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App. Of Stat. Tools


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App. Of Stat. Tools

  1. 1. Application of Statistical Tools to Enhance Productivity and Quality By K. K. Pandey IPCL – GPC Dahej
  2. 3. Introduction Crude oils, petroleum products and lubricants are complex materials. Efforts have been made by oil producers throughout the world to characterize their chemical and physical properties with a high degree of precision to have a quality product with a much emphasis on the management of quality control in process as well as in laboratory. All specialist and scientist have to identify problems unusual incidents and procedures to achieve quality needed for a true chemical industry. The actual performance of methods is accounted in laboratory using statistical tools, which involves the measurement and evaluation of data to control the performance of process.
  3. 4. Historical Background In the modern time we have professional societies, government bodies such as Food & Drugs Administration, factory inspection etc., aimed at assuring the quality of the products sold to customers. So quality control has a long history. On the other hand statistical quality control is comparatively new to petrochemical industry. It was used in astronomy and physics and in the biological and social sciences. From 1920 onwards statistical theory began to be applied effectively to quality control as a result of the development of sampling theory.
  4. 5. The Basic Concept of Statistical Process Control, Quality Control & Process Capability History of statistical quality control Definition of process control Process control techniques Things to be done when process is out of control Things to be done when in control but out of specification The process capability Definition of Process Control   Process control is the active changes of the process, the active changes of the process based on the results of process monitoring.
  5. 6. Process control techniques There are many ways to implement process control. Key monitoring and investigating tools include: Histograms Check sheets Cause and effect diagrams Defect concentration diagrams Scatter diagrams Control charts
  6. 7. The concept of statistical process control is based on a comparision of what is happening today, with what happened previously. We examine the performance of the plant and calculate control limits for the expected measurement of the output of the process. The majority of the measurement should fall within the control limits. Measurements that fall out side the control limits are examined. The limits will be recomputed in the process repeated, this is known as real time process monitoring. Things to be done when process is out of control If the process is out of control, the process engineer looks for an assignable cause by following the out of control action plan (OCAP) to be implemented.
  7. 8. Things to be done when in control but out of specification “ In control” means that the process is predictable in a statistical sense. But the average level is too high or two low, or variability is unacceptable.   Process capability A process capability index uses both the process variability and the process specifications to determine whether the process is “capable” : We are often required to compare the output of a stable process with the process specifications and make a statement about how well the process meets specification. To do this we compare the natural variability of a stable process with the process specification limits.
  8. 9. In order to achieve above mentioned objectives we may adopt the following outlines as a guidance to enhance productivity and performance in Industry. * Establish a practical process for managing quality in your plant and laboratory. * Plan your quality logically efficiently and quickly. * Move beyond compliance and other rules to meet the basic requirements. * Optimise quality control to minimize waste and maximize performance. * Select the best control rules for your test.  
  9. 10. The methodology to obtain quality and quantity may be as given below.   (a) Basic planning for quality (i) Training in analytical quality management for petrochemical products. (ii) Laboratories provide a practical introduction to quality management and planning with an emphasis on key quality control concepts and issues related to petrochemicals laboratory. These valuable tools have been used world wide to facilitate the education of many individuals with in the department as well as the connected person of the process. That is the application of QMP (Quality Management Principles) to our processes.  
  10. 11. * The techniques of sampling are as follows. Acceptance of sampling Kind of sampling plan Choosing single sample plan Double sampling plan Multiple sampling plan Skip lot sampling plan Test Product for Acceptability : Lot Acceptance Sampling To make decisions on a lot – by – lot basis, whether to accept a lot as likely to meet requirements or reject the lot as likely to have too many defects.
  11. 12. What is Acceptance Sampling   Acceptance sampling is an important field of statistical quality control that was popularized by Dodge and Romig. Definition of Lot Acceptance Sampling   Dodge reasoned that a sample should be picked at random from the lot, on the basis of information that was yielded by the sample. A decision should be made regarding the disposition of the lot, in general the decision is either to accept or reject the lot. The process is called Lot Acceptance Sampling or just Acceptance Sampling .  
  12. 13. “ Attributes” (i.e., defect counting)   Acceptance sampling is on “the middle of the road” approach between   * No acceptance and 100% acceptance. * There are two major classifications of acceptance plan : by attributes (“go, no-go”) and by variables. * The attribute case is the most common for acceptance sampling.   Important point : A point to remember is that the main purpose of acceptance sampling is to decide whether or not the lot is likely to be acceptable.
  13. 14. Scenarios leading to acceptance sampling : Acceptance sampling is employed when one or several of the following hold good :   Distructive sampling and testing The cost of 100% inspection is very high 100% inspection takes too long   Acceptance Sampling: “ Acceptance sampling when implemented indicate the conditions for acceptance or rejection of the immediate lot that is being inspected. The data to be converted in the form of control chart using the specifications and standard deviation is monitored.”
  14. 15. An observation by Harold Dodge : The concept of protecting the consumer from getting unacceptable defective product, and encouraging the producer in the use of process quality control by : varying the quantity and severity of acceptance. * Acceptance sampling plans are one – shot deals. * Quality control is of the long run variety, and is part of a well – designed system for lot acceptance. Control of product quality using acceptance control charts : According to the ISO standard, an acceptance control chart combines consideration of control implications with elements of acceptance sampling. It is an appropriate tool for helping to make decisions with process acceptance. The difference between acceptance control charts and control limits is the emphasis on process acceptability rather than on product disposition decisions.
  15. 16. What kinds of Lot Acceptance Sampling Plants (LASPs) are there? LASP is a sampling scheme and a set of rules : (LASP) is a sampling scheme based on counting the number of defectives. * To accept the lot, reject the lot, or to take another sample and then repeat the decision process. Types of acceptance plants to choose from : LASPs fall into the following categories : Single sampling plans : One sample of items is selected at random from a lot and the disposition of the lot is determined from the resulting information. These are the most common (and easiest) plans to use although not the most efficient in terms of average number of sample needed.  
  16. 17. Double sampling plans : After the first sample is tested, there are three possibilities : (1) Accept the lot (2) Reject the lot (3) No decision If the outcome is (3), and a second sample is taken, the procedure is to combine the results of both samples and make a final decision, based on that information. Multiple sampling plans: This is an extension of the double sampling plans where more than two samples are needed to reach a conclusion. The advantage of multiple sampling is smaller sample sizes. Sequential sampling plans: This is the ultimate extension of multiple sampling where items are selected from a lot one at a time and after inspection of each item a decision is made to accept or reject the lot or select another unit.
  17. 18. Skip lot sampling plans: Skip lot sampling means that only a fraction of the submitted lots are inspected. The basic acceptance sampling terms which are used in statistical process control and quality control for monitoring are as follows in a normal process operation. Acceptable Quality Level (AQL) : The AQL is a percent defective that is the base line requirement for the quality of the producer’s product. The producer would like to design a sampling plan such that there is a high probability of accepting a lot that has a defect level less than or equal to the AQL. Lot Tolerance Percent Defective (LTPD): The LTPD is a designated high defect level that would be unacceptable to the consumer. The consumer would like the sampling plan to have low probability of accepting a lot with a defect level as high as the LTPD.
  18. 19. Operating Characteristic (OC) Curve : This curve plots the probability of accepting the lot (Y – axis) versus the lot fraction or percent defectives (X – axis). The OC curve is the primary tool for displaying and investigating the properties of a LASP. Average Outgoing Quality (AOQ) : A common procedure, when sampling and testing is non- destructive, is to 100% inspection and rejected lots are replaced with good units. In this case, all rejected lots are made perfect and the only defects left are those in lots that were accepted. AOQ’s refer to the long term defect level for this combined LASP and 100% inspection of rejected lots process. If all lots come in with a defect level of exactly p, and the OC curve for the chosen (n,c) LASP indicates a probability p a of accepting such a lot, over the long run the AOQ can easily be shown to be :  
  19. 20. AOQ = PaP (N – n) N Where N is the lot size Average Sample Number (ASN): For a single sampling LASP, we know each and every lot has a sample of size n taken and inspected or tested. For double, multiple and sequential LASP’s, the amount of sampling varies depending on the number of defects observed. For any given double, multiple or sequential plan, a long term ASN can be calculated assuming all lots come in with a defect level of p. A plot of the ASN, versus the incoming defect level p, describes the sampling efficiency of a given LSP scheme.
  20. 21. The final choice is a tradeoff decision : Making a final choice between single or multiple sampling plans that have acceptable properties is a matter of deciding whether the average sampling savings gained by the various multiple sampling plans justifies the additional complexity of these plans and the uncertainty of not knowing how much sampling and inspection will be done on a day – by – day basis. How do you choose a single sampling plan ? Choosing a sampling plan with a given Operation Control (OC) curve for polymeric lot acceptance   Sample OC curve : We start by looking at a typical OC curve. The OC curve for a sampling plan is shown below.
  21. 23. Number of defectives is approximately binomial : It is instructive to show how the points on this curve are obtained, once we have a sampling plan we can demonstrate the same. We assume that the lot size N is very large, as compared to the sample size n, so that removing the sample doesn’t significantly change the remains of the lot, no matter how many defects are in the sample. Then the distribution of the number of defectives, d, in a random sample of n items is. Approximately binomial with parameters n and p, where p is the fraction of defectives per lot. Average Outgoing Quality (AOQ) Calculating AOQ’s : We can also calculate the AOQ for a sampling plan, provided rejected lots are 100% inspected and defectives are replaced with good parts.
  22. 24. Assume all lots come in with exactly a p o proportion of defectives. After screening a rejected lot, the final fraction defectives will be zero for that lot. However, accepted lots have fraction defective p o . Therefore, the outgoing lots from the inspection stations are a mixture of lots with fractions defective po and 0. Assuming the lot size is N, we have.   AOQ = p a p (N – n) N For example, let N = 10000, n = 52, c = 3, and p, the quality of incoming lots, = 0.03, from the OC curve table that pa = 0.930 and   AOQ = (0.930) (0.03) (10000 – 52) / 10000 = 0.02775 Sample table of AOQ versus p : setting p = 0.01, 0.02, ……..0.12, we can generate the following table
  23. 25. ACQ p .0010 .01 .0196 .02 .0278 .03 .0338 .04 .0369 .05 .0372 .06 .0351 .07 .0315 .08 .0270 .09 .0223 .10 .0178 .11 .0138 .12
  24. 26. Sample plot of AOQ versus p : A plot of the AOQ versus p is given below.  
  25. 27. Interpretation of AOQ plot : From the examining this cure we observe that when the incoming quality is very good (very small fraction of defectives coming in), then the outgoing quality is also very good (very small fraction of defectives going out). When the incoming lot quality is very bad, most of the lots are rejected and then inspected. The “duds” are eliminated or replaced by good ones, so that the quality of the out going lots, the AOQ, becomes very good. In between these extremes, the AOQ rises, reaches a maximum, and then drops. The maximum ordinate on the AOQ curve represents the worst possible quality that results from the rectifying inspection program. IT is called the average outgoing quality limit, (AOQL). From the table we see that the AOQL = 0.0372 at p = .06 for the above example. One final remark : if N>> n, then the AOQ ~ p a p. 
  26. 28. The Average Total Inspection (ATI) : There are the basics of accepting and rejecting the optimizing the rejection of lots batches based on quality involved. Process Capability Indices A process capability index uses both the process variability and the process specifications to determine whether the process is “capable” : We are often required to compare the output of a stable process with the process specifications and make a statement about how well the process meets specification. To do this we compare the natural variability of a stable process with the process specification limits. A capable process is one where almost all the measurements fall inside the specification limits. This can be represented pictorially by the plot below.  
  27. 30. Most capability indices estimates are valid only if the sample size used is “large enough : Large enough is generally thought to be about 50 independent data values. The C p’ C pk’ and C pm’ statistical assume that the population of data values is normally distributed. Assuming a two–sided specification. If  and  are the mean and standard deviation, respectively, of the normal data and USL, LSL and T are the upper and lower specification limits and the target value, respectively, then the population capability indices are defined as follows.   Definitions of various process capability indices   Cp = USL – LSL 6    Cpk = min [ USL -  ,  - LSL ] 3  3 
  28. 31. Cpm = USL – LSL 6  2 + (  - T) 2 This can be expressed numerically by the table below.   Translating capability into “rejects”   USL – LSL 6  8  10  12  Cp 1.00 1.33 1.66 2.00 Rejects .27% 64ppm .6 ppm 2 ppb % of spec used 100 75 60 50 where ppm = parts per million and ppb = parts per billion. Note that the reject figures are based on the assumption that the distribution is centered at  . 
  29. 32. We have discussed the situation with two spec. limits, the USL and LSL. This is known as the bilateral or two – sided case. There are many cases where only the lower or upper specifications are used. Using one spec limit is called unilateral or one – sided. The corresponding capability indices are esimators of Cpu and Cpl are obtained by replacing  and  by x and s, respectively. The following relationship holds   Cp = (Cpu + Cpl)2. One sided specifications and the corresponding capability indices   Cpu = allowable upper spread = USL -  actual upper spread 3  and Cpl = allowable lower spread =  - LSL actual lower spread
  30. 33.   This can be represented pictorially by
  31. 34.   Capability Index Example   For a certain process the USL = 20 and the LSL = 8. The observed process average, X = 16, and the standard deviation, s = 2. from this we obtain   Cp = USL – LSL = 20 – 8 = 1.0 6 8 6(2)   This means that the process is capable as long as it is located at the midpoint, m = (USL + LSL) / 2 = 14.    
  32. 35.   Conclusion : From the above we conclude that statistical tools i.e. standard deviation and various control charts are used in a process for determination of the degree of variation in a set of measurements or a process. At present most of the industries are working on three sigma (3  ), which is equivalent to non defective output of 93.319%. Which is not acceptable to our customers in the present competitive global market. It has become necessary to achieve the defect level to the extent of 3 – 4 defects per million opportunities for customer satisfaction and profitability. It emphasizes what you should know to reduce the erosion in any process to enhance productivity and profitability.
  33. 36.   As we know “knowledge is power” we at present using only three sigma (3  ) to measure a true process and quality control . If we start using the statistical concept that measures a true process capability, correlating in terms of eliminating defects through practices that emphasizes understanding measuring and improving processes will bring excellence to Industry reaching 3 to 4 defects per million, i.e. “six sigma (6  )” . -----------------------------------xxxxxxxx--------------------------------