequence of activities or the flow of materials and information in a process. Process maps help the people involved in the process understand it much better and more objectively by providing a picture of the steps needed to accomplish a task. Process maps help to identify appropriate metrics for process control.

Value Stream Maps Value stream map – a map of all activities involved in designing, producing, and delivering goods and services to customers. Value stream maps highlight value-added versus non-value-added activities and include the amount of time activities take.

Developing Process Maps 1. Begin with the process output and ask, “What is the last essential subprocess that produces the output of the process?” 2. For that subprocess, ask, “What input does it need to produce the process output?” For each input, test its value to ensure that it is required. 3. For each input, identify its source. In many cases, the input will be the output of the previous subprocess. In some cases, the input may come from external suppliers. 4. Continue backward, one subprocess at a time, until each input comes from an external supplier

Example: Pizza Fulfillment

Possible Metrics Number of pizzas, by type per hour Order accuracy as a percentage of correct orders Number of pizza rejected per number prepared Delivery time Number of errors in collections Raw materials and finished pizza inventory levels.

CTQ Tree Y = f(X), where Y is the set of CTQs and X represents the set of critical input variables that influence Y. “drill down” from Y to identify the critical X -factors; this structure is often called a CTQ tree.

Data Collection Key Questions What questions are we trying to answer? What type of data will we need to answer the question? Where can we find the data? Who can provide the data? How can we collect the data with minimum effort and with minimum chance of error?

Data Sheets and Check Sheets Data sheets use simple columnar or tabular forms to record data. Check sheets are special types of data collection forms in which the results may be interpreted on the form directly without additional processing.

Example 12

Other Types of Check Sheets 13

Sampling What is the objective of the study? What type of sample should be used? What possible error might result from sampling? What will the study cost?

Sampling Methods Simple random sampling Stratified sampling Systematic sampling Cluster sampling Judgment sampling

Selecting a Sampling Plan A good sampling plan should select a sample at the lowest cost that will provide the best possible representation of the population, consistent with the objectives of precision and reliability that have been determined for the study.

Sampling Error Sampling error (statistical error) Nonsampling error (systematic error) Factors to consider: Sample size Appropriate sample design

Sample Size Calcuation To have a sampling error for a population mean of ± E or less for a confidence level of 100(1 – a): For a proportion (use sample estimate for p or 0.5):

Data Classification 1. Type of data • Cross-sectional — data that are collected over a single period of time • Time series — data collected over time 2. Number of variables • Univariate — data consisting of a single variable • Multivariate — data consisting of two or more (often related) variables

Measurement Scales Categorical data – data sorted into categories according to specified characteristics. Ordinal data – ordered or ranked according to some relationship to one another Interval data – ordinal, but have constant differences between observations and have no natural zero. Ratio data – continuous and have a natural zero.

Descriptive Statistics: Measures of Location Sample Mean Median – the middle value (or 50th percentile) when the data are arranged from smallest to largest. Mode – the observation that occurs most frequently

Descriptive Statistics: Measures of Dispersion Range – the difference between the maximum value and the minimum value in the data set. Sample variance Sample standard deviation

Descriptive Statistics: Proportions Proportion – the fraction of data that have a certain characteristic. Proportions are key descriptive statistics for categorical data, such as defects or errors.

Descriptive Statistics: Measures of Shape Coefficient of skewness (CS) – a measure of the degree of asymmetry of observations around the mean. Coefficient of kurtosis (CK) measures the peakedness (i.e., high, narrow) or flatness (i.e., short, flat-topped) of a histogram. 24

Excel Tools for Descriptive Statistics Analysis ToolPak Descriptive Statistics Histogram 25

Descriptive Statistics Tool

Histogram Tool 27

Measurement System Evaluation Observed variation in process output stems from the natural variation that occurs in the output itself as well as the measurement system. If there is little variation in the measurement system, then the observed measurements reflect the true variation in the process. However, if the variation in the measurement system is high, then it is difficult to separate the true variation in the process from the variation in the measurement system, resulting in misleading conclusions about quality.

Metrology - Science of Measurement Accuracy – the difference between the true value and the observed average of a measurement. Precision – closeness of repeated measurements to each other.

Accuracy vs. Precision

Calibration Calibration – the process of verifying the capability and performance of an item of measuring and test equipment compared to traceable measurement standards.

Repeatability and Reproducibility Repeatability (equipment variation) – variation in multiple measurements by an individual using the same instrument. Reproducibility (appraiser variation) - variation in the same measuring instrument used by different individuals

Repeatability & Reproducibility Studies Study the variation in a measurement system using statistical analysis Select m operators and n parts Calibrate the measuring instrument Randomly measure each part by each operator for r trials Compute key statistics to quantify repeatability and reproducibility

Spreadsheet Template The Student Companion Site provides an easy-to-use Excel template, R&R.xlsx, for all the calculations in an R&R study. See Figure 4.14

Process Capability Process capability – the ability of a process to produce output that conforms to specifications. Process capability study – a carefully planned and designed to yield specific information about the performance of a process under specified operating conditions.

Types of Capability Studies Process characterization study - how a process performs under actual operating conditions Peak performance study - how a process performs under ideal conditions Component variability study - relative contribution of different sources of variation (e.g., process factors, measurement system)

Process Capability Study Choose a representative machine or process Define the process conditions Select a representative operator Provide the right materials Specify the gauging or measurement method Collect the measurements and interpret the data

Process Variation Examples

Peak Performance Study and Variation To conduct a peak performance study, we must ensure that the variation in the process results only from common causes and does not include any special causes. When the variation in the process results from common causes alone, we say it is in statistical control (or simply, in control). When special causes are present, the process is said to be out of control.

Process Capability Indexes

Spreadsheet Template A spreadsheet template, Process Capability.xlsx, is available on the Student Companion Site for computing process capability indexes and displaying a histogram of the data.

Process Performance Indexes If a process may include special causes of variation, practitioners use alternative capability indexes, called process performance indexes: Pp, Ppl, Ppu, and Ppk. Mathematically, these are exactly the same as the process capability indexes Cp, Cpl, Cpu, and Cpk, but represent the actual, rather than ideal, performance in a noncontrolled environment (which may include special causes of variation).

Process Capability for Attributes Data For attributes data, such as nonconformances that are simply counted, we can use the proportion nonconforming in an analogous fashion as the mean of a continuous measurement. the higher the proportion, the worse the capability.