Managing Flow Variability: Process Control and Capability

Managing Flow Variability: Process Control and Capability
Managing Business Process Flows: Managing Flow Variability: Process Control and Capability

Managing Flow Variability
9.1 Performance Variability 9.2 Analysis of Variability 9.3 Process Control 9.4 Process Capability 9.5 Process Capability Improvement 9.6 Product and Process Design

Managing Business Process Flows:
Great year……. Great Products! Service! Reputation! Congratulations!! Good Job everyone! Sorry to burst the bubble... But we are not doing well. You’re Fired I heard customers are not satisfied with our products and services Hhhmmm… we need hard data. We need to identify, correct and prevent future problems! Yikes…more work

Managing Business Process Flows:
All Products & Services VARY in Terms Of Cost Quality Availability Flow Times Variability often leads to Customer Dissatisfaction Chapter covers some geographical/statistical methods for measuring, analyzing, controlling & reducing variability in product & process performance to improve customer satisfaction

§ 9.1 Performance Variability
All measures of product & process performance (external & internal) display Variability. External Measurements - customer satisfaction, relative product rankings, customer complaints (vary from one market survey to the next) Possible sources: supplier delivery delays or changing tastes Internally - flow units in all business processes vary with respect to cost, quality & flow times Possible sources: untrained workers or imprecise equipment Example 1 ~ No two cars rolling off an assembly line are identical. Even under identical circumstances, the time & cost required to produce the same product could be quite different. Example 2 ~ Cost of operating a department within a company can vary from one quarter to the next.

Variability refers to a discrepancy between the actual and the expected performance. Can be due to gap between the following: What customer wants and what product is designed for What product design calls for and what process for making it is capable of producing What process is capable of producing and what it actually produces How the produced product is expected to perform and how it actually performs How the product actually performs and how the customer perceives it This often leads to: higher costs, longer flow times, lower quality & DISSATISFIED CUSTOMERS

Processes with greater performance variability are generally judged LESS satisfactory than those with consistent, predictable performance. Variability in product & process performance, not just its average, Matters to consumers! Customers perceive any variation in their product or service from what they expected as a LOSS IN VALUE. In general, a product is classified as defective if its cost, quality, availability or flow time differ significantly from their expected values, leading to dissatisfied customers.

Quality Management Terms
BOOK COVERS A FEW QUALITY MANAGEMENT TERMS: Quality of Design: how well product specifications aim to meet customer requirements (what we promise consumers ~ in terms of what the product can do) Quality Function Deployment (QFD): conceptual framework for translating customers’ functional requirements (such as ease of operation of a door or its durability) into concrete design specifications (such as the door weight should be between 75 and 85 kg.) Quality of conformance: how closely the actual product conforms to the chosen design specifications (how well we keep our promise in terms of how it actually performs) Measures: fraction of output that meets specifications, # defects per car, percentage of flights delayed for more than 15 minutes OR the number of reservation errors made in a specific period of time.

§ 9.2 Analysis of Variability
To analyze and improve variability there are diagnostic tools to help us: Monitor the actual process performance over time Analyze variability in the process Uncover root causes Eliminate those causes Prevent them from recurring in the future Again we will use MBPF Inc. as an example and look at how their customers perceive the experience of doing business with the company & how it can be improved. Need to present raw data in a way to make sense of the numbers, track change over time, or identify key characteristics of the data set.

§ Check Sheets A check sheet is simply a tally of the types and frequency of problems with a product or a service experienced by customers.

Example 9.1 Type of Complaint Number of Complaints Cost IIII IIII
Response Time IIII Customization Service Quality IIII IIII IIII Door Quality IIII IIII IIII IIII IIII

Check Sheets Pros Easy to collect data Cons Not very enlightening
No numerical characteristics

§ Pareto Charts A Pareto chart is simply a bar chart that plots frequencies of occurrences of problem types in decreasing order. The Pareto principle states that 20% of problem types account for 80% of all occurrences.

Example 9.2

Pareto Charts Pros Ranks problems Shows relative size of quantities
Cons No numerical characteristics Only categorizes data No comparison process information

§ Histograms A histogram is a bar plot that displays the frequency distribution of an observed performance characteristic.

Example 9.3

Histograms Pros Visualizes data distribution
Shows relative size of quantities Cons No numerical characteristics Dependant on category size No focus on change over time

Table 9.1 Day Time 1 2 3 4 5 6 7 8 9 10 9:00 AM 81 82 80 74 75 83 86 88 11:00 AM 73 87 79 84 1:00 PM 85 76 91 89 3:00 PM 90 78 77 5:00 PM 11 12 13 14 15 16 17 18 19 20 72 92

Raw Data Pros Actual information Specific numbers Cons Not intuitive
Does not help with understanding of relationships

§ Run Charts A run chart is a plot of some measure of process performance monitored over time Advantage is that it is dynamic

Example 9.4

Run Charts Pros Shows data in chronological order
Displays relative change over time (trends, seasonality) Cons Erratic graph No numerical characteristics

§ Multi-Vari Charts A multi-vari chart is a plot of high-average-low values of performance measurement sampled over time.

Example 9.5

Table 9.2 Day 1 2 3 4 5 6 7 8 9 10 High 90 88 84 91 86 83 89 Low 73 78 76 74 75 81 79 80 Average 81.8 83.8 81.0 80.8 80.4 79.2 83.0 84.4 11 12 13 14 15 16 17 18 19 20 87 85 92 72 77 82 82.0 81.2 85.0

Multi-Vari Charts Pros Shows numerical range and average
Displays relative change over time Cons Erratic graph No numerical characteristics Lacks distribution information Does not provide guidance for taking actions

§ 9.3 Process Control Goal  Actual Performance vs. Planned Performance Involves  Tracking Deviations Taking Corrective Actions Principle of feedback control of dynamical systems Process Control Involves: The goal of process control is to continually ensure that in the short run, actual process performance conforms to the planned performance Taking into consideration that there are various reasons behind the variation, PROCESS CONTROL involves Tracking deviations Taking corrective action to identify and eliminate sources of variations Process performance management is based on the general principle of feedback control of dynamical systems. Applying the feedback control principle to process control.. “involves periodically monitoring the actual process performance (in terms of cost, quality, availability, and response time), comparing it to the planned levels of performance, identifying causes of the observed discrepancy between the two, and taking corrective actions to eliminate those causes.”

Plan-Do-Check-Act (PDCA)
Process planning and process control are similar to the Plan-Do-Check-Act (PDCA) cycle. PDCA cycle… “involves planning the process, operating it, inspecting its output, and adjusting it in light of the observation.” Performed continuously to monitor and improve the process performance Main Problems When to Act …. Variances beyond control … Performance variances are determined by comparison of the current and previous period’s performances. Decisions are based on results of this comparison. Some variances may be due to factors beyond a worker’s control. According to W. Edward Deming, incentives based on factors that are beyond a worker’s control is like rewarding or punishing workers according to a lottery. Two categories of performance variability Variability due to factors within a worker’s control. Variability due to factors beyond a worker’s control.

Process Control Two types of variability Normal variability
Statistically predictable Structural variability and stochastic variability Variations due to random causes only (worker cannot control) PROCESS IS IN CONTROL Process design improvement 2. Abnormal variability Unpredictable Disturbs state of statistical equilibrium of the process Identifiable and can be removed (worker can control) Abnormal - due to assignable causes PROCESS IS OUT OF CONTROL Normal variability is to be expected of any process of a given design Statistically predictable and includes both structural variability and stochastic variability Structural Variability – refers to systematic changes in the process performance, including seasonality and trend patterns Stochastic Variability – arises from chance and is due to a stable system of random causes that are inherent to every process Random causes have unpredictable effect, and cannot be removed easily. Not in worker’s control. Can be removed only by process re-design, more precise equipment, skilled workers, better quality material etc. Abnormal variability occurs unexpectedly from time to time Is unpredictable and disturbs the state of statistical equilibrium of the process by changing parameters of its distribution in an unexpected way Unpredictable Implies that one or more performance affecting factors may have changed. Due to causes superimposed externally or process tampering. Within worker’s control. Can be identified and removed easily therefore worker’s responsibility.

When is observed variability normal and abnormal???
Process Control The short run goal is: Estimate normal stochastic variability. Accept it as an inevitable and avoid tampering Detect presence of abnormal variability Identify and eliminate its sources The long run goal is to reduce normal variability by improving process. When is observed variability normal and abnormal???

§ 9.3.3 Control Limit Policy Control Limit Policy Control band
Range within variation in performance  normal Due to causes that cannot be identified or eliminated in short run Leave alone and do not tamper Variability outside this range is abnormal Due to assignable causes Investigate and correct At the most basic level, if the process performance varies “too much” from a planned level, we shld conclude that this variability is abnormal and we shld look for assignable causes. What is “too much?” This is where we establish a control band Control band - A range within which any variation in performance is interpreted as normal due to causes that cannot be identified or eliminated in short run. Example is mileage of car that we can track…. 25 mpg. If within 20 mpg (consider as normal may be due to weather, traffic conditions, gas quality). If falls outside control band, take in mechanic to check the car. Applications: Managing inventory, process capacity and flow time. - Cash management - liquidate some assets if cash falls below a certain level - Stock trading - purchase a stock if and when its price drops to a specific level. Control limit policy has usage in a wide variety of business in form of critical threshold for taking action Applications Inventory, Process Flow Cash management Stock trading

9.3.4 Control Charts … Continued
Process Control Chart:  - expected value of the performance UCL and LCL Standard Deviation  Assign z Let  be the expected value of the performance Set up a “control band” around  UCL = Upper Control Limit LCL = Lower Control Limit Calculate the standard deviation,  Decide how “tightly” we want to monitor and control the process The smaller the value of “z”, the tighter the control LCL =  - z UCL =  + z The smaller the value of “z”, the tighter the control

Within the control band  Performance variability is normal Outside the control band Process is “out of control” Data Misinterpretation Type I error, : Process is “in control”, but data outside the Control Band Type II error, : Process is “out of control”, but data inside the Control Band Data Misinterpretation: Due to the stochastic variability, we may make the mistake of concluding that EVEN when the process is in control, the performance may fall outside the band and thus, we look for assignable cause when none actually exist. Type I error – probability of false alarm due to mistaking normal variability as abnormal is called type I error. Type II error – process may fall within control limits by chance BUT in fact there is a need to investigate for assignable cause. This probability of missing a signal due to mistaking abnormal variation as normal is called Type II error.

Optimal Degree of Control Acceptable Frequency “z” too small  unnecessary investigation; additional cost “z” to large  accept more variations, less costly Optimal Degree of Control - Depends on 2 things: 1. How much variability in the performance measure we consider acceptable 2. How frequently we monitor the process performance. Optimal frequency of monitoring is a balance between the costs and benefit (example). The value of “z” determines how tightly we control the process. Recall that a small value of “z”: Narrower Control Band -- Tighter Control. The correct choice of z would balance the cost of investigation and failure to eliminate assignable causes of variability. Assign low z on processes wherein you want minimal error. BOTTOM LINE: Trade Off between control and benefits of conformance to the planned performance. If within Z = 3, then we can conclude that process is in control and take no action, variations outside needs investigation/correction. In practice, a value of z = 3 is used 99.73% of all measurements will fall within the “normal” range

Average and Variation Control Charts To calculate: Calculate the average value, A1, A2….AN Calculate the variance of each sample, V1, V2….VN A = /n (n = sample size) LCL =  - z/n and UCL =  + z/n Average and Variation Control Charts - We talk about mean and standard deviation but in practical application, we often do not know the true mean and sd of a process. Thus, we have to ascertain this by sampling of actual performance and establishing limits based on the samples estimates. We monitor process performance by taking random samples over time. Multi-vari charts shows performance variability within each sample and between samples BUT do not tell us which variability is normal (shld be left alone) and which is abnormal (need action). This is accomplished by variation control charts. - Take N random samples over time, each containing n observations. Compute for 2 summary statistics – Sample Average and Sample Variation. For each Sample: Calculate the average value, A1, A2….AN Calculate the variance of each sample, V1, V2….VN Each sample average is an estimate of the mean performance of a process Each variance average indicates the variability in process performance Take it one step further: Estimate  by the overall average of all the sample averages, A A = (A1+ A2+…+AN) / N (N = # of samples) Also estimate  by the standard deviation of all N x n observations, S

New, Improved equations for UCL and LCL are: LCL = A - zs/n and UCL = A + zs/n Average and Variation Control Charts CalculateV -- the average variance of the sample variances V = (V1+ V2+…+VN) / N (N = # of samples) Also calculate SV -- the standard deviation of the variances Sample Variances New equation for variance control limits: LCL = V - z sV and UCL = V + z sV If observed variations fall within this range: Process Variability is stable If not: Need to investigate the cause of abnormal variations Variance Control Limits LCL = V - z sV and UCL = V + z sV If fall within this range  Process Variability is stable If not within this range  Investigate cause of abnormal variations

Average and Variation Control Charts Garage Door Example revisited… Ex: A1 = ( ) / 5 = kg Ex: V1 = ( ) = 17 kg

Average and Variation Control Charts Average Weights of Garage Door Samples: A = kg V = 10.1 kg Std. Dev. of Door Weights: s = 4.2 kg Std. Dev. of Sample Variances: sV = 3.5 kg

Average and Variation Control Charts Let z = Sample Averages UCL = A + zs/n = (4.2) / 5 = LCL = A - zs/n = – 3 (4.2) / 5 = Process is Stable!

Average and Variation Control Charts Let z = Sample Variances UCL = V + z sV = (3.5) = 20.6 LCL = V - zs sV = – 3 (3.5) =

Extensions Continuous Variables - Garage Door Weights, Processing Costs, Customer Waiting Time Use Normal distribution Discrete Variables - Number of Customer Complaints, Whether a Flow Unit is Defective, Number of Defects per Flow Unit Produced Use Binomial or Poisson distribution Control Limit formula differs, but basic principles is same.

9.3.5 Cause-Effect Diagrams
Sample Observations Plot Control Charts Abnormal Variability !! Now what?!! Brainstorm Session!! Answer 5 “WHY” Questions !

9.3.5 Cause-Effect Diagrams … Continued
Why…? Why…? Why…? Our famous “Garage Door” Example: 1. Why are these doors so heavy? Because the Sheet Metal was too ‘thick’. 2. Why was the sheet metal too thick? Because the rollers at the steel mill were set incorrectly. 3. Why were the rollers set incorrectly? Because the supplier is not able to meet our specifications. 4. Why did we select this supplier? Because our Project Supervisor was too busy getting the product out – didn’t have time to research other vendors. 5. Why did he get himself in this situation? Because he gets paid by meeting the production quotas.

9.3.5 Cause-Effect Diagrams … Continued
Fishbone Diagram

9.3.6 Scatter Plots Change Settings on Rollers
The Thickness of the Sheet Metals Change Settings on Rollers Measure the Weight of the Garage Doors Determine Relationship between the two Plot the results on a graph: Scatter Plot

9.3 Section Summary Process Control involves Dynamic Monitoring
Ensure variability in performance is due to normal random causes only Detect abnormal variability and eliminate root causes

9.4 Process Capability Ease of external product measures (door operations and durability) and internal measures (door weight) Product specification limits vs. process control limits Individual units, NOT sample averages - must meet customer specifications. Once process is in control, then the estimates of μ (82.5kg) and σ (4.2k) are reliable. Hence we can estimate the process capabilities. Process capabilities - the ability of the process to meet customer specifications Three measures of process capabilities: 9.4.1 Fraction of Output within Specifications 9.4.2 Process Capability Ratios (Cpk and Cp) 9.4.3 Six-Sigma Capability

9.4.1 Fraction of Output within Specifications
To compute for fraction of process that meets customer specs: Actual observation (see Histogram, Fig 9.3) Using theoretical probability distribution Ex. 9.7: US: 85kg; LS: 75 kg (the range of performance variation that customer is willing to accept) See figure 9.3 Histogram: In an observation of 100 samples, the process is 74% capable of meeting customer requirements, and 26% defectives!!! OR: Let W (door weight): normal random variable with mean = 82.5 kg and standard deviation at 4.2 kg, Then the proportion of door falling within the specified limits is: Prob (75 ≤ W ≤ 85) = Prob (W ≤ 85) - Prob (W ≤ 75) The fraction of the process output that meets customer specifications. We can compute this fraction by: Actual observation (see Histogram, Fig 9.3) Using theoretical probability distribution Ex. 9.7: US: 85kg; LS: 75 kg (the range of performance variation that customer is willing to accept) See figure 9.3 Histogram: In an observation of 100 samples, the process is 74% capable of meeting customer requirements, and 26% defectives!!! OR: Let W (door weight): normal random variable with mean = 82.5 kg and standard deviation at 4.2 kg, Then the proportion of door falling within the specified limits is: Prob (75 ≤ W ≤ 85) = Prob (W ≤ 85) - Prob (W ≤ 75)

9.4.1 Fraction of Output within Specifications cont…
Let Z = standard normal variable with μ = 0 and σ = 1, we can use the standard normal table in Appendix II to compute: AT US: Prob (W≤ 85) in terms of: Z = (W-μ)/ σ As Prob [Z≤ ( )/4.2] = Prob (Z≤.5952) = .724 (see Appendix II) (In Excel: Prob (W ≤ 85) = NORMDIST (85,82.5,4.2,True) = ) AT LS: Prob (W ≤ 75) = Prob (Z≤ ( )/4.2) = Prob (Z ≤ -1.79) = in Appendix II (In Excel: Prob (W ≤ 75) = NORMDIST(75,82.5,4.2,true) = ) THEN: Prob (75≤W≤85) = = .6873

9.4.1 Fraction of Output within Specifications cont…
SO with normal approximation, the process is capable of producing 69% of doors within the specifications, or delivering 31% defective doors!!! Specifications refer to INDIVIDUAL doors, not AVERAGES. We cannot comfort customer that there is a 31% chance that they’ll get doors that are either TOO LIGHT or TOO HEAVY!!!

9.4.2 Process Capability Ratios (C pk and Cp)
2nd measure of process capability that is easier to compute is the process capability ratio (Cpk) If the mean is 3σ above the LS (or below the US), there is very little chance of a product falling below LS (or above US). So we use: (US- μ)/3σ (.1984 as calculated later) and (μ -LS)/3σ (.5952 as calculated later) as measures of how well process output would fall within our specifications. The higher the value, the more capable the process is in meeting specifications. OR take the smaller of the two ratios [aka (US- μ)/3σ =.1984] and define a single measure of process capabilities as: Cpk = min[(US-μ/)3σ, (μ -LS)/3σ] (.1984, as calculated later)

Cpk of 1+- represents a capable process Not too high (or too low) Lower values = only better than expected quality Ex: processing cost, delivery time delay, or # of error per transaction process If the process is properly centered Cpk is then either: (US- μ)/3σ or (μ -LS)/3σ As both are equal for a centered process.

9.4.2 Process Capability Ratios (C pk and Cp) cont…
Therefore, for a correctly centered process, we may simply define the process capability ratio as: Cp = (US-LS)/6σ (.3968, as calculated later) Numerator = voice of the customer / denominator = the voice of the process Recall: with normal distribution: Most process output is 99.73% falls within +-3σ from the μ. Consequently, 6σ is sometimes referred to as the natural tolerance of the process. Ex: 9.8 Cpk = min[(US- μ)/3σ , (μ -LS)/3σ ] = min {( )/(3)(4.2)], ( )/(3)(4.2)]} = min {.1984, .5952} =.1984

If the process is correctly centered at μ = 80kg (between 75 and 85kg), we compute the process capability ratio as Cp = (US-LS)/6σ = (85-75)/[(6)(4.2)] = .3968 NOTE: Cpk = (or Cp = .3968) does not mean that the process is capable of meeting customer requirements by 19.84% (or 39.68%), of the time. It’s about 69%. Defects are counted in parts per million (ppm) or ppb, and the process is assumed to be properly centered. IN THIS CASE, If we want no more than 100 defects per million (.01% defectives), we SHOULD HAVE the probability distribution of door weighs so closely concentrated around the mean that the standard deviation is kg, or Cp=1.3 (see Table 9.4) Test: σ = (85-75)/(6)(1.282)] = 1.300kg

Table 9.4

9.4.3 Six-Sigma Capability Sigma measure
S = min[(US- μ /σ), (μ -LS)/σ] (= min(.5152,1.7857) = to be calculated later) S-Sigma process If process is correctly centered at the middle of the specifications, S = [(US-LS)/2σ] Ex: 9.9 Currently the sigma capability of door making process is S=min[( )/(4.2), ( )/4.2] = .5952 By centering the process correctly, its sigma capability increases to S=min(85-75)/[(2)(4.2)] = 1.19 THUS, with a 3σ that is correctly centered, the US and LS are 3σ away from the mean, which corresponds to Cp=1, and 99.73% of the output will meet the specifications. The 3rd process capability Known as Sigma measure, which is computed as S = min[(US- μ /σ), (μ -LS)/σ] (= min(.5152,1.7857) = to be calculated later) S-Sigma process If process is correctly centered at the middle of the specifications, S = [(US-LS)/2σ] Ex: 9.9 Currently the sigma capability of door making process is S=min( )/[(2)(4.2)] = .5952 By centering the process correctly, its sigma capability increases to S=min(85-75)/[(2)(4.2)] = 1.19 THUS, with a 3σ that is correctly centered, the US and LS are 3σ away from the mean, which corresponds to Cp=1, and 99.73% of the output will meet the specifications.

9.4.3 Six-Sigma Capability cont…
Correctly centered six-sigma process has a standard deviation so small that the US and LS limits are 6σ from the mean each. Extraordinary high degree of precision. Corresponds to Cp=2 or 2 defective units per billion produced!!! (see Table 9.5) In order for door making process to be a six-sigma process, its standard deviation must be: σ = (85-75)/(2)(6)] = .833kg Adjusting for Mean Shifts standard deviation from the center of specifications. - Producing an average of 3.4 defective units per million. (see table 9.5) SIMILARLY, a correctly centered six-sigma process has a standard deviation so small that the US and LS limits are 6σ from the mean each. Extraordinary high degree of precision. Corresponds to Cp=2 or 2 defective units per billion produced!!! (see Table 9.5) In order for door making process to be a six-sigma process, its standard deviation must be: σ = (85-75)/(2)(6)] = .833kg Adjusting for Mean Shifts Allowing for a shift in the mean of standard deviation from the center of specifications. Allowing for this shift, a six-sigma process amounts to producing an average of 3.4 defective units per million. (see table 9.5)

Table 9.5

Why Six-Sigma? See table 9.5 Improvement in process capabilities from a 3-sigma to 4-sigma = 10-fold reduction in the fraction defective (66810 to 6210 defects) While 4-sigma to 5-sigma = 30-fold improvement (6210 to 232 defects) While 5-sigma to 6-sigma = 70-fold improvement (232 to 3.4 defects, per million!!!). Average companies deliver about 4-sigma quality, where best-in-class companies aim for six-sigma.

Why High Standards? The overall quality of the entire product/process that requires ALL of them to work satisfactorily will be significantly lower. Ex: If product contains 100 parts and each part is 99% reliable, the chance that the product (all its parts) will work is only (.99)100 = .366, or 36.6%!!! Also, costs associated with each defects may be high Expectations keep rising

Safety capability We may also express process capabilities in terms of the desired margin [(US-LS)-zσ] as safety capability It represents an allowance planned for variability in supply and/or demand Greater process capability means less variability If process output is closely clustered around its mean, most of the output will fall within the specifications Higher capability thus means less chance of producing defectives Higher capability = robustness

9.4.4 Capability and Control
In Ex. 9.7: the production process is not performing well in terms of MEETING THE CUSTOMER SPECIFICATIONS. Only 69% meets output specifications!!! (See 9.4.1: Fraction of Output within Specifications) Yet in example 9.6, “the process was in control!!!”, or within us & ls limits. Being in control and meeting specifications are two different measures of performance. The former indicates internal stability, the latter indicates the ability to meet the customers specifications. Observation of a process in control ensures that the resulting estimates of the process mean and standard deviation are reliable so that our measurement of the process capability is accurate. The final step is to improve process capability, so it is satisfactory from the customers viewpoint as well.

9.5 Process Capability Improvement
How do we improve the process capability? Shift the process mean Reduce the variability Both

9.5.1 Mean Shift Examine where the current process mean lies in comparison to the specification range (i.e. closer to the LS or the US) Alter the process to bring the process mean to the center of the specification range in order to increase the proportion of outputs that fall within specification

Ex 9.10 MBPF garage doors (currently)
specification range: 75 to 85 kgs process mean: 82.5 kgs proportion of output falling within specifications: .6873 The process mean of 82.5 kgs was very close to the US of 85 kgs (i.e. too thick/heavy) To lower the process mean towards the center of the specification range the supplier could change the thickness setting on their rolling machine.

Ex 9.10 Continued Center of the specification range: ( )/2 = 80 kgs New process mean: 80 kgs If the door weight (W) is a normal random variable, then the proportion of doors falling within specifications is: Prob (75 =< W =< 85) Prob (W =< 85) – Prob (W =< 75) Z = (weight – process mean)/standard deviation Z = (85 – 80)/4.2 = 1.19 Z = (75 – 80)/4.2 = -1.19

Ex 9.10 Continued [from table A2.1 on page 319] Z = Z = ( ) Prob (W =< 85) – Prob (W =< 75) = = .7660 By shifting the process mean from 82.5 kgs to 80 kgs, the proportion of garage doors that falls within specifications increases from to .7660

9.5.2 Variability Reduction
Measured by standard deviation A higher standard deviation value means higher variability amongst outputs Lowering the standard deviation value would ultimately lead to a greater proportion of output that falls within the specification range

9.5.2 Variability Reduction Continued
Possible causes for the variability MBPF experienced are: old equipment poorly maintained equipment improperly trained employees Investments to correct these problems would decrease variability however doing so is usually time consuming and requires a lot of effort

Ex 9.11 Assume investments are made to decrease the standard deviation from 4.2 to 2.5 kgs The proportion of doors falling within specifications: Prob (75 =< W =< 85) Prob (W =< 85) – Prob (W =< 75) Z = (weight – process mean)/standard deviation Z = (85 – 80)/2.5 = 2.0 Z = (75 – 80)/2.5 = -2.0

Ex 9.11 Continued [from table A2.1 on page 319] Z = Z = ( ) Prob (W =< 85) – Prob (W =< 75) = = .9544 By shifting the standard deviation from 4.2 kgs to 2.5 kgs and the process mean from 82.5 kgs to 80 kgs, the proportion of garage doors that falls within specifications increases from to .9544 Changing standard deviation alone = .84 (proportion falling within spec)

9.5.3 Effect of Process Improvement on Process Control
Changing the process mean or variability requires re-calculating the control limits This is required because changing the process mean or variability will also change what is considered abnormal variability and when to look for an assignable cause

9.6 Product and Process Design
Reducing the variability from product and process design simplification standardization mistake proofing

Simplification Reduce the number of parts (or stages) in a product (or process) less chance of confusion and error Use interchangeable parts and a modular design simplifies materials handling and inventory control Eliminate non-value adding steps reduces the opportunity for making mistakes

Standardization Use standard parts and procedures
reduces operator discretion, ambiguity, and opportunity for making mistakes

Mistake Proofing Designing a product/process to eliminate the chance of human error ex. color coding parts to make assembly easier ex. designing parts that need to be connected with perfect symmetry or with obvious asymmetry to prevent assembly errors

9.6.2 Robust Design Designing the product in a way so its actual performance will not be affected by variability in the production process or the customer’s operating environment The designer must identify a combination of design parameters that protect the product from the process related and environment related factors that determine product performance

9.6 Product and Process Design
Summary Variability is inevitable. It is a problem when it creates process instability, lower capability, and customer dissatisfaction. The goal of this chapter has been to study how to measure, analyze, and minimize sources of this variability. The point of this it to improve consistency in product process and performance, which will hopefully lead to… Total customer satisfaction, and.. A better competitive position.

Managing Flow Variability: Process Control and Capability

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