SPCAID - Statistical Process Control tool.xlsm

	A	F	G	L
1	Statistical Process Control Excel Tool - Introduction to SPC
2				SPCAID Excel Tool Developed 2023 - Pearl International Nicholas Vena, President Lumberton, NJ USA +1(215) 820-1600 vena@pearlaudits.com
3	1. Purpose and Scope
4	This worksheet is intended to provide a basic description of Statistical Process Control application, including the use of control charts, process capability (Cp, Cpk), and process performance metrics. The SOP worksheet in this Excel tool will additionally provide work instructions for entering test and inspection data into this Excel tool, editing/formatting control charts, and performing data analysis. The scope of this procedure is limited to the control charts and supplemental information worksheets contained within this Excel file.
5
6	II. Background
7	Statistical Process Control (SPC) is defined as the use of statistical techniques to control a process or production method. If the output of a process is assumed to be randomized across a probability distribution function (Normal/Gaussian, Poisson, Binomial distributions), then statistical tools can be used in order to identify statistical anomalies that are indicative of non-random variations in the process. This Excel tool primarily uses a form of SPC known as the control chart. Control charts plot the average value of a process output over time. By adding control limits that are created based on the standard deviation of those values, it can be determine whether a non-random value or pattern of values exist. These non-random events are determined by eight statistical rules, and are indicitave that a change in the process (known as a special cause) may exist. These rules are outlined in the Rules worksheet within this Excel tool.
8
9	Additionally, this tool provides statistical determination of process capability (Cp, Cpk, etc.), histograms to allow visualization of the distribution of sample values, and various process performance metrics.
10
11	SPC can be used in receiving inspection, in-process inspection, and final inspection. Some benefits of applying SPC to production processes include:
12	Real-time analytics and identification of out-of-control packaging processes	Increased productivity and operational efficiency
13	Process Capability metrics determine likelihood of process output meeting specification (Cp, Cpk)	Decreased manual inspections
14	Estimation of percent yield and defective parts-per-million	Reduced Costs
15
16	III. Probability Distribution Functions
17	Most process outputs are assumed to follow the central limit theorem, which states if a significantly large number of samples are taken from a population with mean μ and standard deviation (sigma, σ), the distribution of that sample set will approximately be a Normal distribution. Normal distributions possess a number of defining characteristics; specifically, control charts use the fact that there is a known percentage of samples of a Normal distribution that will fall within +/- 1σ of the mean (68.26%), +/-2σ (95.46%), and +/- 3σ (99.73%). Similarly, other distributions (Poisson, Binomal) can have control limits based on σ. Under certain conditions, the Normal distribution can in fact be an adequate approximation of Poisson and Binomial distributions.
18
19	Since processes that are considered in-control can be assumed to have randomized samples across a probability distribution, it can be determined when a sample has a value that is statistically improbable for a process. For most processes, this is considered any point that lies outside of the +/- 3σ range (0.26% likelihood of occurring randomly). Similarly, specific patterns of samples can be determined to be statistically improbable to occur. In both cases, these statistical anomalies typically will represent a bias or non-random event that has occurred in a process, and the process is then considered to be out-of-control. The eight rules typically used for control charts (known as the Nelson rules) are listed in the Rules worksheet within this Excel tool.
20
21	The control charts used in this Excel tool plot the average of process samples vs. time. Control charts for various continuous data (any value) and discrete data (integer value) sets have been developed to identify the eight rules for control. Users of this Excel tool will choose the chart specific to their data set, paste or query their data from another source into the inspection form for that chart, and then be able to review whether any out-of-control event or pattern has occurred by reviewing the control chart.
22
23	IV. Process Capability and Process Performance
24	Process Capability is a measure of the ability of a process to conform to a given specification. It is typically given in terms of two indices, known as Cp and Cpk. Given an Upper and Lower Specification Limit (USL, LSL) for a product, the Cp value indicates the ratio of the +/- 3σ range of the probability distribution function to that of the USL/LSL, if the probability distribution function were exactly centered between the two specification limits. For example, if the USL/LSL are four standard deviations (4σ) away from the centered probability distribution function, the Cp value would be 4/3 = 1.33. Similarly, the Cpk value indicates the ratio of the +/- 3σ range from the closest value of USL or LSL, based on where the probability distribution function actually sits between the specfication limits (un-centered, as-is based on the data). Since values are seldom centered exactly between the USL and LSL, Cpk is often used to review how well a process characteristic's distribution is capable of meeting specification as-is, whereas Cp can be used to determine how well that characteristic could fit between the USL and LSL if the process was adjusted to be centered between the two. For reference, Cp is always greater than or equal to Cpk. For reference, typical values of Cpk required in product specifications for different industries are 1.00 and 1.33.
25
26	Similarly, process performance reviews how a process has met a specification over a duration, and is given in terms of two indices, Pp and Ppk. The indices use the entirety of data over time, and use a different form of standard deviation than is calculated for Cp and Cpk values. These values are typically used for evaluating the "long-term" performance of a process. Conversely, Cp and Cpk are used in "short-term" review of a process, or at times, prior to a process being in a production run.
27
28	For most chart types that follow or can be approximated by a Normal distribution, this Excel tool includes the use of histograms, which plot sample value against a count of how many samples exist within that range. This chart additionally plots the USL/LSL and probability distribution (applied as a Normal distribution), to allow visualization of where sample values lie with respect to the specification limits. Three additional tools, Chi-Squared Test, Kurtosis and Skewness are also included to quantify how well the data fits to a Normal distribution.
29
30	V. Control Chart Types
31	This Excel tool contains several different chart types, to be used with different forms of sample data.
32
33	Continuous Data Charts		Discrete Data Charts
34	I-MR chart		P Chart
35	Plots the value of individual data points over time, as well as the Moving Range, which is the variability between one data point and the next. This set of charts is used when a data set has a subgroup size (number of observed data points per sample) of one (1). Typically these charts follow Normal distribution.		Counts the number of nonconforming parts (pass/fail) for samples of varying subgroup size. This chart follows a Binomial distribution.
36
37	Xbar-R chart		NP Chart
38	Plots the value of subgroup average (Xbar) over time, as well as the range (R) of the values within each subgroup. These charts are typically used when a data set has a subgroup size of between 2-10. Typically these charts follow Normal distribution.		Counts the number of nonconforming parts (pass/fail) for samples of equal subgroup size. This chart follows a Binomial distribution.
39
40	Xbar-S chart		U Chart
41	Plots the value of subgroup average (Xbar) over time, as well as the standard deviation (S) of the values within each subgroup. These charts are typically used when a data set has a subgroup size of more than 10 observations. Typically these charts follow Normal distribution.		Counts the number of defects for samples of varying subgroup size. This chart follows a Poisson distribution.
42
43	Levey-Jennings Chart		C Chart
44	A variation of the Xbar chart, the Levey-Jennings chart can be used when a series of observations are made for the same sample. This chart is typically used in laboratory quality control. The Levey-Jennings chart additionally uses a different set of rules (known as Westgard Rules) to identify out-of-control processes. See Rules worksheet.		Counts the number of defects for samples of equal subgroup size. This chart follows a Poisson distribution.
45	T Chart		G Chart
46	Counts time/events between rare events (continuous)		Counts time/events between rare events (discrete)
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100